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Abstract
Many respiratory pathogens co-circulate within human populations. Yet, how pathogen community structure shapes the dynamics of infectious diseases remains poorly understood. At the population level, investigating polymicrobial dynamics, with potential underlying competitive or cooperative interactions, is challenging, because of confounding factors such as differing seasonality. This is particularly true for endemic pathogens which typically exhibit stable periodic dynamics. Their disruption due to the implementation of non-pharmaceutical interventions during the COVID-19 pandemic thus represents a unique large-scale natural experiment that can be leveraged to provide valuable insights into the complex interplay between respiratory pathogens. Here, we focus on the population dynamics of human rhinovirus (common cold) and on the potential viral interference of influenza A virus (flu A), which is hypothesized to account for their asynchronous circulation. Using a Bayesian framework, we first show based on simulations that exogenous perturbations can be a powerful tool to disentangle the contribution of pathogen interaction from other epidemiological factors. We then apply our framework to surveillance time series from the US and Canada spanning the COVID-19 pandemic. We estimate key parameters of rhinovirus but find no conclusive support for an influence of influenza A virus at the population level.
Author summary
A wide range of respiratory viruses (influenza viruses, coronaviruses, respiratory syncytial virus, ...) circulate in the same communities and can infect the same individuals. Yet, the extent to which these pathogens interact and shape each other’s spread remains under-explored and represents an emerging frontier in public health. We focus here on the dynamics of human rhinovirus, a leading cause of the common cold, particularly among young children. Rhinovirus and influenza A virus typically peak at different times of the year, raising the possibility of some negative interactions. For viruses that peak at consistent times each year, it is however challenging to determine whether differences in their timing are due to true virus-virus interactions or simply reflect their own, independent, seasonal trends. We develop a mathematical modeling approach that leverages the disruption of these dynamics due to the COVID-19 pandemic as a large-scale natural experiment. Our work demonstrates how such epidemiological perturbations can be used to uncover interactions among co-circulating pathogens. Using multi-year surveillance incidence data from the United States and Canada, we estimate key parameters governing rhinovirus transmission and immunity, but find no substantial impact of influenza A virus.
Citation: Benhamou W, Howerton E, Park SW, Viboud C, Metcalf CJE, Grenfell BT (2026) Leveraging perturbations to infer the population dynamics of human rhinovirus and interaction of influenza A virus. PLoS Comput Biol 22(9): e1014784. https://doi.org/10.1371/journal.pcbi.1014784
Editor: Michael J. Plank, University of Canterbury, NEW ZEALAND
Received: March 23, 2026; Accepted: September 1, 2026; Published: September 11, 2026
This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.
Data Availability: Data and codes are publicly available at: https://github.com/WakinyanB/Rhinovirus_dynamics
Funding: B.T.G., C.J.E.M. and W.B. acknowledge support from Princeton Catalysis Initiative, Princeton Precision Health, and the High Meadows Environmental Institute at Princeton University. S.W.P. was supported by the New Faculty Startup Fund from Seoul National University, the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2026- 25474574), and the Global-LAMP Program of the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. RS-2023-00301976). E.H. has been funded with Federal funds from the National Cancer Institute, National Institutes of Health, under Prime Contract No. 75N91019D00024, Task Order No. 75N91023F00016. The findings and conclusions in this report are those of the authors and do not necessarily represent the official position of the National Institutes of Health or Department of Health and Human Services, nor does mention of trade names, commercial products or organizations imply endorsement by the U.S. Government. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
1 Introduction
Human rhinoviruses (RVs) are one of the most prevalent pathogens responsible for the common cold, accounting for more than 50% of upper respiratory tract infections, especially among young children [1–4]. They are are non-enveloped, positive-sense, single-stranded RNA viruses belonging to the family Picornaviridae and genus Enterovirus (EV) [1,3]. RVs are ubiquitous, circulating globally and year-round [1,3,5,6], usually with seasonal peaks in spring and fall. Transmission occurs via direct person-to-person contacts, aerosols, and fomites [7–10]. RVs are currently classified into three species (RV-A, B, and C), encompassing over 170 subtypes [1,3,11]. Importantly, cross-reactivity between subtypes appears to be weak (i.e., offering little protection against heterotypic infection), such that this wide antigenic diversity has hampered the development of antiviral treatment or vaccines [1,3,4,12]. While infections are typically mild, they may occasionally lead to more severe diseases like asthma exacerbation and chronic obstructive pulmonary disease [1,4]. Additionally, the associated global health and economic burden is substantial (albeit difficult to assess precisely [11]), costing billions of US dollars annually due to medical visits and work absenteeism [1,3].
One mystery about RV remains its potential interaction with influenza virus (IV), particularly influenza A virus (IAV). We refer here to negative heterologous virus-virus interactions (or viral interference), whereby one respiratory virus suppresses another, for example by triggering an antiviral defense or through the competition for susceptible cells [13–19]. A range of observational and experimental studies supports the existence of viral interference between RV and I(A)V at different scales, although with some conflicting findings:
- Uncertain directionality or bidirectional interaction: At the population level, RV and IAV dynamics are typically asynchronous [15,17,18,20,21] – though this could also reflect other factors such as differences in seasonality [18] –, and can also exhibit divergent spatial distribution patterns [22]. Statistical analyses in [17] found a strong negative correlation between RV and IAV monthly prevalence, even after adjusting for seasonality. Reduced likelihood of co-detection have also often been reported [15,17,18,20,23,24], but co-detection prevalence studies may be unreliable for the inference of interaction [25,26]. In [27], the authors found a mutual reduction in infection risk.
