Characterizing the interactions between influenza and respiratory syncytial viruses and their implications for epidemic control

Domain: earth_science
Published: 2024-11-20
Editorial outcome: accept

Abstract
Pathogen-pathogen interactions represent a critical but little-understood feature of infectious disease dynamics. In particular, experimental evidence suggests that influenza virus and respiratory syncytial virus (RSV) compete with each other, such that infection with one confers temporary protection against the other. However, such interactions are challenging to study using common epidemiologic methods. Here, we use a mathematical modeling approach, in conjunction with detailed surveillance data from Hong Kong and Canada, to infer the strength and duration of the interaction between influenza and RSV. Based on our estimates, we further utilize our model to evaluate the potential conflicting effects of live attenuated influenza vaccines (LAIV) on RSV burden. We find evidence of a moderate to strong, negative, bidirectional interaction, such that infection with either virus yields 40-100% protection against infection with the other for one to five months. Assuming that LAIV reduces RSV susceptibility in a similar manner, we predict that the impact of such a vaccine at the population level would likely depend greatly on underlying viral circulation patterns. More broadly, we highlight the utility of mathematical models as a tool to characterize pathogen-pathogen interactions.

Introduction
Although pathogens are often studied in isolation, mounting evidence suggests that interactions, in which one pathogen impacts the risk of infection or disease due to another pathogen, are a common and important feature governing their epidemiological dynamics1–3. These interactions can be characterized according to their major components: they may be positive (i.e., infection with one pathogen facilitates or exacerbates infection with another) or negative (i.e., infection with one pathogen inhibits or mitigates infection with another); may have a strong or a weak effect; may be short-lived or long-lasting; may be symmetric (i.e., both pathogens impact each other in the same way) or asymmetric; and may operate according to a range of biological mechanisms, including changes to the immune response or to host-cell gene expression4.

The mechanisms underlying these interactions often occur at the individual level, but the existence of an interaction can lead to significant, and sometimes unexpected, consequences at the population level5,6. For example, if infection with one pathogen increases susceptibility to another, as demonstrated for influenza viruses and the Streptococcus pneumoniae bacterium7,8, public health measures designed to reduce infection with the first pathogen may also succeed in combating the cocirculating pathogen. Conversely, if infection with one pathogen reduces susceptibility to another, then measures to control this pathogen may lead to unintentional increases in the burden of the other. For example, seasonal influenza vaccination has been associated with an increased risk of both pandemic influenza H1N1 2009 (H1N1pdm09)9 and non-influenza respiratory virus infection10, a finding that could be due to the existence of negative interactions. For this reason, it is critical that interactions between pathogens be understood and taken into account when developing public health policy.

One such interaction of public health relevance may exist between influenza and respiratory syncytial viruses (RSV), both of which represent significant public health threats, particularly in young children and the elderly11. Experimental studies have found that ferrets and mice infected with influenza were less likely to be infected with RSV upon challenge12,13, and that infection with either of the two viruses can reduce morbidity upon subsequent infection with the other12,14,15. In human populations, this interaction is tentatively supported by epidemiologic observations revealing delays in RSV epidemics occurring during and immediately after the 2009 influenza pandemic16,17. Evidence to date is far from conclusive; studies on the severity of influenza-RSV coinfections, in particular, often come to conflicting results, with some studies suggesting that the interaction instead leads to increased disease severity18,19. A better understanding of this interaction may play a key role in informing public health practice. In the presence of a negative interaction, preventing influenza cases through widespread vaccination may lead to an unintentional increase in RSV burden. However, if vaccination with a live attenuated influenza vaccine (LAIV) induces an immune response similar to natural infection, widespread use of this vaccine, in particular, could help prevent RSV transmission. Understanding which of these conflicting effects is likely to dominate will help medical and public health practitioners alike better prepare for the RSV season.

