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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">pnasnexus</journal-id>
      <journal-title-group>
        <journal-title>PNAS Nexus</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2752-6542</issn>
      <publisher>
        <publisher-name>Oxford University Press</publisher-name>
        <publisher-loc>US</publisher-loc>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.1093/pnasnexus/pgae471</article-id>
      <article-id pub-id-type="publisher-id">pgae471</article-id>
      <article-categories>
        <subj-group subj-group-type="category-toc-heading">
          <subject>Biological, Health, and Medical Sciences</subject>
        </subj-group>
        <subj-group subj-group-type="category-taxonomy-collection">
          <subject>AcademicSubjects/MED00010</subject>
          <subject>AcademicSubjects/SCI00010</subject>
          <subject>AcademicSubjects/SOC00010</subject>
        </subj-group>
        <subj-group subj-group-type="category-taxonomy-collection">
          <subject>PNAS_Nexus/pop-bio</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Revisiting immunity vs. exposure in schistosomiasis: A mathematical modeling study of delayed concomitant immunity</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9594-3321</contrib-id>
          <name>
            <surname>Milne</surname>
            <given-names>Gregory C</given-names>
          </name>
          <aff>
            <institution>Department of Pathobiology and Population Sciences, Royal Veterinary College</institution>, <addr-line>Hatfield, AL9 7TA</addr-line>, <country country="GB">United Kingdom</country></aff>
          <aff>
            <institution>London Centre for Neglected Tropical Disease Research, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London</institution>, <addr-line>London, W12 0BZ</addr-line>, <country country="GB">United Kingdom</country></aff>
          <xref ref-type="fn" rid="FM1" />
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Oettle</surname>
            <given-names>Rebecca C</given-names>
          </name>
          <aff>
            <institution>Department of Pathology, University of Cambridge</institution>, <addr-line>Cambridge, CB2 1QP</addr-line>, <country country="GB">United Kingdom</country></aff>
          <xref ref-type="fn" rid="FM1" />
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-5003-2575</contrib-id>
          <name>
            <surname>Whittaker</surname>
            <given-names>Charles</given-names>
          </name>
          <aff>
            <institution>London Centre for Neglected Tropical Disease Research, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London</institution>, <addr-line>London, W12 0BZ</addr-line>, <country country="GB">United Kingdom</country></aff>
          <aff>
            <institution>MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London</institution>, <addr-line>London, W12 0BZ</addr-line>, <country country="GB">United Kingdom</country></aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Kabatereine</surname>
            <given-names>Narcis B</given-names>
          </name>
          <aff>
            <institution>Vector Control Division, Ugandan Ministry of Health</institution>, <addr-line>PO Box 1661, Kampala</addr-line>, <country country="UG">Uganda</country></aff>
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5031-3361</contrib-id>
          <name>
            <surname>Basáñez</surname>
            <given-names>Maria-Gloria</given-names>
          </name>
          <aff>
            <institution>London Centre for Neglected Tropical Disease Research, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London</institution>, <addr-line>London, W12 0BZ</addr-line>, <country country="GB">United Kingdom</country></aff>
          <aff>
            <institution>MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London</institution>, <addr-line>London, W12 0BZ</addr-line>, <country country="GB">United Kingdom</country></aff>
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8616-4919</contrib-id>
          <name>
            <surname>Webster</surname>
            <given-names>Joanne P</given-names>
          </name>
          <aff>
            <institution>Department of Pathobiology and Population Sciences, Royal Veterinary College</institution>, <addr-line>Hatfield, AL9 7TA</addr-line>, <country country="GB">United Kingdom</country></aff>
          <aff>
            <institution>London Centre for Neglected Tropical Disease Research, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London</institution>, <addr-line>London, W12 0BZ</addr-line>, <country country="GB">United Kingdom</country></aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8714-5365</contrib-id>
          <name>
            <surname>Walker</surname>
            <given-names>Martin</given-names>
          </name>
          <aff>
            <institution>Department of Pathobiology and Population Sciences, Royal Veterinary College</institution>, <addr-line>Hatfield, AL9 7TA</addr-line>, <country country="GB">United Kingdom</country></aff>
          <aff>
            <institution>London Centre for Neglected Tropical Disease Research, Department of Infectious Disease Epidemiology, School of Public Health, Imperial College London</institution>, <addr-line>London, W12 0BZ</addr-line>, <country country="GB">United Kingdom</country></aff>
          <xref ref-type="fn" rid="FM3" />
          <xref ref-type="corresp" rid="pgae471-cor1" />
          <email xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple">mwalker@rvc.ac.uk</email>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-5725-4376</contrib-id>
          <name>
            <surname>Wilson</surname>
            <given-names>Shona</given-names>
          </name>
          <aff>
            <institution>Department of Pathology, University of Cambridge</institution>, <addr-line>Cambridge, CB2 1QP</addr-line>, <country country="GB">United Kingdom</country></aff>
          <xref ref-type="corresp" rid="pgae471-cor1" />
          <email xmlns:xlink="http://www.w3.org/1999/xlink" xlink:type="simple">sw320@cam.ac.uk</email>
        </contrib>
      </contrib-group>
      <contrib-group>
        <contrib contrib-type="editor">
          <name>
            <surname>An</surname>
            <given-names>Zhiqiang</given-names>
          </name>
          <role>Editor</role>
        </contrib>
      </contrib-group>
      <author-notes>
        <corresp id="pgae471-cor1">To whom correspondence should be addressed: Email: <email>mwalker@rvc.ac.uk</email> (M.W.); Email: <email>sw320@cam.ac.uk</email> (S.W.)</corresp>
        <fn id="FM1">
          <p>G.C.M. and R.C.O. contributed equally to this work.</p>
        </fn>
        <fn id="FM3">
          <p>
            <bold>Competing Interest:</bold> The authors declare no competing interests.</p>
        </fn>
      </author-notes>
      <pub-date pub-type="cover">
        <month>October</month>
        <year>2024</year>
      </pub-date>
      <pub-date pub-type="collection" iso-8601-date="2024-10-01">
        <day>01</day>
        <month>10</month>
        <year>2024</year>
      </pub-date>
      <pub-date pub-type="epub" iso-8601-date="2024-10-17">
        <day>17</day>
        <month>10</month>
        <year>2024</year>
      </pub-date>
      <volume>3</volume>
      <issue>10</issue>
      <elocation-id>pgae471</elocation-id>
      <supplementary-material xmlns:xlink="http://www.w3.org/1999/xlink" id="sup1" content-type="data-supplement" mimetype="application" xlink:href="pgae471_supplementary_data.pdf">
        <label>pgae471_Supplementary_Data</label>
      </supplementary-material>
      <history>
        <date date-type="received">
          <day>12</day>
          <month>06</month>
          <year>2024</year>
        </date>
        <date date-type="accepted">
          <day>09</day>
          <month>10</month>
          <year>2024</year>
        </date>
        <date date-type="corrected-typeset">
          <day>29</day>
          <month>10</month>
          <year>2024</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>© The Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences.</copyright-statement>
        <copyright-year>2024</copyright-year>
        <license xmlns:xlink="http://www.w3.org/1999/xlink" license-type="cc-by-nc" xlink:href="https://creativecommons.org/licenses/by-nc/4.0/">
          <license-p>This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial License (<ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by-nc/4.0/">https://creativecommons.org/licenses/by-nc/4.0/</ext-link>), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact reprints@oup.com for reprints and translation rights for reprints. All other permissions can be obtained through our RightsLink service via the Permissions link on the article page on our site—for further information please contact journals.permissions@oup.com.</license-p>
        </license>
      </permissions>
      <self-uri xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="pgae471.pdf" />
      <abstract abstract-type="abstract">
        <title>Abstract</title>
        <p>The relative contributions of exposure vs. acquired immunity to the epidemiology of human schistosomiasis has been long debated. While there is considerable evidence that humans acquire partial immunity to infection, age- and sex-related contact patterns with water bodies contaminated with infectious cercarial schistosome larvae also contribute to typical epidemiological profiles of infection. Here, we develop a novel schistosome transmission model that incorporates both partially protective “delayed concomitant” acquired immunity—stimulated by dying worms—and host age- and sex-dependent patterns of exposure. We use a contemporary Bayesian approach to fit the model to historical individual data on exposure to infectious cercaria, eggs per gram of feces, and immunoglobulin E antibodies specific to <italic>Schistosoma mansoni</italic> Tegumental-Allergen-Like protein 1 collected from a highly endemic community in Uganda, estimating the relative contributions of exposure and acquired immunity. We find that model variants incorporating or omitting delayed concomitant immunity describe equally well the age- and sex-specific immunoepidemiological patterns observed before intervention and 18 months after treatment. Over longer time horizons, we find that acquired immunity creates subtle differences in immunoepidemiological profiles during routine mass drug administration that may confer resilience against elimination. We discuss our findings in the broader context of the immunoepidemiology of schistosomiasis.</p>