- RV affecting IAV: Epidemiological data suggested that a major RV outbreak may have delayed the 2009 IAV (H1N1pdm09) pandemic in Europe [28–30]. Similarly, [22] found a suppressing effect of RV on influenza outbreaks. At the within-host level, experimental studies showed that prior RV infection can inhibit infection with IAV [18], reduce disease mortality and enhance IAV clearance [31], or inhibit IAV replication [20].
- IAV affecting RV: Conversely, analyses of virus detection frequency in [32] suggested interference of RV infection by IV. Experimental evidence found that IAV H1N1 can inhibit RV replication, whereas RV does not inhibit subsequent IAV H1N1 infection [33]. Besides, mathematical simulations supported the idea that a transient immune-mediated refractory period induced by IAV could account for the observed decline in RV infections during peak IAV activity [17]. This asymmetric interaction is further consistent with longitudinal (individual-level) data from 2009 showing that IAV H1N1 infection reduced the subsequent risk of RV infection the following week, while RV infection did not confer a protective effect against IAV H1N1 [34–36].
In summary, although various studies support its existence, RV-IAV interaction still largely remains unclear, in particular whether it might be mutual or more asymmetric. This viral interference has mostly been experimentally associated to interferons (IFNs) [18,31,33]; although IFN signaling is part of the host innate (non-specific) immunity, asymmetric interactions may still arise due to differences in response timing and/or magnitude, as well as in the sensitivity of each virus. Besides, ecological (as opposed to immunological) mechanisms [37], such as changes in contact rates after a primary infection, may also play a role. In this work, we adopt a phenomenological approach to examine the potential influence of IAV on RV population dynamics.
The recent implementation of non-pharmaceutical interventions (NPIs) during the coronavirus disease 2019 (COVID-19) pandemic significantly disrupted the dynamics of respiratory pathogens [38–42]. The COVID-19 pandemic is particularly relevant to our analysis for two reasons. First, in most locations, RV continued to circulate at appreciable levels. At the onset of the pandemic, RV infections declined in many countries across the globe during periods of strict NPIs, though to a lesser extent than other respiratory pathogens [39–41,43–51], and rebounded sharply following NPI relaxation [39,43,44,48,49,52]. IAV, on the other hand, remained largely undetected during periods of strict NPIs as well as periods of gradual NPI relaxation, finally rebounding in 2022 or later. Interactions between respiratory pathogens such as RV and IAV were often cited to have potentially played a role during the COVID-19 pandemic, e.g., [32,39,44]. One question would thus be: is the persistence of RV during this period enhanced by the absence of IAV? Second, endemic pathogens typically exhibit stable endemic cycles, complicating the possibility of teasing apart the contributions of different transmission drivers. Extrinsic shocks – such as sudden changes in the recruitment rate of susceptibles (e.g., baby booms) or vaccination campaigns – have previously been used to better understand pathogen dynamics [53,54], and NPIs represent another form of such shocks that could be leveraged opportunistically [55].
Here, we focus on the population dynamics of RV and on the potential influence of IAV. In contrast to other respiratory pathogens, population-level model fitting remains rare for RV. Using a Bayesian inferential framework, we develop a simple mathematical model to capture RV incidence dynamics, including IAV detection as an external input to test the hypothesis of IAV interference on RV dynamics. We first conduct a simulation study to validate our approach, and in particular to assess how exogenous perturbations can help to quantify the strength of interaction between endemic pathogens. We then apply our framework to historical national and regional time series data in the US and Canada. Using COVID-19 pandemic NPI perturbations, we estimate key parameters of RV and evaluate the strength of the effect of IAV.
2 Results
2.1 RV and IAV population dynamics across the US and Canada
We collected time series of weekly tests and detections for RV/EV and IAV from longstanding respiratory virus surveillance systems in the US and Canada at both the national and regional level (a map is shown in Fig A in S1 Appendix). Rapid laboratory diagnostic testing does not differentiate RVs from other EVs, though RVs are expected to account for most detections [56,57]. For brevity, we thus refer to RV/EV simply as RV. We plot longitudinal data at the national level in Fig 1 (see Figs B-C in S1 Appendix for time series at the regional level).
Top: RV (blue) and IAV (red) surveillance detections in (A) the US and (B) Canada; data have been rescaled to mitigate biases due to circulation of other respiratory pathogens and changes in testing effort (see Materials and Methods §4.1). Mean change in mobility (colored background) during the COVID-19 pandemic were computed from Google COVID-19 Community Mobility Reports [83]. See Figs B-C in S1 Appendix for time series at the regional and provincial level. Bottom: Cross-wavelet transform of IAV and RV detections in (A) the US and (B) Canada. We used the function xwt from the R package biwavelet [93] (see details in Note A in S1 Appendix). Colors indicate standardized cross-wavelet power, with 95% significance region outlined by a contour. Arrows pointing left (resp. right) suggest IAV and RV detections are out-of-phase (resp. in phase) and arrows pointing down (resp. up) suggest IAV detections lead (resp. lag) RV detections (with vertical arrows indicating a phase difference of (quarter cycle)). Here, results confirm the asynchronous circulation of IAV and RV at the national scale: we find that detections are predominantly out-of-phase at subannual periods ( weeks), as well as an anti-phase behavior with RV lagging at more annual periods ( weeks). This pattern is transiently disrupted during the COVID-19 period (2021-2022), but is restored in the subsequent years. See Figs F-G in S1 Appendix for plots at the regional and provincial level.
Across these locations, RV exhibit biannual outbreaks before the pandemic, with a peak in fall and a (usually smaller) peak in spring. Pre-pandemic IAV dynamics are annual with a peak (of varying magnitude) in winter. We used cross-wavelet transform analyses to confirm and complement the initial visualization and description of the time series. Results in Fig 1 confirm that national IAV and RV detections are predominantly out-of-phase at subannual periods ( weeks), except in 2016 when the IAV outbreak seems delayed; and indicate an anti-phase behavior with RV lagging at more annual periods ( weeks). We recover similar patterns at the regional level, though with some variability across locations (Figs F-G in S1 Appendix).