Epidemiologic evidence alone is insufficient to confirm the existence of this interaction. Observable metrics such as phase differences (i.e., the difference in timing between two outbreaks) and the prevalence of coinfections are prone to mischaracterizing both the strength and direction of interactions6,20. The applicability of studies in animal models to human populations is also unclear. Mathematical modeling approaches offer a promising alternative to standard epidemiologic study designs because they are able to capture the complex and nonlinear dynamics inherent to infectious disease transmission21, and to explicitly account for the mechanisms underlying an interaction5,20,22. By confronting these models with data, it is possible to understand the role these properties may play in generating the outbreak patterns we observe in reality. Mathematical models are also well-suited to exploring the impacts of prospective public health control measures, as they can be used to generate counterfactual scenarios5. Despite this potential, to our knowledge, only one modeling study has attempted to infer the characteristics of the interaction between influenza and RSV, and found that data were equally consistent with either a moderate negative interaction or no interaction23.

Here, we fit a mathematical model of influenza and RSV cocirculation to multiple seasons of data from two locations, Hong Kong and Canada, in order to infer the strength and duration of the interaction between RSV and different (sub)types of influenza at the individual level. Additionally, we use our model to assess the potential impact of widespread LAIV use on the burden of RSV. We find evidence that infection with influenza or RSV moderately or strongly reduces susceptibility to the other virus, and that this reduction may persist for up to several months. Furthermore, we demonstrate that this interaction may, in some cases, play a substantial role at the population level. Finally, we show that the impact of LAIV on RSV burden is likely to be highly dependent on the circulation patterns of both viruses.

Results
Influenza and RSV epidemic patterns are consistent from year to year
We analyzed weekly data on (1) the number and rate of samples testing positive for influenza and RSV and (2) the proportion of influenza-like illness (ILI) per all-cause consultation in Hong Kong and Canada over several years. Because testing was primarily performed on samples taken from hospitalized and emergency department patients, these data are likely biased toward the most severe cases. To achieve a more representative picture of influenza and RSV circulation among the population as a whole, we incorporated ILI data as well. Despite Hong Kong’s subtropical climate, epidemics of influenza A(H1N1) and B typically followed a clear seasonal pattern, with a single peak occurring during the winter or spring of each year (Fig. 1a and Supplementary Fig. 2). Thus, we summed cases of influenza A(H1N1) and B for our main analyses in Hong Kong. Due to the presence of multi-peak epidemics, which are challenging to describe using simple models, we did not consider interactions with influenza A(H3N2) (Supplementary Fig. 2), although supplementary analyses attempt to account for its circulation (see Supplementary Text). In Canada, where outbreaks of all influenza subtypes display a clear seasonal pattern, we summed all influenza cases for our analyses (Fig. 1b).

In Hong Kong, epidemics of RSV displayed weaker seasonality than those of influenza, with less definite peaks and more persistent circulation throughout the year. This was not the case in Canada, where outbreaks of both viruses exhibited similar durations and noisiness. There was considerable overlap of influenza and RSV activity during most outbreaks across all locations, although peak activity for influenza almost always preceded peak activity for RSV (median difference = 20 weeks in Hong Kong, 8.5 weeks in Canada). We observed no clear correlation between time series of influenza and RSV positivity rates (p=0.08, Kendall’s τ=−0.067, 95% confidence interval −0.14–0.008) in Hong Kong, and a moderate positive correlation in Canada (p<1e-10, Kendall’s τ=0.62, 95% confidence interval=0.57–0.66). However, as discussed in the Introduction, such correlations alone are uninformative about the underlying interaction between the two viruses. The total percentage of samples testing positive for each virus was higher in Canada than in Hong Kong. Across both locations, season-to-season attack rates were more variable for influenza than for RSV (Supplementary Table 1).

Peak ILI activity often coincided with influenza and RSV activity, although the ILI data were typically noisier (Fig. 1c). This is likely due to ILI being a nonspecific, symptomatic measure that can be caused by a wide array of pathogens.