      </abstract>
      <kwd-group>
        <kwd>schistosomiasis</kwd>
        <kwd>adaptive immunity</kwd>
        <kwd>public health</kwd>
        <kwd>modeling</kwd>
        <kwd>praziquantel</kwd>
      </kwd-group>
      <funding-group>
        <award-group award-type="grant">
          <funding-source>
            <institution-wrap>
              <institution>European Union</institution>
              <institution-id institution-id-type="DOI">10.13039/501100000780</institution-id>
            </institution-wrap>
          </funding-source>
        </award-group>
        <award-group award-type="grant">
          <funding-source>
            <institution-wrap>
              <institution>UK Medical Research Council</institution>
              <institution-id institution-id-type="DOI">10.13039/501100000265</institution-id>
            </institution-wrap>
          </funding-source>
        </award-group>
        <award-group award-type="grant">
          <funding-source>
            <institution-wrap>
              <institution>UK Doctoral Training Partnership</institution>
            </institution-wrap>
          </funding-source>
          <award-id>MR/K50127X/1</award-id>
        </award-group>
        <award-group award-type="grant">
          <funding-source>
            <institution-wrap>
              <institution>Sir Henry Wellcome Postdoctoral Fellowship</institution>
            </institution-wrap>
          </funding-source>
          <award-id>224190/Z/21/Z</award-id>
        </award-group>
        <award-group award-type="grant">
          <funding-source>
            <institution-wrap>
              <institution>Centre for Global Infectious Disease Analysis</institution>
            </institution-wrap>
          </funding-source>
          <award-id>MR/X020258/1</award-id>
        </award-group>
      </funding-group>
      <counts>
        <page-count count="10" />
      </counts>
    </article-meta>
  </front>
  <body>
    <boxed-text id="pgae471-box1" position="anchor">
      <caption>
        <title>Significance Statement</title>
      </caption>
      <p>A longstanding question in schistosome epidemiology is the relative contributions of exposure and immunity to observed age-infection profiles. Previous attempts to disentangle these processes have been hampered by a lack of paired data on markers of exposure, infection, and immunity. Furthermore, most studies have assumed immunostimulation by living adult worms—not dying worms, for which there is currently the most compelling evidence. To combat these limitations, here we collate a unique dataset comprising individual-level data on cercarial exposure, infection intensity, and immunoglobulin E antibodies stimulated by an antigen (<italic>Schistosoma mansoni</italic> Tegumental-Allergen-Like protein 1) released upon death of adult <italic>Schistosoma mansoni</italic>. We use these data to calibrate a new mathematical model, allowing for robust inference on the relative contributions of exposure and immunity.</p>
    </boxed-text>
    <sec id="pgae471-s1" sec-type="intro">
      <title>Introduction</title>
      <p>Schistosomiasis is a parasitic neglected tropical disease of considerable public health importance. Schistosomiasis affects approximately 240 million people worldwide (<xref rid="pgae471-B1" ref-type="bibr">1</xref>), causing chronic and acute morbidity, including anemia, wasting, and damage to intestinal or urogenital systems. The global burden of schistosomiasis was estimated in 2021 at 1.75 (95% uncertainty interval [UI] 1.04–2.99) million disability adjusted life years, with 12,900 deaths (95% UI 11,400–14,700), the majority of which occurred in sub-Saharan Africa (<xref rid="pgae471-B2" ref-type="bibr">2</xref>). The World Health Organization (WHO) has targeted schistosomiasis for elimination as a public health problem (&lt;1% prevalence of heavy-intensity infections) by 2030, principally using a strategy of annual or semi-annual mass drug administration (MDA) with praziquantel (<xref rid="pgae471-B1" ref-type="bibr">1</xref>).</p>
      <p>Schistosomes are transmitted indirectly via intermediate freshwater snail hosts; consequently, exposure is linked to contact with water bodies containing infectious cercarial larvae. Five decades ago, Warren (<xref rid="pgae471-B3" ref-type="bibr">3</xref>) first noted the difficulty of distinguishing the contributions of “immunology or ecology” to the convex age-intensity profiles of schistosome infections (<xref rid="pgae471-B4" ref-type="bibr">4</xref>). Repeated exposure may promote a partially protective immune response, causing peak infection intensity to occur in earlier childhood in areas of intense transmission due to the more rapid acquisition of immunity (“peak shift”) (<xref rid="pgae471-B5 pgae471-B6 pgae471-B7 pgae471-B8" ref-type="bibr">5–8</xref>). However, childhood peaks in infection intensity are also likely driven by age-dependent contact rates with contaminated water bodies, which are often greater in children than adults (<xref rid="pgae471-B9" ref-type="bibr">9</xref>, <xref rid="pgae471-B10" ref-type="bibr">10</xref>). Hence, the relative importance of acquired immunity (“immunology”) vs. exposure (“ecology”) to the epidemiology of schistosomiasis has remained elusive.</p>
      <p>Resolving the contributions of immunity and exposure is critical for understanding the transmission dynamics of schistosomiasis and for modeling responses to interventions. Protective immunity increases the resilience of helminthiases to intervention, making it more difficult to achieve elimination targets (<xref rid="pgae471-B9" ref-type="bibr">9</xref>, <xref rid="pgae471-B11" ref-type="bibr">11</xref>). Recent advances have indicated that immunoglobulin E (IgE) responses against Tegumental-Allergen-Like (TAL) proteins are likely a major component of so-called “delayed concomitant immunity” (<xref rid="pgae471-B12" ref-type="bibr">12</xref>). By this proposed mechanism, protective immunological responses are mediated by the death of adult schistosomes which induce antibodies that are cross-reactive with TAL proteins present on invading cercariae (<xref rid="pgae471-B12" ref-type="bibr">12</xref>, <xref rid="pgae471-B13" ref-type="bibr">13</xref>). Delayed concomitant immunity may also provide a strong passive vaccination effect following praziquantel treatment of heavily infected individuals, initially boosting immunity and enhancing protection against reinfection (<xref rid="pgae471-B14" ref-type="bibr">14</xref>), but waning following subsequent treatments.</p>
      <p>In recent years, schistosomiasis transmission models have been increasingly used for public health decision-making, including on the frequency and population coverage of MDA required to achieve the 2030 elimination goals (reviewed previously (<xref rid="pgae471-B15" ref-type="bibr">15</xref>)). However, due to uncertainty on the relative contributions of exposure vs. immunity, these models have typically attributed age-infection patterns exclusively to exposure (e.g. (<xref rid="pgae471-B16" ref-type="bibr">16</xref>), although see also Refs. (<xref rid="pgae471-B9 pgae471-B10 pgae471-B11" ref-type="bibr">9–11</xref>, <xref rid="pgae471-B17" ref-type="bibr">17</xref>, <xref rid="pgae471-B18" ref-type="bibr">18</xref>)). Depending on the nature and strength of acquired immunity, this assumption may make current projections on the long-term effectiveness of MDA too optimistic. Improved understanding of acquired immunity in natural populations would also benefit the development of effective schistosomiasis vaccines (<xref rid="pgae471-B19" ref-type="bibr">19</xref>, <xref rid="pgae471-B20" ref-type="bibr">20</xref>).</p>
      <p>Here, we develop a novel mathematical transmission model to resolve the contributions of exposure and acquired immunity to the epidemiology of intestinal schistosomiasis using a unique immunoepidemiological dataset collected from 110 individuals aged between 7 and 50 years living on the shores of Lake Albert, Uganda, before the initiation of MDA (<xref rid="pgae471-B21" ref-type="bibr">21</xref>, <xref rid="pgae471-B22" ref-type="bibr">22</xref>). We use data on water contact and malacological surveys (<xref rid="pgae471-B23" ref-type="bibr">23</xref>, <xref rid="pgae471-B24" ref-type="bibr">24</xref>) to infer age- and sex-dependent patterns of cercarial exposure and estimate the protective effect of delayed concomitant immunity using individual-level parasitological data on infection intensity and immunological data on <italic>Schistosoma mansoni</italic> Tegumental-Allergen-Like protein 1 (SmTAL1) IgE antibodies. We compare model variants with and without protective acquired immunity to determine its importance in capturing observed immunoepidemiological profiles. We also explore how immunity affects transmission dynamics during MDA. We discuss our findings in the context of the longstanding debate on schistosome exposure vs. immunity and the broader immunoepidemiology of schistosomiasis.</p>
    </sec>
    <sec id="pgae471-s2" sec-type="results">
      <title>Results</title>