Importantly, IAV effectively disappeared following NPI implementation at the onset of the COVID-19 pandemic. In the US, this period was followed by a small rebound late 2021/early 2022 and a bigger rebound in the following season, similar to pre-pandemic levels) (Fig 1A and Fig B in S1 Appendix). IAV rebounds occurred later in Canada, between mid-2022 and early 2024 across regions of Canada (Fig 1B and Fig C in S1 Appendix). Conversely, while RV detections dropped at the very beginning of the COVID-19 pandemic, they continued to circulate during the pandemic at approximately similar levels (Fig 1 and Figs B-C in S1 Appendix).
In the following, we use a seasonally-forced Susceptible-Infectious-Recovered-Susceptible (SIRS) model to fit RV incidence time series (see Materials and Methods §4.2 and Table 1). Briefly, the transmission rate is decomposed into three terms: (i) a periodic term consisting of weekly transmission rates that can handle any seasonal pattern within a year, similar to [58], (ii) a time-varying term that captures contact changes due to COVID-19 pandemic NPIs and (iii) a time-varying term that phenomenologically captures potential effect of viral interaction due to IAV. We use IAV incidence data as an external input (or covariate, as in [59]), which is assumed to force RV transmission by some factor . Our aim is to detect whether signatures of an interaction of IAV on RV dynamics exist at the population level. These effects could be derived from within-host viral interference mechanisms (e.g., IFNs in the context of innate immunity) or ecological interaction mechanisms (e.g., changes in contact rates after a primary infection) [37,55]. While viral interaction effects can be characterized by their direction, intensity and duration, however our approach cannot easily estimate the duration of these effects. We start by using the concurrent weekly incidence of IAV, assuming the duration of interaction is short-term (on the order of days to one week consistent with, e.g., interactions mediated primarily by IFNs).
2.2 Exogenous perturbations as a powerful tool to infer pathogen-pathogen interaction
We first conducted a simulation study to assess our ability to recover model parameter values, and in particular the direction and intensity of the viral interaction of IAV on RV, . Using a two-pathogen transmission model, we first simulated epidemiological trajectories for RV and IAV (Fig H in S1 Appendix), from which we generated synthetic time series; we then fitted RV simulated data while IAV simulated data was only used as an external input. The primary confounder of the population-level effects of viral interactions is seasonality in transmission, so here we generated simulated data under three main scenarios, each consistent with the sub-annual patterns of RV epidemics. In scenario 1, RV transmission corresponds to a bimodal seasonality with no interaction (); in scenario 2, IAV negatively impacts RV () but we adjust the seasonal forcing so that the overall transmission rate matches scenario 1 (“masked interaction”); in scenario 3, RV seasonality corresponds to a classic unimodal, sinusoidal forcing, and the two annual RV outbreaks arise from the interference by IAV. We plot the different seasonal transmission profiles in Fig 2A and 2B. Simulated data include a pre-pandemic period of 6 years and a (post-)pandemic of 4 years, aligned with our empirical surveillance data. See more details on model structure and fitting in Materials and Methods §4.2-4.3 and simulation experiment in Materials and Methods §4.4.
We conducted a simulation study to validate our ability to estimate model parameters. For simplicity, we only display here the results obtained with the main simulations of each scenario. (A) RV seasonal transmission (solid blue lines) and effect of the interference due to IAV when the latter is at its endemic attractor (i.e., no perturbation, dashed blue lines). Importantly, RV and IAV are independent in scenario 1 (no interaction) and this seasonal forcing is mimicked in scenario 2 in the presence of IAV. (B) IAV seasonal transmission (same across scenarios). (C-E) Posterior distributions of the estimated viral interaction term. (F-H) Estimated profiles of RV basic reproduction number (median values (lines) and 95% CrIs (shaded envelopes)), reflecting seasonal forcing terms. Black dashed lines represent true values used in the simulations. See Table A in S1 Appendix for parameter values and see Figs I, J and K in S1 Appendix for the full results.
Simulation study results showed that including exogenous perturbations can enable us to infer pathogen-pathogen interaction. In scenario 1 (no interaction), the model consistently inferred that RV dynamics is independent of IAV (Fig 2C and top panel of Fig I in S1 Appendix). In scenario 2 (“masked interaction”), the model failed to detect the presence of viral interaction when using the pre-pandemic data alone, but including pandemic perturbations substantially improved the inference, enabling both the viral interaction and the seasonal forcing terms to be estimated correctly (Fig 2D and 2G and top panel of Fig J in S1 Appendix). In scenario 3 (simple seasonality with interaction), model fit using pre-pandemic data correctly detected a negative interaction but did not accurately estimate its magnitude, which was underestimated with a wide CrI (Fig 2E and 2H and top panel of Fig K in S1 Appendix). Here, viral interaction was only partially captured by other parameters (in particular the seasonal forcing), likely because the reduction in the force of infection coincident with the increase in IAV was more abrupt than in scenario 2. However, fitting the model with and without interaction (i.e., estimating or fixing , respectively) yielded similar fits to the pre-pandemic data (top panel of Fig K in S1 Appendix). Including the (post-)pandemic period resulted in much better estimates of both the viral interaction effect and seasonal forcing. Across scenarios, restricting the inference to the pre-pandemic period resulted in wider CrIs for all model parameters, with the exception of initial conditions (Fig 2 and top panels of Figs I, J and K in S1 Appendix); in particular, the mean duration of immune protection, , and the under-reporting factor , were more difficult to estimate precisely and were usually positively correlated. Our results were robust to observation noise (Fig L in S1 Appendix). As a sensitivity analysis, we also varied the chosen values of some key parameters of the viruses, showing that most estimates remained robust across the explored range of values (Fig M in S1 Appendix).
