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The authors have declared that no competing interests exist.

‡ Equal senior contribution

Understanding the underlying risk of infection by dengue virus from surveillance systems is complicated due to the complex nature of the disease. In particular, the probability of becoming severely sick is driven by serotype-specific infection histories as well as age; however, this has rarely been quantified. Island communities that have periodic outbreaks dominated by single serotypes provide an opportunity to disentangle the competing role of serotype, age and changes in surveillance systems in characterising disease risk.

We develop mathematical models to analyse 35 years of dengue surveillance (1979–2014) and seroprevalence studies from French Polynesia. We estimate the annual force of infection, serotype-specific reporting probabilities and changes in surveillance capabilities using the annual age and serotype-specific distribution of dengue.

Eight dengue epidemics occurred between 1979 and 2014, with reporting probabilities for DENV-1 primary infections increasing from 3% to 5%. The reporting probability for DENV-1 secondary infections was 3.6 times that for primary infections. We also observed heterogeneity in reporting probabilities by serotype, with DENV-3 having the highest probability of being detected. Reporting probabilities declined with age after 14 y.o. Between 1979 and 2014, the proportion never infected declined from 70% to 23% while the proportion infected at least twice increased from 4.5% to 45%. By 2014, almost half of the population had acquired heterotypic immunity. The probability of an epidemic increased sharply with the estimated fraction of susceptibles among children.

By analysing 35 years of dengue data in French Polynesia, we characterised key factors affecting the dissemination profile and reporting of dengue cases in an epidemiological context simplified by mono-serotypic circulation. Our analysis provides key estimates that can inform the study of dengue in more complex settings where the co-circulation of multiple serotypes can greatly complicate inference.

Characterising the true extent of dengue circulation and the level of population immunity is essential to assess the burden of disease, evaluate epidemic risk and organise prevention strategies against future epidemics. However, this is difficult in a context where most people who are infected by dengue virus (DENV) only have mild symptoms which may not be reported to surveillance systems. In this article, we develop a mathematical model to evaluate the fraction of unreported dengue infections from case data. The key idea is to introduce reporting probabilities that depend on the infecting serotype and the infection history of patients. These factors are known to contribute to variations in the severity of symptoms and hence the reporting probabilities, but have rarely been taken into account in model frameworks to study population immunity from the case data. Using the developed model, we study long-term dengue virus immunity in French Polynesia.

Dengue, which has four serotypes (DENV-1, DENV-2, DENV-3, DENV-4), is the most widespread mosquito-borne virus infection of humans. The vectors that transmit the dengue virus (DENV) are

Many studies have shown evidence of higher incidence rates of severe dengue in secondary infected individuals [

Here we aim to characterise how the history of dengue infection of a patient (i.e., when they were infected and by which serotype) may affect disease severity, considering over 30 years of surveillance as well as serological studies from French Polynesia, which consists of 119 islands, located in the middle of the Pacific Ocean [

(_{10}P with the population size P. The colours of the circles represent the number of reported cases. (

The islands constituting French Polynesia are grouped into five administrative subdivisions: Windward, Leeward, Marquesas, Austral, and Tuamotu-Gambier (

In this work, we focus on the most inhabited subdivision, Windward, that includes three populated islands including Tahiti that alone accounts for 70% of the entire population of French Polynesia. We use the data from January 1979 to October 2014 and ignore data for children less than 1 year old to exclude the effect of maternal passive immunity [

Seroprevalence of antibodies against DENV was studied during May-June 2014 and during September-November 2015 in French Polynesia [

Our model is composed of the following three parts: a model of dengue circulation in the population, a model of the surveillance system, and a model of serological surveys. We detail these models one by one and combine them in a likelihood function at the end.

The Force of Infection (FOI) characterises the transmission intensity of DENV and is defined as the per-capita rate at which susceptible individuals are infected. We denote _{i}(_{j} (_{j} and _{j}, respectively. Since epidemics are mono-serotypic [_{i}(_{i}(

Using _{i}(

Similarly, we denote by _{i}(

See Section A in

Denote _{j} for primary and secondary infections, respectively. These are computed as
_{j} is given as

Finally, we consider the effect of cross protection [_{i}(_{i}(_{i′}(_{i}(_{j} by DENV-

Not all infected individuals are reported to the surveillance system. Some may be asymptomatic and not seek medical attention. Others may consult a medical doctor and yet not be recommended for a dengue test. Reporting of infected individuals can depend on

the age of the individual (infants, adolescents, or adults)

the time when the individual is infected

the infection history of the individual (primary infection or secondary infection)

the infecting serotype (DENV-1, DENV-2, DENV-3, DENV-4)

In order to take into account these different factors, we define the reporting probability

The predicted number of reported cases of age _{j} is modelled using negative binomial distributions with mean
^{2}/