      <p>Cercarial exposure shows a similar convex-like pattern in males and females, peaking at 11 and 15 years, respectively, before gradually declining throughout adulthood (Fig. <xref rid="pgae471-F1" ref-type="fig">1</xref>). The fit of the transmission model (Fig. <xref rid="pgae471-F2" ref-type="fig">2</xref>) to preintervention immunoepidemiological data is shown in Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>A and B (“Baseline”) for the model variant without protective immunity (“standard model”) and with protective immunity (“immunity model”). The immunity model shows a sharper peak in infection intensity (eggs per gram of feces [epg]) in school-aged children (SAC) and a steeper decline into older ages than the standard model (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>A, “Baseline”; see Fig. <xref ref-type="supplementary-material" rid="sup1">S2</xref> for an overlaid plot). Accordingly, in older ages the rate of increase in SmTAL1-IgE optical density (OD) is lower for the immunity model than for the standard model (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>B, “Baseline”). The deviance information criterion (DIC) indicates the standard model to be a more parsimonious and adequate fit to the data than the more complex immunity model (standard model 50.94 [95% credible interval, crI, 50.67–51.44] and immunity model 51.12 [95% crI 50.73–51.59]).</p>
      <fig id="pgae471-F1" position="float" fig-type="figure">
        <label>Fig. 1.</label>
        <caption>
          <p>Fit of nonlinear exposure function (see Supporting methods) to cercarial exposure data (<italic>n</italic> = 110 individuals) (<xref rid="pgae471-B23" ref-type="bibr">23</xref>). Points and error bars show, respectively, the observed means and associated 95% CI (calculated using 1,000 nonparametric bootstrap samples). Lines and shaded areas show, respectively, the best-fit model estimates obtained via maximum likelihood estimation using a quasi-Newton optimization algorithm, and the modeled 95% CI (estimated using 1,000 parametric bootstrap samples of parameter values from a multivariate normal distribution parameterized with the variance–covariance matrix of the best-fit model). Note that best-fit model estimates were normalized (to sum to 1) before use in the transmission model such that only the relative shapes and magnitudes of the functional forms influenced model dynamics. See the Supporting Information for further details.</p>
        </caption>
        <graphic xmlns:xlink="http://www.w3.org/1999/xlink" mimetype="image" xlink:href="pgae471f1.jpeg" />
      </fig>
      <fig id="pgae471-F2" position="float" fig-type="figure">
        <label>Fig. 2.</label>
        <caption>
          <p>Transmission model structure. The model tracks the mean worm burden of adult <italic>S. mansoni</italic> divided into <inline-formula><mml:math id="IM1" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>i</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> latent compartments, <inline-formula><mml:math id="IM2" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>W</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, across time and host age and sex. The infection dynamics are driven by the force of infection, <inline-formula><mml:math id="IM3" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow></mml:math></inline-formula>, which is a function of the vector of model parameters, <italic>θ</italic>, the age- and sex-specific cercarial exposure, <inline-formula><mml:math id="IM4" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ψ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, and the host population structure, <inline-formula><mml:math id="IM5" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>a</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> (with age- and sex-dependencies omitted in the figure for brevity). Worms enter compartment <inline-formula><mml:math id="IM6" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>W</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math></inline-formula>, pass between <italic>n</italic> contiguous compartments at rate <inline-formula><mml:math id="IM7" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi><mml:mi>μ</mml:mi></mml:math></inline-formula> and die after leaving the <italic>n</italic>th compartment. Eggs are excreted from the host by worms in all compartments (indicated by the gray dashed box) at a rate determined by a constant egg-shedding parameter, <italic>λ</italic>, and a worm mating probability, <inline-formula><mml:math id="IM8" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Φ</mml:mi></mml:mrow></mml:math></inline-formula> (a function of <italic>W</italic> and the among-host worm overdispersion parameter, <italic>k</italic>), producing the number of epg. Worms that die move to compartment <italic>D</italic>, which counts the cumulative number of dead worms experienced by hosts. A function, <inline-formula><mml:math id="IM9" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>D</mml:mi><mml:mo>,</mml:mo><mml:mi>σ</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, relates this cumulative experience to the acquired immune response, <italic>I</italic>, by integrating through past age and time while accounting for antibody decay through rate parameter <italic>σ</italic>. The acquired immune response of compartment <italic>I</italic> is mapped to a measured IgE OD through a constant parameter, <inline-formula><mml:math id="IM10" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>φ</mml:mi></mml:math></inline-formula>. A function, <inline-formula><mml:math id="IM11" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Θ</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>I</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, relates the level of acquired immunity to the probability of cercarial infection establishment; parameter <italic>ω</italic> determines the level of protection, ranging from none (<inline-formula><mml:math id="IM12" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ω</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math></inline-formula>) to increasingly strong (<inline-formula><mml:math id="IM13" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ω</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>) protection. Note that all compartments and outputs are host age- and sex-specific (not shown here for brevity). Dotted gray arrows represent flows to model outputs that do not impact transmission dynamics. For a full description of parameters and model derivation, see the Supporting Information. Figure created with BioRender.</p>
        </caption>
        <graphic xmlns:xlink="http://www.w3.org/1999/xlink" mimetype="image" xlink:href="pgae471f2.jpeg" />
      </fig>
      <fig id="pgae471-F3" position="float" fig-type="figure">
        <label>Fig. 3.</label>
        <caption>
          <p>Model fits against pretreatment data and validation against post-treatment data. Immunoepidemiological outputs—epg and SmTAL1-IgE OD—are presented for the model including (“immunity model”; orange) or excluding (“standard model”; purple) delayed concomitant immunity. In A and B), the first columns show the model fits to baseline (preintervention) data (<italic>n</italic> = 85 individuals; see also Fig. <xref ref-type="supplementary-material" rid="sup1">S2</xref> for an overlaid plot) (<xref rid="pgae471-B24" ref-type="bibr">24</xref>), while subsequent columns show model validation against (without fitting to) post-treatment data collected 5 weeks (<italic>n</italic> = 75 individuals), 12 months (<italic>n</italic> = 63 individuals), and 18 months (<italic>n</italic> = 67 individuals) after the second of two community-wide praziquantel treatments (<xref rid="pgae471-B24" ref-type="bibr">24</xref>). Points represent the mean age-aggregated data and error bars the associated 95% binomial CI (calculated using 1,000 nonparametric bootstrap samples). Lines represent the median modeled estimates (50th percentile of simulated outputs) and shaded areas the associated 95% crI (2.5 and 97.5 percentiles). Posterior distributions were approximated by selecting parameter sets obtaining the top 1% of log likelihoods (<xref rid="pgae471-B25" ref-type="bibr">25</xref>) (i.e. 1,000 parameter sets). In line with the study protocol (<xref rid="pgae471-B24" ref-type="bibr">24</xref>), we simulated two treatments with 40 mg/kg body weight of praziquantel, 2 weeks apart, with 100% coverage over the range of ages of individuals in the study (7–50 years old) (<xref rid="pgae471-B24" ref-type="bibr">24</xref>). Note that SmTAL1-IgE data were only collected until 5 weeks post-treatment. (C) Comparative model posterior dynamics (posterior medians and 95% crI) under 10 rounds of annual MDA, with treatment coverage of 75% in SAC (5–15 years old)—representing the WHO target for this demographic group (<xref rid="pgae471-B1" ref-type="bibr">1</xref>)—and a nominal 30% in adults (≥16 years), yielding a mean (population weighted) coverage of 50.5% in line with Ugandan coverage surveys (<xref rid="pgae471-B26" ref-type="bibr">26</xref>, <xref rid="pgae471-B27" ref-type="bibr">27</xref>) is shown. Outputs are presented as host population density- and sex ratio-weighted means, using demographic data sourced from the United Nations (<xref rid="pgae471-B28" ref-type="bibr">28</xref>). Praziquantel efficacy (egg reduction rate) was set to 95% for all simulations (<xref rid="pgae471-B29" ref-type="bibr">29</xref>).</p>
        </caption>
        <graphic xmlns:xlink="http://www.w3.org/1999/xlink" mimetype="image" xlink:href="pgae471f3.jpeg" />
      </fig>