For each scenario, we also examined two extensions (we refer to the previous cases as the main simulations). First, we considered a six-month shift in the timing of NPIs, such that interventions implemented in winter (typically stricter) occurred in the preceding summer, leading to earlier post-pandemic rebounds of IAV. Overall, varying the timing of NPIs resulted in similar results (middle panels of Figs I, J and K in S1 Appendix). Second, we introduced a one-off exogenous perturbation in the dynamics of IAV in the pre-pandemic period (a “kick”, transferring 35% of the susceptibles to IAV to the recovered compartment, e.g., due to a vaccination campaign). Here, in scenarios with viral interference (2 and 3), fitting the model to the pre-pandemic period alone yielded more accurate parameter estimates than for the main simulations, which only featured regular cycles (bottom panels of Figs I, J and K in S1 Appendix). Overall, in the absence of viral interference, the model performed consistently across all cases. In the presence of viral interference, including any form of perturbations enabled accurate estimation of the viral interaction and seasonal forcing terms. Estimation of seasonal forcing was improved in particular for weeks of high IAV circulation, which peaks around week 52, while errors remained consistently smaller during periods of low IAV circulation (trough centered around week 30) (Fig N in S1 Appendix).
In this section, we used simulations to illustrate how perturbations can be a powerful tool for estimating pathogen-pathogen interactions. This analysis indicates that COVID-19 pandemic NPIs can be used as a large-scale natural experiment for examining such interactions, which would not be not possible when available data only include endemic limit cycles. In contrast to perturbations solely affecting IAV, NPIs represent a distinct class of perturbations that, in addition to potential indirect effects mediated through IAV dynamics, also directly affects RV transmission. One major limitation of NPIs may be the unknown shape of the perturbation through time. Additional simulations showed that, when the model also had to infer this shape without constraints, it tended here to underestimate the magnitude of the interaction effect (though the estimated direction remained correct here) while overestimating seasonal transmission rates (Fig O in S1 Appendix). Constraining the shape of these perturbation seems thus essential for accurately estimating the different drivers of the force of infection. In practice, the true shape is unknown, and we used mobility data as a proxy.
2.3 Modeling of empirical surveillance data does not support an impact of IAV on RV dynamics at the population level
We then fitted our model to RV detection time series from the US and Canada, including both pre- and (post-)pandemic period. The model converged for all locations except the US HHS region 1 and the Canadian Atlantic province; examples of MCMC chains and posterior distributions are provided in Fig P in S1 Appendix. Our model captures most of the RV outbreaks (Fig 3 and Figs Q-R in S1 Appendix) – though it underestimates the 2021 fall outbreaks in several locations. Using the current incidence of IAV, the posterior distributions of – and thus of the change in transmission due to viral interaction, with negative values suggesting that IAV epidemics suppress RV activity – are either not significantly different from 0 or relatively weak in magnitude across locations (Fig 4). For example, at the national level, we obtained a median (95% CrI: ) for the US and (95% CrI: ) for Canada. A sensitivity analysis varying the prior constraint on seasonal transmission variability yielded similar results (Fig S in S1 Appendix). Model comparisons of expected log-predictive density against a null model with no viral interaction (fixing ) did not support an effect of IAV on RV dynamics in any location (Fig T in S1 Appendix). We also explored the possibility that interaction might be better captured by considering longer-lasting effects (i.e., if interaction effects would last more than 1 week), so that prior IAV incidence could also affect RV dynamics. Refitting the model using a lagged sum of IAV incidence, rather than current incidence, with a lag of 1, 3, or 5 weeks (see Materials and Methods §4.3) led to similar results (Fig 4 and Fig T in S1 Appendix). Surprisingly, viral interaction estimates tend to be more positive for Canadian locations and more negative for American locations. Whether these small differences are meaningful is unclear and otherwise difficult to explain. The different surveillance systems and the usually earlier timing of IAV rebounds in US locations seem to be the two main differences between the two countries. These results were obtained when fitting the model independently to each location. We explored how fitting the model simultaneously to all regions/provinces impacted the results, constraining to be shared across locations within a given country, and the rate of immune waning across all locations (see Note C in S1 Appendix). In this case, estimates of viral interaction remained centered around 0 for both US and Canada, with no difference in sign, but the Canadian estimate was highly uncertain (Fig U in S1 Appendix). We also considered different extensions of the main analysis, showing that our results remained robust to: (i) post-pandemic behavioral changes (Fig V in S1 Appendix), (ii) the use of total IV incidence, i.e., including influenza B virus (IBV) detections, (Fig W in S1 Appendix) and (iii) the addition of an exposed RV stage, i.e., infected but not yet infectious, (Fig X in S1 Appendix).
We independently fitted model (3)-(4) with seasonal transmission (8) (see Materials and Methods §4.2-4.3) to rescaled RV detections (black points) in (A) the US and (B) Canada. Detections were rescaled to account for changes in testing patterns. We compare here results of the model where IAV can affect the transmission of RV by estimating (yellow) or not by fixing to 0 (purple). We plot posterior median values (lines) and 95% CrIs (shaded envelopes) for: from top to bottom, (i) the proportion susceptible S/N, (ii) the proportion infected I/N, (iii) the number of detections and (iv) the effective reproduction number (the epidemic grows as soon as (black horizontal line)). Colored backgrounds indicate the pandemic period (mean change in mobility during the COVID-19 pandemic were computed from Google COVID-19 Community Mobility Reports [83]). See Figs Q-R in S1 Appendix for fitted model results at the regional/provincial level.