Our model of the surveillance system is based on [

For the _{m}, _{m}(_{sero,m}(_{1} = 2014.42 and _{2} = 2015.75). From the reconstructed immune profile of the population, the seroprevalence of antibodies against any dengue serotypes _{m},

We assume that the probability that the participants have the antibodies follows a Binomial distribution with the number of trial _{m}(_{m},

We denote by _{j}. The likelihood function _{rep}, _{sero}|

We conducted analyses to understand the sensitivity of our model to the cross-immunity assumptions and to time varying reporting. In the Supporting Information (

In order to evaluate the accuracy of our Bayesian inference to infer the model parameters, we first generate synthetic data by using the model described above. That is, for a fixed parameter set (the force of infection _{i}(_{sero,m}(_{sero,m}(_{i}(

The spatial distribution of the reported cases is reported in

Under the assumption that the surveillance system improves over time, we estimate that, in French Polynesia, the probability of reporting a primary infection by DENV-1 increased from 3.13% in 1979 (95%-CI 2.09%-4.39%) to 5.10% in 2014 (95%-CI 3.86%-7.15%) (

Next, we compare the observed and expected number of reported cases per year in

Using the estimated parameters, we reconstruct the immunity profile of the population during the surveillance period and plot it in

In

In

We next estimate the probability of occurrence of an epidemic as a function of the susceptible fraction by using logistic regression (See Section B in

In the Supporting Information (Fig C in

Our model is robust against constraints we introduce concerning how the reporting probability changes in time as shown in the Supporting Information (Figs D, E, and F in

We evaluate our inferential framework. In

Using the model described in the main text, we generate synthetic data for given model parameters. Using this synthetic data, we then infer the model parameters using the Bayesian inference. The original parameters are plotted as crosses (true), while the inferred results are plotted as lines or circles with 95%-CIs (predictions). In (A), the parameter k for the negative binomial distribution is shown. In (B), the relative strength of the reporting probabilities of secondary infections (DENV-1) compared with primary infections (DENV-1) φ(1,2)/φ(1,1) is shown. In (C), the reporting probabilities relative to serotype 1, φ(i,1)/φ(1,1) for primary infections and φ(i,2)/φ(1,2) for secondary infections, are shown. Here i = 1,2,3,4 corresponds to DENV-i. In (D), the reporting probability of primary infections by DENV-1 T(t) is shown as a function of time. In (E), the age-factor of the reporting probability A(a) is shown. In (F), the FOI is shown as a function of time.

In this article, we studied how the reporting probabilities of dengue infections depend on serotype, age, and the infection history of patients. To this goal, we generalised the sero-catalytic model with a reporting structure [

The results also show that for DENV-1, the reporting probability for secondary infections is about three times higher than for primary infections. We estimated reporting probabilities for different serotypes and showed that DENV-3 infections were the most likely to be reported both for primary and secondary infections. In French Polynesia data, the DENV-3 epidemic and endemic transmission (1990–1996) happened just after the DENV-1 epidemic (1989). This sequence of events, DENV-1 (or DENV-2) followed by DENV-3, showed the highest severity in the Cuban epidemics [

The epidemic of DENV-1 that took place in 2001 was followed by endemic circulation of DENV-1 for 5 years [

In our model, we assumed that only a single serotype circulates at a given time. This assumption is valid before the 2013/2014 DENV outbreak [

Systematic deviations are observed for the seropositive fraction between the model estimation and the data. One possible reason for these deviations is from residual cross reactivity between DENV and Zika virus occurring during the final years of our surveillance period, which our model does not take into account. Another explanation could be the lack of case data before 1979. Our model infers the susceptible fraction by gradually reducing it from 1 starting from the year where the targeted population are born. Since the case data are not available before 1979, this indicates that the susceptible fraction of the adults older than 35 years old, who were born before 1979, is less accurate than those younger than 35 years old. Indeed, deviations in

We assumed that the force of infection is constant over a year (or constant over each epidemic period), as our focus is on annual force of infection. It would be interesting in the future to consider a compartmental model where the force of infection can vary during an epidemic period.

The comparative study between our models with and without cross immunity suggested that the reporting probabilities for secondary infections tend to be underestimated without adding cross immunity to the model. On the other hand, we observed a small tendency that the lower the variations in the reporting probability during the surveillance period, the larger the relative risk for secondary infections compared with primary infections. These results imply a potential trade-off between modelling cross-immunity and modelling the variations of reporting probability over time.

Finally, the currently available licensed dengue vaccine, Dengvaxia, developed by Sanofi Pasteur, is recommended to be used on individuals who have already been infected by one of DENV serotypes [

By analysing 35 years of dengue data in French Polynesia, we characterised key factors affecting the dissemination profile and reporting of dengue cases in an epidemiological context simplified by mono-serotypic circulation. Our analysis provides key estimates that can inform the study of dengue in more complex settings where the co-circulation of multiple serotypes can greatly complicate inference.

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