      <p>Parameter posterior distributions from each model are summarized in Fig. <xref rid="pgae471-F4" ref-type="fig">4</xref> (see also Figs. <xref ref-type="supplementary-material" rid="sup1">S3 and S4</xref>, Figs. <xref ref-type="supplementary-material" rid="sup1">S5 and S6</xref> for pairwise correlations, and Fig. <xref ref-type="supplementary-material" rid="sup1">S7</xref> for posterior log likelihoods). The median SmTAL1-IgE half-life (12 ln(2)/<italic>σ</italic>, where <italic>σ</italic> is the rate of loss; Fig. <xref rid="pgae471-F4" ref-type="fig">4</xref>) is 1.1 months for both models, with 95% crI of 1.0–1.6 months for the standard model and 1.0–1.5 months for the immunity model. For the immunity model, the strength of protection against cercarial infection establishment is highly uncertain (<italic>ω</italic>, posterior distribution uniform over prior range; Figs. <xref rid="pgae471-F4" ref-type="fig">4</xref> and <xref ref-type="supplementary-material" rid="sup1">S4</xref>) despite mild and statistically nonsignificant pairwise correlations with other fitted parameters (correlation coefficient range −0.15 to 0.11, Fig. <xref ref-type="supplementary-material" rid="sup1">S6</xref>). Some resolution was obtained for the human-to-snail population density parameter (<italic>N</italic><sub>1</sub>/<italic>N</italic><sub>2</sub>, greater posterior vs. prior densities for values over ∼0.3; Figs. <xref rid="pgae471-F4" ref-type="fig">4</xref>, <xref ref-type="supplementary-material" rid="sup1">S3, and S4</xref>), but other parameter posterior estimates were largely indistinguishable from priors (Fig. <xref rid="pgae471-F4" ref-type="fig">4</xref>).</p>
      <fig id="pgae471-F4" position="float" fig-type="figure">
        <label>Fig. 4.</label>
        <caption>
          <p>Summary of the posterior distributions of parameters estimated by fitting the model including (“immunity model”) or omitting (“standard model”) delayed concomitant immunity to immunoepidemiological data (<xref rid="pgae471-B24" ref-type="bibr">24</xref>). For each parameter, dots show the median posterior estimate (the top 1% of log likelihoods from 100,000 simulations (<xref rid="pgae471-B25" ref-type="bibr">25</xref>)), whiskers the lower and upper 95% crI (the 2.5 and 97.5 percentiles of the posterior distributions), and gray shaded areas the (uniform) prior ranges. Note that the immune protection parameter, <italic>ω</italic>, was fixed to 0 for the standard model, hence no parameter estimation was performed here. Parameter notation: <inline-formula><mml:math id="IM14" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></inline-formula>, basic reproduction number; <italic>π</italic>, weighting parameter defining asymmetry of transmission (humans-to-snails vs. snails-to-humans); <italic>k</italic>, among-host worm overdispersion; <italic>ω</italic>, SmTAL1-IgE mediated protection against cercarial establishment; <italic>σ</italic>, rate of decay of SmTAL1-IgE antibodies; <italic>ϕ</italic>, constant that maps acquired immunity to antibody optical densities; <inline-formula><mml:math id="IM15" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math></inline-formula>, human-to-snail population density.</p>
        </caption>
        <graphic xmlns:xlink="http://www.w3.org/1999/xlink" mimetype="image" xlink:href="pgae471f4.jpeg" />
      </fig>
      <p>Both model variants show good predictive performance against epg and SmTAL1-IgE OD values collected at 5 weeks (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>A and B, “5 weeks”) after praziquantel treatment and against epg collected additionally at 12 months (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>A, “12 months”), and 18 months (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>A, “18 months”) post-treatment (note that SmTAL1-IgE was only measured up to 5 weeks after treatment) (<xref rid="pgae471-B24" ref-type="bibr">24</xref>). There was no difference in model performance by root mean squared error (RMSE) in capturing post-treatment epg (standard model, 255 [95% crI 47.3–617]; immunity model, 260 [95% crI 47.7–628]) or SmTAL1-IgE (standard model, 0.24 [95% crI 0.18–0.34]; immunity model, 0.23 [95% crI 0.17–0.32]) (Fig. <xref ref-type="supplementary-material" rid="sup1">S8</xref>).The long-term epg dynamics through 10 rounds of annual MDA—assuming 75% coverage of SAC (<xref rid="pgae471-B1" ref-type="bibr">1</xref>) and a nominal 30% of adults (≥16 years old), yielding a mean coverage of 50.5% in line with Ugandan coverage surveys (<xref rid="pgae471-B26" ref-type="bibr">26</xref>, <xref rid="pgae471-B27" ref-type="bibr">27</xref>)—are consistently lower for the immunity model compared to the standard model (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>C, “epg”), likely since infection intensities are more concentrated in SAC in the former (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>A, “Baseline”). SmTAL1-IgE OD dynamics are similar in both models until approximately 5 years after MDA initiation, after which antibodies decline faster in the immunity model (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>C, “SmTAL1-IgE (OD)”), reflecting a lower antigenic stimulus from lowered worm burdens (and, consequently, epg; Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>C). For both models, SmTAL1-IgE ODs fall below preintervention levels (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>C). The immunity model projections are associated with wide uncertainty intervals, particularly for epg (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>C), reflecting uncertainty in both preintervention fits (chiefly in SAC; Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>A, “Baseline”) and the strength of protection afforded by SmTAL1-IgEs (<italic>ω</italic>, Fig. <xref rid="pgae471-F4" ref-type="fig">4</xref>). This translates into more uncertain prevalence dynamics for the immunity model, further compounded by uncertainty in the among-host worm overdispersion parameter (<italic>k</italic>, used to calculate prevalence; Fig. <xref ref-type="supplementary-material" rid="sup1">S9</xref>). Some immunity model simulations initially show stark epg decreases which thereafter remain persistently low (Fig. <xref rid="pgae471-F3" ref-type="fig">3</xref>C “epg,” immunity model lower 95% crI). These are associated with low values of basic reproduction number (<inline-formula><mml:math id="IM16" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></inline-formula>), human-to-snail population density (<italic>N</italic><sub>1</sub>/<italic>N</italic><sub>2</sub>), SmTAL1-IgE decay (<italic>σ</italic>), and immune constant (<italic>ϕ</italic>), and high values of immune protection (<italic>ω</italic>) (Fig. <xref ref-type="supplementary-material" rid="sup1">S10</xref>).</p>
    </sec>
    <sec id="pgae471-s3" sec-type="discussion">
      <title>Discussion</title>
      <p>The relative importance of age-dependent exposure vs. acquired immunity to typical convex age-intensity profiles is a major unresolved question in schistosomiasis epidemiology (<xref rid="pgae471-B3" ref-type="bibr">3</xref>, <xref rid="pgae471-B9 pgae471-B10 pgae471-B11" ref-type="bibr">9–11</xref>, <xref rid="pgae471-B30" ref-type="bibr">30</xref>). Understanding the relative contributions of these two processes has important implications for transmission dynamics, responses to MDA, including the feasibility of achieving the WHO 2030 goals (<xref rid="pgae471-B1" ref-type="bibr">1</xref>). Here, we have used a unique immunoepidemiological dataset (<xref rid="pgae471-B24" ref-type="bibr">24</xref>)—which includes individual data on exposure to infectious cercariae (<xref rid="pgae471-B23" ref-type="bibr">23</xref>)—combined with a mathematical transmission model to attempt to resolve the effects of delayed concomitant immunity and age-dependent exposure on the epidemiology of intestinal schistosomiasis in a highly endemic region of western Uganda. We found that the model variants incorporating or omitting acquired immunity captured equally well observed age profiles of infection intensity and SmTAL1-IgE antibodies before and up to 18 months after praziquantel treatment. It therefore appears that delayed concomitant immunity is not required to adequately describe the transmission of intestinal schistosomiasis in this highly endemic epidemiological setting and its protective effect is highly uncertain. However, we also stress that we have taken a conservative approach to parameter inference, that the protective effects of immunity may only become apparent over longer time horizons in populations subject to MDA, and that the proxy of immunity used is a necessary simplification of the proposed delayed concomitant mechanism (<xref rid="pgae471-B12" ref-type="bibr">12</xref>). We also emphasize that these conclusions are based on findings from a single highly endemic setting, using data from 110 individuals. It is conceivable that a larger sample size would be required to detect acquired immunity if its effects are relatively weak. Therefore, acquired immunity should not be entirely discounted from future modeling efforts aimed at projecting the effectiveness of interventions.</p>
      <p>Many previous mathematical modeling studies have considered the role of acquired immunity on the epidemiology of schistosomiasis, but these have generally focused on the theoretical implications of immunity for control and elimination efforts (<xref rid="pgae471-B9 pgae471-B10 pgae471-B11" ref-type="bibr">9–11</xref>, <xref rid="pgae471-B18" ref-type="bibr">18</xref>). While some models have been calibrated against exposure and infection data (<xref rid="pgae471-B9 pgae471-B10 pgae471-B11" ref-type="bibr">9–11</xref>), data have typically been lacking on antibody responses, limiting inference on the role of immunity (<xref rid="pgae471-B3" ref-type="bibr">3</xref>). The key novelty of our study is the use of individual data on exposure, infection, and immunological responses which permits, in principle, the relative contributions of exposure and immunity to be disaggregated. We focused on delayed concomitant immunity (as opposed to other postulated mechanisms of acquired immunity (<xref rid="pgae471-B31" ref-type="bibr">31</xref>)) to align with the available immunological data on SmTAL1-IgEs which comprise the primary antibody response following the death of adult worms (<xref rid="pgae471-B13" ref-type="bibr">13</xref>, <xref rid="pgae471-B14" ref-type="bibr">14</xref>, <xref rid="pgae471-B17" ref-type="bibr">17</xref>, <xref rid="pgae471-B32 pgae471-B33 pgae471-B34 pgae471-B35" ref-type="bibr">32–35</xref>) and which have been previously associated with reduced rates of reinfection (e.g. (<xref rid="pgae471-B36" ref-type="bibr">36</xref>) and references therein). Notwithstanding, SmTAL1-IgE is a proxy for a proposed immunity-generating process acting via TAL family members such as SmTAL3, SmTAL5, and SmTAL11, since SmTAL3/SmTAL5/SmTAL11 responders are known to be a subset of SmTAL1 responders (<xref rid="pgae471-B12" ref-type="bibr">12</xref>, <xref rid="pgae471-B13" ref-type="bibr">13</xref>, <xref rid="pgae471-B37" ref-type="bibr">37</xref>). SmTAL3 and SmTAL11 are expressed predominantly in adult worms, and IgE specific to these antigens is cross-reactive with SmTAL5 (<xref rid="pgae471-B13" ref-type="bibr">13</xref>) expressed on cercariae and early schistosomulae. Hence, while immunity is stimulated by worm death (i.e. “delayed”), the protective response is thought to be protective against invading stages (i.e. “concomitant”).</p>