There exists a negative, bidirectional interaction between influenza and RSV, with a duration of up to several months
In order to characterize the strength and duration of the interaction between influenza and RSV, we fit a deterministic, compartmental model of influenza and RSV cocirculation (Fig. 2) to the data described above. We modeled the interaction effect as a decrease in the susceptibility to infection with one virus that occurs during infection with the other virus and that persists for some time after recovery. We fit the model to all available seasons for a given location simultaneously, such that parameters describing the interaction effect were constrained to take the same value in all seasons, whereas several season-specific parameters were allowed to vary. Confidence intervals were obtained using a parametric bootstrap24. A description of all model parameters can be found in Table 1, and full model equations can be found in Supplementary Equation (1). All model fitting was conducted using a maximum likelihood approach. More details on how models were fit can be found in the Methods and in the Supplementary Text.

Among those currently or recently infected with influenza, we found evidence of a reduction in susceptibility to RSV by almost 100% in Hong Kong (θ λ1=0, 95% confidence interval=0–0.0003), and by 39% in Canada (θ λ1=0.61, 95% confidence interval=0.51–0.62). The inferred duration of this reduction was roughly 100 days (95% confidence interval=96–112 days) in Hong Kong and roughly 75 days (95% confidence interval=32–144 days) in Canada (Table 1). We find comparable estimates for the strength of the effect of RSV on susceptibility to influenza (θ λ2=0, 95% confidence interval=0–0.13 in Hong Kong; θ λ2=0, 95% confidence interval=0–0.013 in Canada). However, the duration of this effect was considerably shorter than that of the effect of influenza on RSV (36 days, 95% confidence interval=36–44 days in Hong Kong; 20 days, 95% confidence interval=19–22 days in Canada).

To assess the role that these interactions play at the population level, we simulated epidemics at the maximum likelihood estimate (MLE) in the absence of an interaction effect. We predicted that RSV epidemics would be, on average, 27% larger (range across seasons: 7 to 40%) in Hong Kong and 5% larger (range: 0 to 11%) in Canada if influenza had no effect on RSV susceptibility. Meanwhile, attack rates of influenza would be, on average, 26% larger (range: 9 to 38%) in Hong Kong and 31% larger (range: 21 to 45%) in Canada if RSV had no impact on influenza susceptibility (Supplementary Fig. 12). Overall, our results suggest that the negative interaction between influenza and RSV can act to noticeably limit the yearly attack rates of both viruses, although this is dependent on the circulation patterns of both viruses.

Both temperature and absolute humidity modulate the dynamics of influenza and RSV
Optimal model fit data from Hong Kong was achieved when both temperature and absolute humidity were included in the model (Supplementary Table 5, tested for significance using a likelihood-ratio test), suggesting that temperature and absolute humidity both modulate the transmission of influenza and RSV. Specifically, our results suggest that transmission rates of both influenza and RSV are negatively influenced by temperature when controlling for absolute humidity, and positively influenced by absolute humidity when controlling for temperature (Table 1). The impact of temperature appears to be stronger for influenza than for RSV, while the impact of absolute humidity is similar for both viruses. The overall extent of seasonal forcing over time for both viruses is shown in Supplementary Fig. 8. Because of the large geographic range over which data from Canada were collected, we did not explicitly incorporate climate forcing in the model when fitting to data from Canada.

Inferred reproductive numbers and immune fractions are similar across locations but highly variable between seasons
In addition to the parameters discussed above, we also fit several season-specific parameters, including the effective reproductive numbers (R i1 for influenza and R i2 for RSV, where i indicates the season) and the proportion of the population immune to influenza (R 10 + R 120) and RSV (R 20 + R 120) at the beginning of each season (where R 10 indicates the proportion of the population immune to influenza alone, R 20 to RSV alone, and R 120 to both viruses) (Table 1 and Supplementary Fig. 3). The season-specific MLEs of the effective reproductive numbers for influenza ranged from 1.3 to 1.7 in Hong Kong, and from 1.3 to 1.6 in Canada. Estimates for RSV ranged from 1.2 to 2.0 in Hong Kong, and from 1.8 to 1.9 in Canada.