Posterior median values (points) and 95% CrIs (segments) of the maximum change in RV transmission due to IAV interaction. We recall that, for the purpose of model fitting, the effect of viral interaction is modeled as , where denotes the observed incidence of IAV, so that represents the maximum change in the force of infection of RV due to viral interaction (i.e., during periods of highest IAV circulation). If is positive, it means IAV facilitates RV transmission, if negative, it suppresses RV transmission, and if zero, there is no interaction. We also considered lagged sums of IAV incidence, substituting by with a maximum lag l of 1, 3 or 5 weeks (l = 0 refers to current incidence only).
We plot in Fig 5A and 5C the estimated weekly transmission rates of the more parsimonious model (i.e., without viral interaction). Both the magnitude and seasonal profile vary across locations (in particular in the US) but, as expected, a common seasonal pattern includes a drop in transmissibility around the summer (typically between week 20 and 35), followed by an increase in fall. We also plot in Fig 5B and 5D the posterior distributions of the mean duration of immune protection to RV reinfection, . Immune protection was estimated to be quite short (typically around 1–3 months), despite some variability across locations (e.g., a median of 20 weeks (95% CrI: [16.41, 24.43]) in the HHS region 9). Posteriors of the remaining parameters are displayed in Fig Y in S1 Appendix and summarized in Table C in S1 Appendix. Note that estimates of the under-reporting factor cannot be interpreted quantitatively as can also compensate for the arbitrary rescaling of detections. Using our estimates, the median of the basic reproduction number was estimated between for the US (Fig 5A) and for Canada (Fig 5C), which is consistent with existing literature suggesting a range between 1.2 and 2.7 [60–63]. Averaged over the entire seasonal profile, mean values range from 1.16 to 2.04 for the United States and from 1.24 to 1.42 for Canada. The effective reproduction number ranges between approximately 0.8 and 1.5 in classic seasons, following the biannual pattern of RV (primary peak in fall and a smaller secondary peak in spring). During the first implementation of NPIs at the onset of the COVID-19 pandemic (March-May 2020), shows its biggest decline, but followed by a rapid return to historical levels (Fig 3 and Figs Z-AA in S1 Appendix).
We plot results obtained with the model with no viral interaction (). First column: estimated profiles of RV weekly transmission rate (left y axis) and basic reproduction number (right y axis) in (A) the US and (C) Canada; the lines indicate the median values and the envelopes represent and 95% CrIs of the inferred posterior distributions. Second column: posterior distributions of the mean duration of immune protection in (B) the US and (D) Canada; vertical black lines represent 2.5%, 50% (median) and 97.5% quantiles, respectively. Hat symbols denote estimated values. CA = Canada (national), BC = British Columbia, ON=Ontario, PR = Prairies.
3 Discussion
Here, we investigated the population dynamics of human RVs and aimed to characterize the presence of potential viral interaction due to IAV. Historical time series from the US and Canada (at both the national and regional level) confirmed the asynchronous dynamics of RV and IAV, as well as their contrasting responses to COVID-19 pandemic perturbation, during which IAV disappeared while RV continued to circulate. In line with other studies, we hypothesized that IAV-RV viral interference may (partly) explain these epidemiological patterns; and we leveraged pandemic perturbations as a large-scale natural experiment to put this hypothesis to the test.
We modeled RV population dynamics using a seasonally-forced SIRS model, using IAV incidence as an external input. Note that this does not imply that RV cannot also influence IAV dynamic. We first conducted a simulation study to evaluate our ability to accurately estimate model parameters in various settings, and especially viral interaction due to IAV. Simulation results demonstrated that including exogenous perturbations such as COVID-19 pandemic NPIs can be key to accurately estimate endemic pathogen interaction. Using only stationary oscillatory dynamics hinders the identifiability of different epidemiological factors on the force of infection, such as seasonality and virus-virus interaction, but perturbations can provide additional information to disentangle these different drivers. The utility of such perturbations may depend on characteristics such as their intensity, duration, and timing. In contrast to perturbations that only affect the dynamics of one infectious disease (e.g., vaccination, antigenic shift), NPIs affect the transmission of both diseases. The shape of these perturbations is usually unknown, which can hamper the estimation process in the absence of additional constraints. Here, we relied on Google mobility data, although this approach still remains imperfect. We then fitted our phenomenological model to historical RV time series, including both pre- and (post-)pandemic periods. Results did not support an effect of IAV on RV dynamics at the population level in any location, although this does not completely rule out the possibility of an interaction. For example, available data may lack sufficient statistical power to detect more subtle effects – in particular, RV dynamics are extremely fast due to rapid loss of immunity, IAV is likely to have (if any) only a short-lived interaction, and IAV circulation is low most of the year. Even strong individual-level effects can be masked at the population level [59]. Viral interactions may also affect disease severity without altering susceptibility or transmission. For example, IAV infection could reduce the probability of hospitalization or severe disease following RV infection, an effect that we would not be able to see in our surveillance data which include many mild clinical infections. Moreover, RV seasonal forcing may be driven by other factors for which we have little data, such as a combination of climatic effects and human behavior (which is expected to vary geographically). Additionally, waning immunity can also drives sub-annual epidemics [64,65]. More broadly, many “unknowns” may be contributing to RV dynamics, but resolving one or a few of them could substantially improve inference of interaction effects.