      <p>We found that most model parameters were only weakly identifiable from the data, such that many different parameter combinations could yield similar immunoepidemiological patterns that adequately captured the data. We deliberately chose a conservative approach to parameter inference by assigning vague priors to all unknown parameters and avoided harder assumptions associated with fixing values to uncertain model parameters. While this avoids potential bias, it also highlights the limitations and challenges of parameter inference using transmission models with multiple unknown or highly uncertain parameters (<xref rid="pgae471-B38" ref-type="bibr">38</xref>). The data were most informative on the half-life of SmTAL1-IgE antibodies, with both model variants yielding a central estimate of 1.1 months and an uncertainty range of 1–1.6 months. Without replacement, IgE has a circulating half-life of 2 days, and a half-life in the skin, the proposed site of parasite killing, of 16–20 days (<xref rid="pgae471-B39" ref-type="bibr">39</xref>). The half-life of IgE secreting plasma cells—which replace circulating IgE—is more contentious, spanning from months to years. Blockage of plasma cell production with the immunotherapeutic drug Dupilumab shows &gt;80% loss of circulating IgE over 1 year (reviewed in Ref. (<xref rid="pgae471-B40" ref-type="bibr">40</xref>)), a slower kinetic than found here. While no other studies have examined SmTAL1-IgE half-life, previous unpublished work found significantly lower titers of schistosome worm antigen-specific IgE 1 year after treatment of Kenyan SAC (<xref rid="pgae471-B37" ref-type="bibr">37</xref>). Further, <italic>S. haematobium</italic> models developed to investigate antibody isotype switching (<xref rid="pgae471-B32" ref-type="bibr">32</xref>, <xref rid="pgae471-B33" ref-type="bibr">33</xref>) estimated an initial antibody response from short-lived plasma cells of 5–46 days (<xref rid="pgae471-B33" ref-type="bibr">33</xref>) and 3.2–32 days (<xref rid="pgae471-B32" ref-type="bibr">32</xref>), while estimates of the longer-lived antibody response were 9–90 years (<xref rid="pgae471-B33" ref-type="bibr">33</xref>) and 10 months–87 years (<xref rid="pgae471-B32" ref-type="bibr">32</xref>). The difference in estimates between previous work and ours could reflect biological differences between schistosome species, the modeled mechanism of protective immunity, and other modeling assumptions (e.g. age-exposure patterns and worm life-span). While we do not find that delayed concomitant immunity is necessary to explain immunoepidemiological profiles at endemic equilibrium and 18 months post-treatment in this population, we cannot rule out its importance for the longer-term epidemiology and transmission dynamics of intestinal schistosomiasis.</p>
      <p>A principle of helminth epidemiology is that acquired immunity increases the resilience of parasite populations to interventions via the release of immune-mediated density-dependent constraints (<xref rid="pgae471-B11" ref-type="bibr">11</xref>, <xref rid="pgae471-B41" ref-type="bibr">41</xref>). Previous transmission dynamics modeling of schistosomiasis has demonstrated this explicitly, showing that the loss of acquired immunity during MDA increases rates of reinfection (<xref rid="pgae471-B9" ref-type="bibr">9</xref>, <xref rid="pgae471-B18" ref-type="bibr">18</xref>). By contrast, our modeling of MDA shows that stronger declines in infection and decreased rates of reinfection occur when immunity is incorporated compared to when it is omitted. This occurs because of the protection against reinfection afforded by SmTAL1-IgE antibodies—which are transiently boosted following the death of adult schistosomes after treatment—but also because the accumulation of protective antibodies during childhood increases the aggregation of worms in SAC, the demographic with the highest coverage of MDA.</p>
      <p>Past models have often assumed that cumulative live worms are the source of antigenic stimulation for acquired immunity against schistosomes (<xref rid="pgae471-B9" ref-type="bibr">9</xref>, <xref rid="pgae471-B11" ref-type="bibr">11</xref>, <xref rid="pgae471-B18" ref-type="bibr">18</xref>) but a compelling body of evidence now suggests this role is instead fulfilled by cumulative exposure to dying worms (<xref rid="pgae471-B12 pgae471-B13 pgae471-B14" ref-type="bibr">12–14</xref>, <xref rid="pgae471-B17" ref-type="bibr">17</xref>, <xref rid="pgae471-B32 pgae471-B33 pgae471-B34" ref-type="bibr">32–34</xref>). These different sources of immunostimulation will yield tangible differences in projected dynamics. Assuming a live-worm stimulus, reductions in worm burden caused by treatment will cause a faster decline in protective immunity leading to more rapid rates of reinfection (<xref rid="pgae471-B18" ref-type="bibr">18</xref>). Assuming dead worms provide the stimulus, worms killed by treatment will boost the immune response, initially reducing rates of reinfection. However, in keeping with previous serological (<xref rid="pgae471-B42" ref-type="bibr">42</xref>, <xref rid="pgae471-B43" ref-type="bibr">43</xref>) and modeling (<xref rid="pgae471-B17" ref-type="bibr">17</xref>) studies, our model also highlights that the immunological boosting effect of praziquantel is transient, both immediately after treatment—due to the relatively short estimated half-life of SmTAL1-IgE—and longer-term due to reductions in infection. Thus, in the long term, the qualitative effect on transmission dynamics of different sources of immunostimulation will become similar as population immunity is diminished under both mechanisms. Indeed, premature cessation of MDA can result in a rapid rebound in infections, even “overshooting” pretreatment levels (<xref rid="pgae471-B17" ref-type="bibr">17</xref>, <xref rid="pgae471-B44" ref-type="bibr">44</xref>).</p>
      <p>Our approach to modeling delayed concomitant immunity is necessarily a simplification of the underlying immunological mechanisms and incurs limitations. First, it is possible that our strategy of leveraging the relationship between SmTAL1 and SmTAL3/5 gave insufficient resolution to detect an immune effect. Previous work from Lake Victoria, Uganda, found that of 89 individuals with measureable SmTAL1-IgE titers, only 43% (<italic>n</italic> = 38) were SmTAL3-IgE responders, and 19% (<italic>n</italic> = 17) SmTAL5-IgE responders (<xref rid="pgae471-B13" ref-type="bibr">13</xref>, <xref rid="pgae471-B37" ref-type="bibr">37</xref>). If these proportions were similar for our dataset, it might be challenging to find a protective signal—particularly if it were weak. Second, we do not account for a possible counter-balancing effect of IgG4, which is thought to downregulate IgE by competitively binding to the same epitopes (<xref rid="pgae471-B45" ref-type="bibr">45</xref>). Several studies have reported that the balance of IgE/IgG4 determines the resistance vs. susceptibility to reinfection (<xref rid="pgae471-B24" ref-type="bibr">24</xref>, <xref rid="pgae471-B45" ref-type="bibr">45</xref>, <xref rid="pgae471-B46" ref-type="bibr">46</xref>). Finally, we use a deterministic model which gives a mean-field approximation of transmission dynamics. A stochastic individual-based model would permit individual variability in worm burdens and antibody responses to be captured; albeit this approach would incur considerable technical difficulties in fitting to data. Notwithstanding these limitations, we emphasize the significant utility of the modeling framework presented here, which could be adapted to fit other data or other proposed immune mechanisms.</p>
      <p>Future research could seek to design alternative population sampling strategies to better distinguish the two hypotheses represented by the model variants. Since datasets on long-term TAL family IgE dynamics are lacking, it would be helpful to introduce longer-term immunological monitoring of endemic populations. Data collected from such monitoring could then be used in conjunction with longer-term longitudinally collected parasitological data—such as programmatic data collected during MDA—to better validate and compare the long-term model dynamics. Future modeling studies could also focus on other markers of acquired immunity, including the newly characterized SmTAL11, which has also been implicated in the generation of cross-reactive IgEs specific to SmTAL3 and SmTAL5 (<xref rid="pgae471-B12" ref-type="bibr">12</xref>).</p>
