Postpandemic immunity debt of common cold in England: an interrupted time series study Char Leung 1,2, Li Su3 Affiliation: 1Leicester Medical School, University of Leicester, Leicester, UK. 2Department of Population Health Sciences, University of Leicester, Leicester, UK. 3MRC Biostatistics Unit, School of Clinical Medicine, University of Cambridge, Cambridge, UK. ORCID: 0000-0002-4215-4513, Address correspondence to: Dr Char Leung, George Davies Centre, University of Leicester, 15 Lancaster Road, LE1 7HA, UK. Email: ltc.leung@leicester.ac.uk. Keywords: Common cold; England; Immunity gap; Immunity debt. Funding: None Word count: 1200 Conflicts of interest/Competing interests: None Availability of data and material: Data available upon reasonable request Authors' contributions: CL: study design, literature review, data collection, data analysis, manuscript drafting; LS: data analysis, interpretation of data Ethics approval: Publicly available data, not required in the UK Acknowledgement: For the purpose of open access, the author has applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission. This study was supported by the National Institute for Health and Care Research (NIHR) Applied Research Collaboration East Midlands (ARC EM) and Leicester NIHR Biomedical Research Centre (BRC). The views expressed are those of the author(s) and not necessarily those of the NIHR or the Department of Health and Social Care. Abstract This study investigates immunity debt in five common cold viruses (adenovirus, parainfluenza virus, human metapneumovirus, rhinovirus, and respiratory syncytial virus) in England using weekly positivity rate data from UKHSA. An interrupted time series analysis assessed post-NPI effects with sensitivity analyses conducted to account for potential structural changes in viral dynamics across years. Results indicate significant immunity debt for adenovirus, parainfluenza virus, and respiratory syncytial virus. These findings highlight the need for public health preparedness post-NPI removal, particularly for vulnerable groups, and emphasise challenges in predicting immunity debt for viruses with high serotype diversity. Background has gained attention, describing increased susceptibility to infections following reduced pathogen exposure, often due to non-pharmaceutical interventions (NPIs) like lockdowns [1]. Observations such as the out-of-season resurgence of respiratory syncytial virus in 2020 [2] and evidence of immunity debt in influenza [3] highlight its significance. This study investigates immunity debt in England, focusing on five common cold viruses rhinovirus, respiratory syncytial virus, adenovirus, parainfluenza virus, and human metapneumovirus selected for their prominence in respiratory infections and robust weekly during 2020 2022, which disrupted viral transmission, make it an ideal setting to examine this phenomenon. These airborne pathogens, major contributors to the common cold, exemplify immunity debt as reduced exposure during NPIs likely heightened susceptibility, particularly among the elderly and immunocompromised, who face severe outcomes from such infections. Understanding these dynamics is critical for preparing for future NPIs and protecting high-risk groups in settings like care homes, where limited pathogen exposure can amplify vulnerability. By analysing immunity debt with an ARMA model, this research offers insights to refine public health strategies and mitigate NPI-related consequences. Methods The proportion of positive samples for respiratory viral infections under surveillance (i.e. positivity rate) in England was analysed using weekly data obtained from the Weekly National Flu Reports published by the UK Health Security Agency (UKHSA; https://www.gov.uk/government/collections/weekly-national-flu-reports) covering the period from 6th October 2016 to 9th January 2025. Unlike case counts, the positivity rate remains stable over time and is less influenced by variations in testing practices. The Weekly National Flu reports source data from the Respiratory DataMart System (RDMS), established in 2009 to monitor influenza A (H1N1)pdm09 and subsequently expanded to include other major respiratory viruses, including SARS-CoV-2, influenza, rhinovirus (RV), parainfluenza (PIV), adenovirus (AdV), human metapneumovirus (hMPV), and respiratory syncytial virus (RSV). Samples collected by clinicians in primary care settings such as nasopharyngeal aspirates, tracheal secretions, and nasal and throat swabs were sent to 17 sentinel laboratories across -time polymerase chain reaction testing. These laboratories include UKHSA-operated facilities, hospital-based labs, and NHS partner laboratories. Data uploaded into the RDMS were de-duplicated before analysis. Weekly time series data of AdV, PIV, hMPV, RV, and RSV positivity rates during the study period were used, totalling 432 observations for each virus. The positivity rates were used because they remain stable over time and is less influenced by changes in testing practices. The modelling approach followed that of Leung et al. [3]. For each virus, the data were fitted to an autoregressive moving-average (ARMA) model with seasonal adjustments applied via a sine function. The model included (1) a binary variable to account for the impact of non- pharmaceutical interventions (NPIs) during the period from 26th March 2020 (lockdown introduction) to 24th February 2022 (removal of all legal restrictions). The date of removal of all legal restrictions was chosen because, prior to the complete removal of all legal restrictions, some were relaxed, such as stay-at-home orders, leading to increased social interactions and a subsequent rise in positivity rates. This increase in social interaction could potentially distort our hypothesis on immunity debt. (2) slope-type autoregressive binary variables were included to capture the impact of immunity debt within six months following the removal of NPIs. A six- month period was hypothesised for immunity debt to detect