The mechanisms behind RV resilience to pandemic perturbations still remain unclear, and our results did not support the hypothesis that RV benefited from the absence of IAV during this period. Nevertheless, other hypotheses remain. For example, the efficacy of NPIs against RV transmission may be limited. For instance, face masks seem less effective in blocking RV particles ( 30 nm), smaller than IV or SARS-CoV-2 particles, [66] – although they are unlikely to be entirely ineffective, since RV circulation sometimes increased once mask mandates had been lifted [48]. As a non-enveloped virus, RV may also exhibit greater environmental stability and be less affected by hand washing and surface disinfection, thereby sustaining different transmission routes such as via fomites [32,40,44,46,49]. Yet, the concomitant decrease in the circulation of other non-enveloped viruses may challenge this hypothesis [49]. Besides, numerous studies underscore that children are a key driver of the spread of RVs [45,51,67,68], especially in schools and daycare centers with subsequent transmissions to adults within households. Since children are less likely to adhere to hygiene measures, their role in maintaining RV circulation during NPIs is a plausible explanation [44]. This is supported by the increase in RV frequency among young children reported in Japan during the pandemic [32], and also consistent with the sharp increase in RV infections after schools reopened [39,43]. RV resurgence was first observed among children in Germany [49], but RV cases began rising even before daycare centers and schools reopened in Finland [41]. Last, our estimates of the duration of immune protection support that infection only confers short-lived protection against reinfection, likely reflecting the co-circulation of many serotypes with limited cross-immunity. Specific neutralizing antibodies typically have little cross-reactivity, recognizing only one serotype [4,69,70]. While T-cell immunogenicity exists, with some degree of subtype cross-reactivity [12,69], cellular immunity responses also remain poorly understood. Crucially, shorter immune protection implies a faster replenishment of the susceptible population, consistent with the better resilience of RV to pandemic perturbations [42].
Our work is closely related to [55], which estimated viral interference between two closely related pneumoviruses, respiratory syncytial virus (RSV) and human metapneumovirus (hMPV), by comparing two hypotheses: (i) the two pathogens are independent with different seasonal forcing or (ii) same seasonal forcing but RSV has a negative effect on hMPV. In this work, a two-pathogen model was first fitted to the pre-pandemic period, while post-pandemic rebounds were then used as an out-of-sample test. We could not make the assumption here that RV and IAV are subject to the same seasonal forcing, and had to use a flexible parameterization for RV seasonal transmission, which may make the other components of the force of infection more difficult to estimate. Besides, while using IAV data as an external input also directly introduces observation noise in RV transmission compared to fitting a two-pathogen model – where IAV prevalence could be reconstructed from latent variables –, surveillance time series may contain richer variability and signal capturing the complex dynamics of IAV (including antigenic variation, subtype interference, external seeding, pandemic perturbation) that could be lost if not adequately captured by the model. Our framework preserves this empirical variability, which is noisier (though we smoothed IAV data) but may also be more informative for inferring the potential effect of IAV on RV dynamics. Although our approach is statistically less powerful, it is also more general, and can be more easily extendable to other pathogens. More broadly, viral interference is fundamentally a within-host interaction mechanism that can subsequently shape population-level pathogen transmission dynamics. While a detailed multi-pathogen model (as in, e.g., [17]), may provide a more satisfying mechanistic description of immunity and co-circulation patterns, it would be difficult to fit to incidence data alone without additional information and assumptions. In contrast, our approach is intentionally phenomenological. Our model is intentionally simple and does not aim to explicitly resolve within-host interactions; instead, it provides an effective description of observed incidence dynamics and allows us to probe for epidemiological signatures consistent with altered transmission patterns that integrate both within-host viral interference mechanisms and ecological mechanisms of interactions [37].
There are several limitations to our work, and parameter estimates must therefore be interpreted with care. First, we assumed a homogeneously mixing population. However, children are likely to be a natural reservoir for RV infections, and a key driver of transmission to adults [51,67,68] – infections are usually symptomatic among children but asymptomatic among adults [68]. Heterogeneity in mixing patterns may have profound consequences on pathogen transmission, but accounting for it would also require age-stratified data, alongside contact matrices. Age was not available for the surveillance data used in this study. It may however contribute to residual variation that is not explicitly captured by the model, and the use of aggregated data (despite the advantage of larger sample sizes) may obscure some important age-dependent patterns. Addressing how age-specific differences affect our results would require an extension of the current modeling framework and would therefore constitute a natural future direction to evaluate how this could improve model fit and parameter estimation. It would also be interesting to investigate if RV dynamical patterns could be better captured by school and daycare center openings and closings, which were also disrupted during the pandemic period. Reductions in RV infections in the summer and in the winter may reflect changes in children mixing due to school holidays.
Second, we modeled RVs as a single-strain pathogen, neglecting the different RV species and their wide antigenic diversity. This is important because our estimates therefore represent some averages across multiple strains – whereas quantities such as the basic reproduction number should in theory be defined as the strain level. Strain composition may differ between the US and Canada (and potentially also between regions/provinces), such that the observed differences in estimates might potentially partly reflect differences in strain composition. Understanding the complex RV population-level dynamics and immunity landscape would greatly benefit from a better characterization of this underlying diversity. This underscores the need for improved and continuous measurement of RV epidemiology and genomics, notably through sequencing and seroprevalence studies. Co-circulation of numerous subtypes of the three species is common [71,72], with subtype prevalence and age patterns appearing to remain stable over decades [73]. RV phylogenetic analyses are scarce. Still, in [6,74], RV infections are characterized by many localized subtype-specific ‘mini-epidemics’, with multiple co-circulating RV subtypes and changes over time within a social structure (e.g., school, hospital); [75,76] also reported a high genotype diversity throughout the year (especially RV-A and C), with significant seasonal variation in [76] (tropical climate), and pandemic levels comparable to pre-pandemic in [75]. Other studies observed a shift in dominance before and during the pandemic, e.g., [72].
Third, we focused on the potential viral interference of IAV on RV, but we did not examine the opposite direction which is also supported by several studies (e.g., [18,20,22,31]). The resilience of RV during the COVID-19 pandemic has notably been hypothesized to have contributed to a prolonged suppression of IV circulation [44] and, more generally, shaped the spread of IV [11]. Here, fitting the model to IAV poorly captured the data, indicating that further work is needed to better tailor the model to IAV biology (e.g., antigenic changes, seeding and subtype interference). Revisiting data of the 2009 flu A pandemic in Europe – where the interference of RV on IAV was initially hypothesized [28–30] – may provide further insights into these potential interactions. RV may also interact with other viruses (including SARS-CoV-2) [11,19,27,77–79].