      <p>In conclusion, the contributions of exposure vs. immunity to schistosome epidemiology, first noted five decades ago (<xref rid="pgae471-B3" ref-type="bibr">3</xref>), remain unresolved. This article illustrates that disentangling these two processes is challenging even with complete individual-level immunoepidemiological data. We found that model variants incorporating or omitting delayed concomitant immunity could describe equally well immunoepidemiological patterns of intestinal schistosomiasis before intervention and 18 months after MDA in a highly endemic community of western Uganda. Despite this unresolved uncertainty, our modeling also indicates that the effects of acquired immunity may become apparent after repeated years of MDA and thus immunity should not be discounted from future modeling projections on the effectiveness of schistosomiasis interventions and the feasibility of reaching the WHO 2030 elimination goals.</p>
    </sec>
    <sec id="pgae471-s4" sec-type="materials|methods">
      <title>Materials and methods</title>
      <sec id="pgae471-s4.1">
        <title>Dataset and study population</title>
        <p>Details of the data used in this study have been described previously (<xref rid="pgae471-B21 pgae471-B22 pgae471-B23 pgae471-B24" ref-type="bibr">21–24</xref>). Briefly, a longitudinal reinfection study was conducted in Booma, a fishing village on the eastern shore of Lake Albert, Uganda, highly endemic for <italic>S. mansoni</italic> with an estimated community prevalence in 1998 of 94% (<xref rid="pgae471-B47" ref-type="bibr">47</xref>). Parasitology, serology, and intensive water-contact observations for 12 h per day over a 10-month period were conducted, in conjunction with systematic snail surveys, between 1998 and 2000 (<xref rid="pgae471-B23" ref-type="bibr">23</xref>). Baseline data were collected before the introduction of MDA and can, therefore, be assumed to reflect the epidemiology at endemic equilibrium. This is an advantage for the current analysis as it avoids the need to model explicitly the effect of interventions or other secular changes (e.g. environmental or ecological change) which would introduce additional complexity and uncertainty. Following the collection of baseline (pretreatment) data in May 1998, from July 1998 a randomly sampled subset of the community was treated twice, 2 weeks apart, with praziquantel at 40 mg/kg of body weight. <italic>S. mansoni</italic> eggs per gram of feces (epg) and SmTAL1-IgE OD were longitudinally measured at follow-up at 5 weeks, 12 months, and 18 months after the second treatment (<xref rid="pgae471-B24" ref-type="bibr">24</xref>). The sample used in the current study comprises 110 individuals of the Alur ethnic group (the now dominant ethnic group in the Lake Albert region (<xref rid="pgae471-B48" ref-type="bibr">48</xref>)) aged 7–50 years old from whom data were collected on cercarial exposure and a subset of 85 individuals (aged 7–47) with paired data on epg and SmTAL1-IgE OD (Table <xref ref-type="supplementary-material" rid="sup1">S1</xref>). At each sampling time point, individual epg data were calculated as the average of two Kato-Katz egg counts, from three stool samples, collected on consecutive days. Data on SmTAL1-IgE ODs were calculated from triplicate repeats using control serum to account for between-plate variation.</p>
      </sec>
      <sec id="pgae471-s4.2">
        <title>Ethics</title>
        <p>The original study obtained informed consent from all participants and ethical clearance was granted by the Uganda National Council for Science and Technology (UNCST) (<xref rid="pgae471-B23" ref-type="bibr">23</xref>, <xref rid="pgae471-B24" ref-type="bibr">24</xref>). The current analysis is in line with the approved study aim of determining the roles of exposure and immunity on levels of infection and associated morbidity.</p>
      </sec>
      <sec id="pgae471-s4.3">
        <title>Transmission dynamics model</title>
        <p>We developed a mathematical model in R (<xref rid="pgae471-B49" ref-type="bibr">49</xref>) (using packages <italic>Rcpp</italic> (<xref rid="pgae471-B50" ref-type="bibr">50</xref>), <italic>RcppNumerial</italic> (<xref rid="pgae471-B51" ref-type="bibr">51</xref>), and <italic>RcppEigen</italic> (<xref rid="pgae471-B52" ref-type="bibr">52</xref>)) to describe age- and sex-dependent epg and SmTAL1-IgE antibody OD (Fig. <xref rid="pgae471-F2" ref-type="fig">2</xref>; <ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://www.github.com/gcmilne/SchistoTransmissionModel">www.github.com/gcmilne/SchistoTransmissionModel</ext-link>). The model is based on the population-based deterministic structure originally presented by Anderson and May (<xref rid="pgae471-B4" ref-type="bibr">4</xref>) and more recently in Neves et al. (<xref rid="pgae471-B53" ref-type="bibr">53</xref>) but with the miracidial and cercarial schistosome life-stages compressed into two components of the basic reproduction number, <inline-formula><mml:math id="IM17" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math></inline-formula>, and additional complexity introduced to model the production and loss of SmTAL1-IgE. Here, we give a brief overview of the model (Fig. <xref rid="pgae471-F2" ref-type="fig">2</xref>) with a complete derivation given in the Supporting Information.</p>
        <p>We model the mean number of schistosomes in <italic>i</italic> = 1…<italic>n</italic> worm compartments within human hosts of age <italic>a</italic>, sex <italic>s</italic>, and time <italic>t</italic>, <italic>W<sub>i</sub></italic>(<italic>a</italic>, <italic>s</italic>, <italic>t</italic>), the cumulative number of dead schistosomes <italic>D</italic>(<italic>a</italic>, <italic>s</italic>, <italic>t</italic>), and the average degree of acquired immunity, <italic>I</italic>(<italic>a</italic>, <italic>s</italic>, <italic>t</italic>), using a set of integro-partial differential equations,</p>
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                      <mml:mi>a</mml:mi>
                    </mml:mrow>
                  </mml:mfrac>
                </mml:mrow>
                <mml:mo>=</mml:mo>
                <mml:mi>n</mml:mi>
                <mml:msub>
                  <mml:mi>μ</mml:mi>
                  <mml:mn>1</mml:mn>
                </mml:msub>
                <mml:msub>
                  <mml:mi>W</mml:mi>
                  <mml:mrow>
                    <mml:mi>i</mml:mi>
                    <mml:mo>−</mml:mo>
                    <mml:mn>1</mml:mn>
                  </mml:mrow>
                </mml:msub>
                <mml:mo stretchy="false">(</mml:mo>
                <mml:mrow>
                  <mml:mi>a</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>s</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>t</mml:mi>
                </mml:mrow>
                <mml:mo stretchy="false">)</mml:mo>
                <mml:mo>−</mml:mo>
                <mml:mi>n</mml:mi>
                <mml:msub>
                  <mml:mi>μ</mml:mi>
                  <mml:mn>1</mml:mn>
                </mml:msub>
                <mml:msub>
                  <mml:mi>W</mml:mi>
                  <mml:mi>i</mml:mi>
                </mml:msub>
                <mml:mo stretchy="false">(</mml:mo>
                <mml:mrow>
                  <mml:mi>a</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>s</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>t</mml:mi>
                </mml:mrow>
                <mml:mo stretchy="false">)</mml:mo>
              </mml:mstyle>
            </mml:mstyle>
          </mml:math>
        </disp-formula>
        <disp-formula id="UM0002">
          <mml:math id="UM2" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block">
            <mml:mstyle displaystyle="true" scriptlevel="0">
              <mml:mrow>
                <mml:mfrac>
                  <mml:mrow>
                    <mml:mi>δ</mml:mi>
                    <mml:mi>D</mml:mi>
                    <mml:mo stretchy="false">(</mml:mo>
                    <mml:mrow>
                      <mml:mi>a</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>s</mml:mi>
                      <mml:mo>,</mml:mo>
                      <mml:mi>t</mml:mi>
                    </mml:mrow>
                    <mml:mo stretchy="false">)</mml:mo>
                  </mml:mrow>
                  <mml:mrow>
                    <mml:mi>δ</mml:mi>
                    <mml:mi>t</mml:mi>
                  </mml:mrow>
                </mml:mfrac>
              </mml:mrow>
              <mml:mo>+</mml:mo>
              <mml:mstyle displaystyle="true" scriptlevel="0">
                <mml:mrow>
                  <mml:mfrac>
                    <mml:mrow>
                      <mml:mi>δ</mml:mi>
                      <mml:mi>D</mml:mi>
                      <mml:mo stretchy="false">(</mml:mo>
                      <mml:mrow>
                        <mml:mi>a</mml:mi>
                        <mml:mo>,</mml:mo>
                        <mml:mi>s</mml:mi>
                        <mml:mo>,</mml:mo>
                        <mml:mi>t</mml:mi>
                      </mml:mrow>
                      <mml:mo stretchy="false">)</mml:mo>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mi>δ</mml:mi>
                      <mml:mi>a</mml:mi>
                    </mml:mrow>
                  </mml:mfrac>
                </mml:mrow>
                <mml:mo>=</mml:mo>
                <mml:mi>n</mml:mi>
                <mml:msub>
                  <mml:mi>μ</mml:mi>
                  <mml:mn>1</mml:mn>
                </mml:msub>
                <mml:msub>
                  <mml:mi>W</mml:mi>
                  <mml:mi>n</mml:mi>
                </mml:msub>
                <mml:mo stretchy="false">(</mml:mo>
                <mml:mrow>
                  <mml:mi>a</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>s</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>t</mml:mi>
                </mml:mrow>
                <mml:mo stretchy="false">)</mml:mo>
              </mml:mstyle>
            </mml:mstyle>
          </mml:math>
        </disp-formula>
        <disp-formula id="UM0003">
          <mml:math id="UM3" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block">
            <mml:mi>I</mml:mi>
            <mml:mo stretchy="false">(</mml:mo>