We find that immunity to influenza and RSV is highly dependent on the season. Specifically, the season-specific percentage of the population immune to influenza at the beginning of a season ranged from 43 to 91% in Hong Kong, and from 39 to 83% in Canada. Values inferred for RSV were similarly variable but tended to be lower in magnitude, ranging from 15 to 56% of the model population in Hong Kong, and from 21 to 44% in Canada.

The best-fitting models achieve high-quality fit to data on interacting pathogens
The predicted case counts simulated from the fitted model at the MLE are highly correlated with the observed data (Fig. 3 and Supplementary Fig. 9), indicating that the fit model is capable of accurately reproducing observed epidemic patterns. The quality of the model fit is comparable across viruses and locations, with the exception of RSV in Hong Kong, where model fit quality is substantially lower (Fig. 3b). This could be due to the weaker seasonality of these data (Fig. 1a and Supplementary Table 1), which can be more difficult for simple models like the one used here to capture. When comparing model fit to that of a sine wave fit to all data from a given location, our transmission model still fits substantially better except in the case of RSV in Canada, where our model fits similarly to the sine wave (Supplementary Table 3). Furthermore, we find that simulations at the MLE are generally able to accurately reproduce the peak timing, peak case counts, and overall attack rates observed each season (Supplementary Table 4). Collectively, these results support the utility of mathematical models as tools for describing the characteristics of pathogen–pathogen interactions.

Sensitivity analyses demonstrate the robustness of the results
As described in the Methods below, we conducted multiple rounds of model fitting in order to improve our chances of achieving convergence to the MLE. To further ensure convergence, we calculated profile likelihoods25 for θ λ1 for both locations. The profile likelihoods peaked at or near the MLEs (Supplementary Fig. 10), demonstrating that our model-fitting approach was indeed able to reach the true MLE.

Because transmission patterns of both influenza and RSV are dependent on age26–28, it is possible that an age-structured model would improve the estimation of interaction characteristics. We therefore conducted a sensitivity analysis in order to evaluate whether our model, which assumes homogeneous mixing, was capable of accurately inferring interaction parameters from data derived from an age-structured population. Briefly, we generated synthetic data for all seasons at the MLE for Hong Kong using an age-structured model, and fit our homogeneous mixing model to these data (see Supplementary Text). Fitted values of all shared parameters agreed closely with the values used to generate the data, suggesting that our model is capable of achieving the goals outlined in this work.

Influenza vaccination may increase the burden of RSV, although this effect is highly dependent on underlying patterns of influenza and RSV circulation
There is a wealth of evidence suggesting that some vaccines, especially live vaccines, can lead to temporary, nonspecific protection against non-target pathogens, likely through upregulation of the innate immune system29,30. Although the potential for LAIV to offer such cross-protection has not been widely assessed, one study demonstrated that LAIV was able to reduce RSV replication in mice31, and several studies have shown upregulation of the innate immune system after vaccination with LAIV30. If LAIV can indeed offer protection against RSV, we might expect widespread use of LAIV to reduce the population-level burden of RSV. On the other hand, given the negative interaction between influenza and RSV, a reduced burden of influenza due to widespread LAIV use could lead to inadvertent increases in the burden of RSV.

In order to assess which of these competing effects is expected to dominate during realistic epidemics, we simulated the effect of LAIV administration, assuming imperfect or “leaky” immunity32, at several timepoints and coverage levels on RSV attack rates. Model equations including LAIV vaccination can be found in Supplementary Equation (2), and the model schematic in Supplementary Fig. 13. We modeled two scenarios: a “subtropical” scenario, where parameter values were set to their MLEs as estimated from the Hong Kong data, and a “temperate” scenario, where parameter values were set to their MLEs as estimated from the Canada data. The strength and duration of the interaction effect were set to the values obtained from Hong Kong for both scenarios. This was done to remove these parameters as potential confounders of the relationship between the underlying circulation patterns of both viruses and the impact of the vaccine on RSV burden, although we also conducted a sensitivity analysis using the interaction parameters obtained from Canada. We ran our analysis for two vaccines: one with a strong effect on RSV susceptibility (as found in Hong Kong), and one with a more moderate effect on RSV susceptibility (as found in Canada).