We estimated key parameters of RV population dynamics, yet substantial gaps remain in our understanding of the underlying drivers, underscoring the need for better continuous epidemiological and genomic surveillance. More broadly, understanding pathogen-pathogen interactions is an important emerging frontier in public health, with implications for the prediction and anticipation of future outbreaks. Most studies, including this work, have focused on pairwise pathogen interactions, whereas real-world pathogen ecology may be shaped by more complex polymicrobial/multistrain interaction networks. Identifying when, where and how pathogen-pathogen interactions influence infectious disease dynamics will thus be essential in the future.
4 Materials and methods
4.1 Data
We collected time series of weekly detections for RV/EV and IAV in the US (Fig B in S1 Appendix) and Canada (Fig C in S1 Appendix). US data were collected from the Centers for Disease Control and Prevention (CDC), as reported through the National Respiratory and Enteric Virus Surveillance System (NREVSS). Data were downloaded at both the national and regional level (10 Health and Human Services (HHS) regions, Fig A in S1 Appendix) and ranged from January 4, 2014 to June 28, 2025 (regional level) or September 6, 2025 (national level). Canadian time series were reconstructed from publicly available reports provided by the Respiratory Virus Detection Surveillance System (RVDSS, Public Health Agency of Canada [80]). We analyzed data at the national and regional level – 4 provinces/regions: Atlantic, British Columbia, Ontario and Prairies (which includes Alberta, Manitoba and Saskatchewan) (Fig A in S1 Appendix) – from August 31, 2013 to June 8, 2024. NREVSS and RVDSS are decade-long laboratory-based surveillance systems that monitor respiratory virus activity across the US and Canada, respectively. These systems involve a network of participating laboratories across each country testing patients with respiratory symptoms in outpatient and inpatient settings. Testing is conducted by PCR; in recent years the use of multiplex PCR has become more frequent. We note that rapid laboratory diagnostic testing does not differentiate RVs from other EVs (and, a fortiori, does not distinguish RV species and subtypes), and results are typically reported as a combined RV/EV category. While there is no strong evidence for viral interference between IAV and other EVs, RVs are expected to account for most detections, in line with [56,57]. We therefore considered RV/EV patterns to be primarily driven by RV circulation and, for brevity, we refer to RV/EV simply as RV.
Positivity rates (i.e., proportion of detections among tests performed) can yield a biased measure of pathogen activity levels depending on the co-circulation of other respiratory pathogens [58,81]. We thus calculated an incidence proxy to mitigate this bias and to account for changes in testing effort over time. Following an approach similar to [42,55,82], we rescaled incidence data by multiplying raw cases by a weekly testing factor equal to the average number of tests (over the entire studied period) divided by the one-year moving average of the number of tests (see testing patterns in Fig D for RV and Fig E for IAV in S1 Appendix).
We also used Google COVID-19 Community Mobility Reports [83] as a proxy to capture reductions in transmission due to COVID-19 pandemic NPIs. Google mobility Reports provide percentage changes in the number of visitors relative to baseline days (median value from the 5‑week period from January 3 to February 6, 2020). As in [55,58], we defined a weekly mobility metric, c, by averaging mobility data across four categories (grocery & pharmacy, retail & recreation, transit stations and workplaces), computing a population-weighted average across states or provinces. Google mobility data were only reported between February 15, 2020 and October 15, 2022 and we assumed c = 0 (i.e., same as baseline) outside of this range (we relaxed this assumption in Fig V in S1 Appendix). We approximated population sizes using 2021 census data for Canada [84] and 2020 census data for USA [85].
4.2 Transmission model
We modeled RV epidemiological dynamics using a seasonally-forced SIRS model (details of notation are provided in Table 1). We assumed a homogeneously mixed population in which susceptible hosts (S) become infected and infectious (I) at a per capita rate (force of infection, where t denotes the current time). Infected hosts then enter the recovered state (R) at a per capita rate . Infection provides full immunity against reinfection but immunity naturally wanes at a per capita rate after recovery (in the following we denote the mean duration of immune protection, i.e., the mean sojourn time in R). Last, we define as the per capita host birth and death rate, such that the population size S(t) + I(t) + R(t) = N remains constant over time. These epidemiological trajectories can be written as the following system of ordinary differential equations (ODEs):
(1)where the current incidence is computed by tracking the number of new infections . As with NPIs, potential effect of IAV is assumed to affect susceptibility or transmissibility, modeled phenomenologically as a scalar effect on the transmission term. The force of infection is then given by:
(2)where is the seasonal transmission rate, , the strength of the effect of NPIs (assuming this effect scales linearly with the changes in contacts/visitors, c(t), due to control measures), and where captures the strength and direction of the effect of IAV (assuming this effect scales linearly with IAV prevalence, ).
For the purpose of model fitting, we use in practice the efficient discretization scheme described in [86]:
(3), and represents the density of individuals leaving compartment S, I and R, respectively, between time t and :
(4)where is the probability of leaving a given compartment when r is the sum of rates out of this compartment in the ODE model. Consequently, the corresponding mean sojourn time is given by , which, taking the limit as , yields the sojourn time in the corresponding ODE, 1/r. Besides, the incidence (i.e., number of new cases per time step) now corresponds to the term:
(5)Last, we determine the effective reproduction number (i.e., the expected number of secondary infections by a single infectious individual), as well as the basic reproduction number (defined in an otherwise wholly susceptible population), of the discrete model (3). Multiplying the incidence by the mean number of time steps an individual stays in the the infected compartment, , and linearizing around I[t] = 0 yields:
(6)(we drop the potential effects of NPIs and viral interaction); the case at is a removable singularity. Note that converges towards when .