            <mml:mrow>
              <mml:mi>a</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>s</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>t</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">)</mml:mo>
            <mml:mo>=</mml:mo>
            <mml:mstyle displaystyle="true">
              <mml:munderover>
                <mml:mrow>
                  <mml:mo largeop="false">∫</mml:mo>
                </mml:mrow>
                <mml:mn>0</mml:mn>
                <mml:mi>a</mml:mi>
              </mml:munderover>
            </mml:mstyle>
            <mml:mspace width="0.2em" />
            <mml:msup>
              <mml:mi>e</mml:mi>
              <mml:mrow>
                <mml:mo>−</mml:mo>
                <mml:mi>σ</mml:mi>
                <mml:mo stretchy="false">(</mml:mo>
                <mml:mrow>
                  <mml:mi>a</mml:mi>
                  <mml:mo>−</mml:mo>
                  <mml:msup>
                    <mml:mi>a</mml:mi>
                    <mml:mrow>
                      <mml:mi mathvariant="normal">′</mml:mi>
                    </mml:mrow>
                  </mml:msup>
                </mml:mrow>
                <mml:mo stretchy="false">)</mml:mo>
              </mml:mrow>
            </mml:msup>
            <mml:mi>D</mml:mi>
            <mml:mo stretchy="false">(</mml:mo>
            <mml:mrow>
              <mml:msup>
                <mml:mi>a</mml:mi>
                <mml:mrow>
                  <mml:mi mathvariant="normal">′</mml:mi>
                </mml:mrow>
              </mml:msup>
              <mml:mo>,</mml:mo>
              <mml:mi>s</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>t</mml:mi>
              <mml:mo>−</mml:mo>
              <mml:mi>a</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">)</mml:mo>
            <mml:mo>.</mml:mo>
          </mml:math>
        </disp-formula>
        <p>Here, <inline-formula><mml:math id="IM18" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mspace width="0.25em" /></mml:mrow></mml:math></inline-formula> is the human-to-snail population density, <inline-formula><mml:math id="IM19" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>μ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math></inline-formula> and <inline-formula><mml:math id="IM20" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>μ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math></inline-formula> are the <italic>per capita</italic> mortality rates of schistosomes and infectious snails, respectively, <italic>ρ</italic> is the schistosome sex ratio (proportion female), and <inline-formula><mml:math id="IM21" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ψ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mspace width="0.25em" /></mml:math></inline-formula> is a normalized exposure function, with shape matching observed age- and sex-dependent ceracial exposure scores (<xref rid="pgae471-B23" ref-type="bibr">23</xref>) (Fig. <xref rid="pgae471-F1" ref-type="fig">1</xref>). The function <inline-formula><mml:math id="IM22" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Φ</mml:mi></mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:mi>W</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo stretchy="false">]</mml:mo></mml:math></inline-formula> denotes the (monogamous) mating probability (<xref rid="pgae471-B54" ref-type="bibr">54</xref>), where <inline-formula><mml:math id="IM23" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>k</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> is the overdispersion parameter of a negative binomial distribution which is assumed to adequately capture the distribution of schistosomes among human hosts (<xref rid="pgae471-B4" ref-type="bibr">4</xref>, <xref rid="pgae471-B55" ref-type="bibr">55</xref>), and which is dynamically affected by MDA (aggregation is transiently increased following rounds of treatment) but is assumed constant for age and sex (<xref rid="pgae471-B56" ref-type="bibr">56</xref>). The function <inline-formula><mml:math id="IM24" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Θ</mml:mi></mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>,</mml:mo><mml:mspace width="0.25em" /><mml:mi>ω</mml:mi></mml:mrow><mml:mo stretchy="false">]</mml:mo><mml:mo>∈</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> is the acquired immunity-dependent probability of cercarial establishment,</p>
        <disp-formula id="M0002">
          <label>(2)</label>
          <mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block">
            <mml:mrow>
              <mml:mi mathvariant="normal">Θ</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">[</mml:mo>
            <mml:mrow>
              <mml:mi>I</mml:mi>
              <mml:mo stretchy="false">(</mml:mo>
              <mml:mrow>
                <mml:mi>a</mml:mi>
                <mml:mo>,</mml:mo>
                <mml:mi>s</mml:mi>
                <mml:mo>,</mml:mo>
                <mml:mi>t</mml:mi>
              </mml:mrow>
              <mml:mo stretchy="false">)</mml:mo>
              <mml:mo>,</mml:mo>
              <mml:mi>ω</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">]</mml:mo>
            <mml:mo>=</mml:mo>
            <mml:mspace width="0.25em" />
            <mml:msup>
              <mml:mi>e</mml:mi>
              <mml:mrow>
                <mml:mo>−</mml:mo>
                <mml:mi>ω</mml:mi>
                <mml:mi>I</mml:mi>
                <mml:mo stretchy="false">(</mml:mo>
                <mml:mrow>
                  <mml:mi>a</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>s</mml:mi>
                  <mml:mo>,</mml:mo>
                  <mml:mi>t</mml:mi>
                </mml:mrow>
                <mml:mo stretchy="false">)</mml:mo>
              </mml:mrow>
            </mml:msup>
            <mml:mo>,</mml:mo>
          </mml:math>
        </disp-formula>
        <p>where parameter <italic>ω</italic> describes the strength of protection afforded by acquired immunity. Parameter <italic>σ</italic> is the rate of decay of acquired immunity, such that <inline-formula><mml:math id="IM25" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>12</mml:mn><mml:mspace width="0.25em" /><mml:mi>ln</mml:mi><mml:mspace width="0.2em" /><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>/</mml:mo><mml:mi>σ</mml:mi></mml:math></inline-formula> is the antibody half-life in months. Our approach to modeling acquired immunity aligns with previous methodologies (<xref rid="pgae471-B9" ref-type="bibr">9</xref>, <xref rid="pgae471-B18" ref-type="bibr">18</xref>) but uses cumulative dead, not live, worms as the source of antigenic stimuli (<xref rid="pgae471-B13" ref-type="bibr">13</xref>, <xref rid="pgae471-B57" ref-type="bibr">57</xref>).</p>
      </sec>
      <sec id="pgae471-s4.4">
        <title>Model calibration</title>
        <p>We calibrated the model with data on epg and SmTAL1-IgE OD. The epg is given by,</p>
        <disp-formula id="M0003">
          <label>(3)</label>
          <mml:math id="M3" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block">
            <mml:mi>E</mml:mi>
            <mml:mo stretchy="false">(</mml:mo>
            <mml:mrow>
              <mml:mi>a</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>s</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>t</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">)</mml:mo>
            <mml:mo>=</mml:mo>
            <mml:mi>λ</mml:mi>
            <mml:mi>W</mml:mi>
            <mml:mo stretchy="false">(</mml:mo>
            <mml:mrow>
              <mml:mi>a</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>s</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>t</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">)</mml:mo>
            <mml:mrow>
              <mml:mi mathvariant="normal">Φ</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">[</mml:mo>
            <mml:mrow>
              <mml:mi>W</mml:mi>
              <mml:mo stretchy="false">(</mml:mo>
              <mml:mrow>
                <mml:mi>a</mml:mi>
                <mml:mo>,</mml:mo>
                <mml:mi>s</mml:mi>
                <mml:mo>,</mml:mo>
                <mml:mi>t</mml:mi>
              </mml:mrow>
              <mml:mo stretchy="false">)</mml:mo>
              <mml:mo>,</mml:mo>
              <mml:mi>k</mml:mi>
              <mml:mo stretchy="false">(</mml:mo>
              <mml:mi>t</mml:mi>
              <mml:mo stretchy="false">)</mml:mo>
            </mml:mrow>
            <mml:mo stretchy="false">]</mml:mo>
            <mml:mo>,</mml:mo>
          </mml:math>
        </disp-formula>
        <p>where <italic>λ</italic> is the per worm fecundity of mated female schistosomes and <inline-formula><mml:math id="IM26" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:munderover><mml:mrow><mml:mo movablelimits="false">∑</mml:mo></mml:mrow><mml:mi>i</mml:mi><mml:mi>n</mml:mi></mml:munderover><mml:mspace width="0.2em" /><mml:msub><mml:mi>W</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, i.e. the per host total mean worm burden. Note that in the absence of strong evidence for density-dependent fecundity in <italic>S. mansoni</italic> (<xref rid="pgae471-B58" ref-type="bibr">58</xref>), we assume, in line with previous modeling (<xref rid="pgae471-B59" ref-type="bibr">59</xref>), that <italic>λ</italic> is independent of <inline-formula><mml:math id="IM27" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo><mml:mo>.</mml:mo></mml:math></inline-formula> The OD of SmTAL1-IgE antibodies is given by,</p>
        <disp-formula id="M0004">
          <label>(4)</label>
          <mml:math id="M4" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block">
            <mml:mrow>
              <mml:mi mathvariant="normal">IgE</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">(</mml:mo>
            <mml:mrow>