increased susceptibility post-NPIs while minimising seasonal confounding, which dominates beyond 12 months in the ARMA model. The F-test was used to test whether these binary variables together have a positive impact on the dynamics. The order of the ARMA model was determined using the Akaike Information Criterion, and the Ljung-Box test was applied to assess autocorrelation in residuals. A sensitivity analysis was conducted by incorporating additional binary variables for calendar years from 2016 to 2024 to account for differences in dynamics across different years. The F- test was used to assess the joint effects of the calendar years. All computations were conducted in R Version 4.3.1. A p-value smaller than 0.05 was deemed statistically significant. Results The dynamics of the positivity rates for the five viruses are illustrated in Figure 1, where the light grey shaded area represents the period of NPI implementation, and the dark grey shaded area marks the hypothesised period of immunity debt being tested. The ARMA order (AR order, MA order) for AdV, PIV, hMPV, RV, and RSV was (6,5), (3,11), (13,3), (7,16), and (13,2), respectively. Estimated coefficients are shown in the Supplementary Materials. The p-values from the joint F-tests of the binary variables representing the positive impact of immunity debt were 0.003, 0.027, 0.518, 0.918, and 0.020 for AdV, PIV, hMPV, RV, and RSV, respectively, indicating a statistically significant association between NPI removal and and increase in the positivity rate of the respiratory viruses. In the sensitivity analyses, the p-values of the global F-tests for structural differences in dynamics across different years were 0.917, >0.999, 0.436, 0.626, and 0.838 for AdV, PIV, hMPV, RV, and RSV, respectively. This indicates no evidence of significant structural differences in dynamics across years. The p-values for the global F-tests of the binary variables representing immunity debt in the sensitivity models were 0.002, 0.047, 0.603, 0.780, and 0.037 for AdV, PIV, hMPV, RV, and RSV, respectively. These findings align with those observed in the main analysis. Discussion This study suggested the existence of immunity debt for AdV, PIV, and RSV in England during the immediate 6 months following the removal of NPIs. The results are robust as demonstrated in the sensitivity analyses where structural differences in the dynamics among years were assumed. While we lack sufficient evidence to establish the impact of immunity debt on hMPV and RV, it remains possible that its effects emerged before the full removal of legal restrictions. Consequently, these effects may not be fully captured by the binary variables used in this analysis. If this is the case, the impact of immunity debt may have become conflated with the effects of increased social interaction following the partial lifting of restrictions, complicating the distinction between these two factors. These results suggested that public health authorities and medical practitioners should anticipate increased number of common cold cases upon the removal of large scale NPI implementation. While there is no data on the age structure of the cases, attention should be paid to elderly, children and individuals with pre-existing health conditions. Nevertheless, the results did not discourage the use of NPI. This is partly attributed to the absence of vaccine against these viruses and therefore NPI remains a useful preventive measure. Interestingly, the AR order of most of these viruses, with the exception of PIV, appears to be inversely related to their number of serotypes. Specifically, AdV, PIV, hMPV, RV, and RSV have more than 52 serotypes [4], 4 serotypes [5], 1 serotype (but two genotypes) [6], more than 100 serotypes [7], and 1 serotype (but two antigenic subgroups) [8], respectively. This inverse relationship can be attributed to the fact that a higher number of serotypes reduces the dominance of any single serotype in positivity rates, as different serotypes replace one another over time. Such replacement dilutes the feedback loop inherent in the time series, resulting in a lower AR order. Additionally, antibody-dependent enhancement where antibodies generated by infection with one virus enhance the host cell entry of another virus may contribute to strain coexistence and nonlinear dynamics [9], which are not well captured by linear time series models. As shown in Figure 1, viruses with fewer serotypes tend to exhibit more stable and predictable dynamics, as circulation is dominated by a limited number of serotypes, thereby reducing variability caused by serotype turnover. Consequently, predicting the impact of immunity debt for viruses with a larger number of serotypes, as well as developing effective prevention and control strategies, becomes more challenging. This complexity should not be underestimated, particularly as the emergence of additional serotypes continues to complicate these efforts. There are several limitations to consider. Firstly, asymptomatic individuals or those not seeking medical advice may not undergo testing, leading to their underrepresentation in the surveillance system. This is particularly relevant in the current context, as the common cold is typically mild and often self-diagnosed. As a result, cases included in the surveillance system tend to be from higher-risk population groups, meaning that the impact of immunity debt observed in the present study is more reflective of these groups. Secondly, while the regression model was designed to mitigate the impact of any potential rise in positivity rates due to increased social interactions, residual effects may still persist. Third, there is no data of the age and commordities of the participants that may affect our findings. Lastly, our findings may not be generalisable to countries with different NPI implementation and public health strategies. References [1] Bardsley M, Morbey RA, Hughes HE, Beck CR, Watson CH, Zhao H, et al. 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