4.3 Bayesian inference
Using a Bayesian framework, we fitted the model (3)-(4) to our RV detection proxy C[t]. Because C[t] is a positive, continuous variable, we relied on a log-Normal likelihood:
(7)where is the incidence given in equation (5), accounts for under-reporting and is the residual standard deviation. The log-Normal distribution implies multiplicative observation noise. Poisson and negative binomial likelihoods are also commonly used in similar epidemiological settings, but require discrete case counts.
To estimate the seasonal transmission rate , we used 52 weekly transmission rates (with , the kth week of the year), modeled as a cyclical random-walk on the log scale:
(8)with , some independent step increments (centered by their arithmetic mean to enforce cyclicity), whose magnitude is scaled by , and where is a reference transmission rate (by construction, ).
IAV incidence was directly input from surveillance data, similarly to [59]. Specifically, we substituted the unknown IAV prevalence in the viral interaction term by the observed weekly IAV incidence, , which was assumed to be a reasonable proxy as IAV infectious period is also of the order of one week. Values were slightly smoothed using a geometric three-week moving average to reduce the influence of observation noise. We then scaled the time series between 0 and 1 by dividing by its global maximum (across all seasons of the study period) to enforce a lower bound of -1 for , ensuring that the force of infection is always positive while preserving any relative differences across seasons such as epidemic size. When fitting the model to real data, we also considered a lagged sum of IAV incidence instead of current incidence, substituting by with a lag l of 1, 3 or 5 weeks. This approach assumes a more sustained effect, where individuals infected during the past l weeks remain protected, and is intended to approximate varying durations of potential immune protection or reduced susceptibility. Interaction mechanisms mediated by interferon responses (typically resolve within days to a week) are more consistent with short-term effects (lags 0 or 1), whereas ecological mechanisms could potentially last longer.
We fitted models with a weekly time step ( week) using a Hamiltonian Monte Carlo algorithm (no-U-turn sampler) implemented in Stan [87] and its R interface rstan [88]. RV infections are typically associated with an infectious period between 1 or 2 weeks [3,62,89,90], so we assumed infected individuals to recover at rate , that is a mean infectious period of week (around 8 days). We estimated the rate of immune waning because of lack of information, noting that elapsed time between two infections of the same individual is likely to be relatively short due to the wide antigenic diversity of RVs and the low level of cross-immunity [4,69]. We also fixed the mortality rate, assuming . Let be the vector of parameters to estimate and its estimator. Using the seasonal transmission rate (8), we have ; priors can be found in Table B in S1 Appendix. For each estimation process, we independently ran 4 MCMC chains of 4,000 iterations (including a burn-in period of 2,000 iterations). We assessed the convergence of posterior distributions by the absence of warnings from Stan, including no divergent transitions, sufficient maximum tree depth, Gelman-Rubin statistics (R-hat) below 1.05 and effective sample size (ESS) above 400 (number of chains) for each parameter.
4.4 Simulation study
We conducted a simulation study to validate our approach, and in particular our ability to quantify pathogen-pathogen interaction. Simulated data were generated by extending the ODE model (1) to account for two pathogens (see Note B in S1 Appendix). ODEs were solved using the deSolve package [91] in the R programming language [92]. We considered 3 main scenarios:
- Scenario 1 (bimodal seasonality with no interaction): RV seasonal forcing peaks twice a year, and transmission is independent from IAV ();
- Scenario 2 (“masked interaction”): Building upon the previous scenario, IAV now negatively impacts RV (), but we adjust RV seasonal forcing so that its force of infection mimics scenario 1 when IAV is at its endemic attractor (i.e., in the absence of perturbation);
- Scenario 3 (unimodal seasonality with negative interaction): RV seasonality follows a simple sinusoidal forcing (one peak per year), and the two annual RV outbreaks arise from the interference by IAV ().
Seasonal transmission profiles are shown in Fig 2A and 2B and parameter values are listed in Table A in S1 Appendix; virus parameters are based on existing literature and/or to reproduce the observed epidemiological characteristics of RV and IAV (see caption for more details).
In the last two scenarios, the maximum change in transmission due to viral interference lies around %. Starting from initial conditions on the endemic attractor of both pathogens, we simulated the model for 10 years, corresponding to a 6-year pre-pandemic period (endemic limit cycles) followed by a 4-year (post-)pandemic period. We used Google mobility data from Canada to model more realistically the pandemic period. We also considered two extensions: (i) one with a 6-month shift in the timing of NPIs (e.g., NPIs in winter now occurs in the summer), and (ii) one where we introduced a one-off exogenous perturbation in IAV dynamics (a “kick”, moving 35% of the susceptibles to IAV to the recovered compartment) at t = 1.5 year during the pre-pandemic period. All simulations are presented in Fig H in S1 Appendix.
Simulated pathogen detections were generated using a log-Normal distribution with a residual standard deviation of 0.25 on the log scale. We fitted the model (3) to RV detections using the seasonal transmission (8) and compared the results with those obtained when the model was only fitted to the pre-pandemic period. Additionally, we also contrasted these fits with a null model with no interaction (fixing ). To account for model discretization, the recovery rate was fixed as , where is the recovery rate used in the continuous ODE model. Likewise, we did not directly compare the true and estimated rates of immune waning , but the mean durations of immune protection : (continuous ODE model) vs. (discretized version).
Supporting information
S1 Appendix. Supplementary notes (Notes A to C), figures (Figs Z to AA) and tables (Tables A to C) referenced in the main text.
https://doi.org/10.1371/journal.pcbi.1014784.s001
(PDF)
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