In both the temperate and subtropical scenarios, we found that early vaccination with LAIV typically led to increases in RSV attack rates, although this effect was, on average, weaker in the temperate scenario (Fig. 4 and Supplementary Fig. 14). The increase in RSV burden was most pronounced at vaccine coverage levels of 25-30% in the temperate scenario (Fig. 4a, c) and at coverage levels of 70% and above in the subtropical scenario (Fig. 4b, d). Reductions in RSV attack rates were only consistently observed if LAIV was delayed for several weeks, and if coverage levels were relatively high. In the case of a vaccine with a more moderate impact on RSV susceptibility (Fig. 4c, d), increases in RSV burden were typically larger and reductions smaller, although this pattern did not always hold in the subtropical scenario. Similar results were observed when the interaction parameters were instead set to those fit in Canada (Supplementary Fig. 15), and results were broadly consistent across a range of sensitivity analyses in which the strength and duration of the vaccine effect were varied (Supplementary Fig. 16). However, we note that the impact of LAIV on RSV burden was highly dependent on the timing and intensity of the underlying influenza and RSV outbreaks. In particular, when RSV outbreaks peaked before influenza outbreaks, and when RSV outbreaks were large relative to influenza outbreaks, LAIV more consistently led to decreases in RSV burden (Supplementary Fig. 14).

Methods
Respiratory infection data
Hong Kong. Weekly data on influenza and RSV circulation in Hong Kong from 2014 through 2019 were obtained from the Centre for Health Protection of the Government of the Hong Kong Special Administrative Region69. These data consisted of the number of samples testing positive for influenza and for RSV, as well as the total number of samples tested (Fig. 1a and Supplementary Fig. 1a). Influenza virus detections were broken down by type (A or B) and by subtype (for influenza A viruses). Samples were obtained primarily from public hospitals, although some were also taken from out-patient clinics70,71. Typically, samples were taken from those patients for whom a specific diagnosis would be useful in informing treatment. All samples were tested for both influenza and RSV, and all testing from February 10, 2014, was done using molecular testing rather than viral culture41.

We also obtained data on the weekly proportion of all consultations that were due to influenza-like illness (ILI), defined as fever with cough or sore throat70, within a sentinel surveillance network of public out-patient clinics from the same source72 (Fig. 1c, d).

We then separated the data into seasons, such that seasons began in week 46 (mid-November) and continued through week 45 of the following year. This cutoff was chosen as earlier cutoffs often occurred mid-RSV epidemic, while later cutoffs were prone to occurring during influenza epidemics. We were, therefore, left with six seasons of data (2013–14 through 2018–19) for both viruses in Hong Kong. Although data were not available for 2013, and therefore for the first seven weeks of the 2013–14 season, we retained this season in our dataset to maximize the number of seasons available for analysis. Rather than modeling each influenza (sub)type separately, we summed weekly cases of influenzas A(H1N1) and B. Because epidemics of influenza A(H3N2) in Hong Kong often display multiple peaks per year, we did not consider influenza A(H3N2) here. This allowed us to avoid explicitly modeling loss of immunity to influenza over time, which would needlessly complicate the model and potentially compromise the fitting process.