              <mml:mi>a</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>s</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>t</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">)</mml:mo>
            <mml:mo>=</mml:mo>
            <mml:mi>I</mml:mi>
            <mml:mo stretchy="false">(</mml:mo>
            <mml:mrow>
              <mml:mi>a</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>s</mml:mi>
              <mml:mo>,</mml:mo>
              <mml:mi>t</mml:mi>
            </mml:mrow>
            <mml:mo stretchy="false">)</mml:mo>
            <mml:mi>ϕ</mml:mi>
            <mml:mo>,</mml:mo>
          </mml:math>
        </disp-formula>
        <p>where <italic>ϕ</italic> is a proportionality constant (analogous to <italic>λ</italic>) that maps acquired immunity to observed OD.</p>
      </sec>
      <sec id="pgae471-s4.5">
        <title>Parameter estimation</title>
        <p>We fitted two variants of the model: the “standard model” in which SmTAL1-IgE is a passive marker of past exposure and has no impact on the probability of cercarial establishment (i.e. <inline-formula><mml:math id="IM28" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ω</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math></inline-formula>; <xref rid="M0002" ref-type="disp-formula">Eq. 2</xref>, Fig. <xref rid="pgae471-F2" ref-type="fig">2</xref>), and the “immunity model,” in which SmTAL1-IgE can reduce the probability of cercarial establishment (i.e. <inline-formula><mml:math id="IM29" xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ω</mml:mi><mml:mo>∈</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>; <xref rid="M0002" ref-type="disp-formula">Eq. 2</xref>, Fig. <xref rid="pgae471-F2" ref-type="fig">2</xref>). We employed a Bayesian approach, sampling 100,000 parameter sets from a 6D (“standard model”) or 7D (“immunity model”) Latin hypercube, assuming uniform priors for each parameter (Fig. <xref rid="pgae471-F4" ref-type="fig">4</xref>). For each parameter set, the model was run to endemic stability and the simulated age- and sex-specific epg (<xref rid="M0003" ref-type="disp-formula">Eq. 3</xref>) and SmTAL1-IgE OD (<xref rid="M0004" ref-type="disp-formula">Eq. 4</xref>) profiles extracted and matched to corresponding data (<xref rid="pgae471-B24" ref-type="bibr">24</xref>). A likelihood function was derived that accounts for the dependence among pairs of epg and SmTAL1-IgE OD observations made from the 85 individuals sampled at preintervention endemic equilibrium (Supporting Information, Likelihood function section). Parameter posterior distributions were approximated by selecting parameter sets obtaining the top 1% of log likelihoods (<xref rid="pgae471-B25" ref-type="bibr">25</xref>) (i.e. 1,000 parameter sets), with each set of unique parameter values giving rise to a distinct age- and sex-specific epg and SmTAL1-IgE profile.</p>
      </sec>
      <sec id="pgae471-s4.6">
        <title>Model comparison</title>
        <p>We calculated the DIC for each of the two model variants to compare their goodness-of-fits (<xref rid="pgae471-B60" ref-type="bibr">60</xref>). We calculated the median DIC and 95% crI for each model using 1,000 bootstrap replicates from the parameter posterior distribution, sampling without replacement. The model with the lowest DIC score was assumed to be the most parsimonious and adequate description of the data (Supporting Information, Comparing model performance section).</p>
      </sec>
      <sec id="pgae471-s4.7">
        <title>Model prediction</title>
        <p>We compared the predictive performance of the two model variants against epg and SmTAL1-IgE OD data collected at 5 weeks, 12 months, and 18 months after MDA for each of the 1,000 posterior parameter sets estimated using the preintervention data. We modeled MDA as an instantaneous reduction in worm burden in the treated proportion of the population (<xref rid="pgae471-B59" ref-type="bibr">59</xref>) with the magnitude defined by the product of the age-specific treatment coverage and praziquantel efficacy (Supporting Information, Simulating mass drug administration section). Worms killed by treatment transitioned to the dead worm state, causing treatment to transiently increase SmTAL1-IgE antibodies (Eqs. 1, 2, 4; in line with observational data (<xref rid="pgae471-B14" ref-type="bibr">14</xref>, <xref rid="pgae471-B35" ref-type="bibr">35</xref>)). We fixed the efficacy of praziquantel to 95% (<xref rid="pgae471-B29" ref-type="bibr">29</xref>) and, since the whole study cohort was treated (<xref rid="pgae471-B24" ref-type="bibr">24</xref>), set the coverage to 100% across the range of minimum and maximum ages of individuals in the study (7 and 50 years, respectively) (<xref rid="pgae471-B24" ref-type="bibr">24</xref>) and to 0% outside these ages. We quantified the predictive performance of the model variants against the data for each post-treatment time point (<xref rid="pgae471-B24" ref-type="bibr">24</xref>) by calculating an age- and sex-matched RMSE statistic (<xref rid="pgae471-B61" ref-type="bibr">61</xref>) (Supporting Information, Predictive performance section).</p>
      </sec>
      <sec id="pgae471-s4.8">
        <title>Dynamics through MDA</title>
        <p>We compared the longer-term treatment dynamics of the model variants (via median posterior dynamics and 95% crI) by simulating 10 rounds of annual treatment. Praziquantel coverage was set to 75% in SAC (5–15 years old), reflecting the WHO 2020 target coverage for this demographic group (<xref rid="pgae471-B1" ref-type="bibr">1</xref>), and 30% in adults (≥16 years old), providing a mean (population structure-weighted) coverage of 50.5% in individuals ≥5 years. These assumptions concorded with community-wide coverage surveys in Mayuge District, which estimated population coverage at 52.6% in 2013 (<xref rid="pgae471-B26" ref-type="bibr">26</xref>) and 46.5% in 2016 (<xref rid="pgae471-B27" ref-type="bibr">27</xref>), and demographic group-specific coverage at 70.7% in SAC and approximately 25% in individuals ≥20 years (<xref rid="pgae471-B27" ref-type="bibr">27</xref>).</p>
        <p>In a sub-analysis, we classified the immunity model simulations into iterations reaching the lowest 10% of epg values after ≥5 years of MDA and iterations in the remainder of the epg distribution. This allowed for the investigation of areas of parameter space associated with effective treatment and—where stubbornly low transmission was maintained—immunity-mediated resilience against elimination.</p>
      </sec>
    </sec>
  </body>
  <back>
    <ack id="ack1">
      <title>Acknowledgments</title>
      <p>This work could not be realized without the friendly co-operation of the people of Buliisa District. We would also like to acknowledge VCD technicians, especially the late J. Kemijumbi, A. Wamboko, and D. Nionsaba, and A. Babyesiza and N. Okumu for their dedication in leading the water contact observation team at Lake Albert. We deeply appreciate the field team leadership by Drs F. Kazibwe and E.M. Tukahebwa. The IgE data were generated under the leadership of Prof. D.W. Dunne; SW thanks him for the wealth of immunity data that allowed this work. Dr A. Pinot de Moira is thanked for her tireless work in generating the cercarial exposure scores. Finally, we are most grateful for the late Prof. A.E. Butterworth, Dr J.H. Ouma, Prof. B.J. Vennervald, and A.J.C. Fulford, whose inputs were extremely valuable in shaping the original study design.</p>
    </ack>
    <sec id="pgae471-s5">
      <title>Supplementary Material</title>
      <p>
        <xref ref-type="supplementary-material" rid="sup1">Supplementary material</xref> is available at <italic>PNAS Nexus</italic> online.</p>
    </sec>
    <sec id="pgae471-s6">
      <title>Funding</title>
      <p>G.C.M., R.C.O., J.P.W., M.W., and S.W. were supported through the FibroScHot project which is part of the EDCTP2 programme supported by the European Union (RIA2017NIM-1842-FibroScHot). R.C.O. was initially funded by the UK Medical Research Council UK Doctoral Training Partnership (grant MR/K50127X/1). C.W. was supported by a Sir Henry Wellcome Postdoctoral Fellowship award from Wellcome (224190/Z/21/Z). C.W. and M.-G.B. acknowledge funding from the MRC Centre for Global Infectious Disease Analysis (MR/X020258/1), funded by the UK Medical Research Council (MRC). This UK-funded award is carried out in the frame of the Global Health EDCTP3 Joint Undertaking. M.-G.B. and M.W. also acknowledge funding from the Bill &amp; Melinda Gates Foundation through the NTD Modelling Consortium (grant INV-030046).</p>
    </sec>
    <sec id="pgae471-s7">
      <title>Author Contributions</title>
      <p>Conceptualization: R.C.O., M.-G.B., M.W., and S.W.; Investigation (data collection): R.C.O., N.B.K., and S.W.; Methodology: G.C.M., R.C.O., C.W., and M.W.; Formal analysis: G.C.M. and R.C.O.; Supervision: J.P.W., M.W., and S.W.; Funding Acquisition: J.P.W., M.W., and S.W.; Writing – Original Draft Preparation: G.C.M. and M.W.; Writing – Review and Editing: all authors.</p>
    </sec>
    <sec id="pgae471-s8" sec-type="data-availability">
      <title>Data Availability</title>
      <p>The data used to fit the model in this publication have been deposited in a UK Data Service ReShare Repository. Age has been collapsed into 5-year age groups to improve participant anonymity. [dataset]* Oettle, Rebecca C and Pinot de Moira, Angela and Vennervald, Birgitte J and Dunne, David W and Kabatereine, Narcis B and Wilson, Shona (2024). <italic>Revisiting Immunity Versus Exposure in Schistosomiasis: A Mathematical Modelling Study of Delayed Concomitant Immunity, 1998–2000</italic>. [Data Collection]. Colchester, Essex: UK Data Service. 10.5255/UKDA-SN-857172. The model code is publicly available as an R package at <ext-link xmlns:xlink="http://www.w3.org/1999/xlink" ext-link-type="uri" xlink:href="https://www.github.com/gcmilne/SchistoTransmissionModel">www.github.com/gcmilne/SchistoTransmissionModel</ext-link>.</p>
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