Canada. Weekly data on the number of cases of and tests for influenza and RSV in Canada from 2010 through 2014 were obtained from FluWatch, the national influenza surveillance system run by the Public Health Agency of Canada (PHAC)73 (Fig. 1b and Supplementary Fig. 1b). As in Hong Kong, influenza viruses were categorized by type and subtype, and the majority of tests were conducted on samples taken from emergency departments and hospital inpatients, with some taken from higher-risk outpatients73. Again, samples were typically taken when a diagnosis could potentially inform treatment. Unlike in Hong Kong, not all samples were tested for both viruses. Additionally, we obtained data on the weekly population-weighted proportion of consultations with primary care providers that were due to ILI (Fig. 1d), defined as fever and cough plus sore throat, muscle or joint pain, or fatigue73, also from FluWatch.

In Canada, we chose a seasonal cutoff at week 35 (early September), consistent with the cutoff used by FluWatch. This left us with four seasons of data (2010–11 through 2013–14) in Canada. Again, instead of modeling each influenza (sub)type separately, we summed across all influenza A and B viruses to obtain the total weekly number of influenza cases detected.

Transmission model
We represent the transmission of influenza and RSV throughout the model population using a deterministic, compartmental SITRxSITR model, in which compartments indicate the infection status of individuals according to both viruses (e.g., X SI represents the number of people susceptible to influenza and infected with RSV). This results in a total of sixteen compartments (Fig. 2). The interaction effect is modeled by reducing the force of infection of one virus among those currently (I) or recently (T) infected with the other virus (i.e., the interaction operates by reducing susceptibility to infection). Both the strength (i.e., the extent of this reduction) and duration (i.e., the amount of time spent in compartment T) of the interaction are allowed to vary according to whether an individual is initially infected with influenza or with RSV (i.e., the interaction is allowed to be asymmetric). This model is comparable to the one initially developed by ref. 20.

Because we model each yearly epidemic separately, we assume no within-season waning immunity. This assumption is in line with estimates of the duration of immunity for both influenza and RSV. Immunity to influenza is consistently estimated to last for multiple years74,75. While estimates for RSV are less certain, past modeling work has suggested that immunity persists for at least one year39,53. Furthermore, our assumption is consistent with other RSV modeling work, which also does not account for the within-season waning of immunity23,76.

Average infectious periods were fixed at 5 days for influenza77 and 10 days for RSV37,78. The size of the model population is taken to be the population size of Hong Kong or Canada during each epidemic, based on data from the Census and Statistics Department of the Government of the Hong Kong Special Administrative Region79 and Statistics Canada80.

Climate forcing. Evidence suggests that climatic conditions act as important modulators of influenza and RSV transmission. Specifically, a U-shaped effect of absolute humidity on influenza transmission has been suggested, with higher transmission occurring when humidity is either low or very high40,41. The effect of temperature, meanwhile, is monotonic, such that increased transmission occurs at lower temperatures40–42. Although RSV has received less attention, existing work suggests that temperature and humidity modulate RSV transmission in a similar manner43,81.

In Hong Kong, we allow the force of infection for each virus to vary according to an exponential function of weekly average mean temperature and absolute humidity, such that:
β i (t) = β^ i e η AH i AH(t) + η temp i T(t) (1)
where η temp1 and η AH1 represent the extent to which temperature and absolute humidity, respectively, impact the transmission of influenza, and η temp2 and η AH2 represent the extent to which temperature and absolute humidity, respectively, impact the transmission of RSV; β^ 1 and β^ 2 represent the force of infection of influenza and RSV in the absence of climate forcing. Although we do not expect the effect of absolute humidity to be monotonic based on past studies40,41, we chose to model the relationship with a simple exponential function. We believe this is a reasonable simplification because (1) absolute humidity in Hong Kong is high year-round (Supplementary Fig. 3b), likely rendering the effect of low absolute humidity less important, and (2) temperature and absolute humidity are highly correlated (Supplementary Fig. 3c), such that we may expect transmissibility to increase monotonically with absolute humidity once the temperature is controlled for.

Daily temperature and absolute humidity data were obtained from the US National Centers for Environmental Information Surface Summary of the Day (GSOD) data using the R package GSODR82,83, and absolute humidity was calculated using the Clausius–Clapeyron relation84. Weekly values were taken to be the mean value of the daily temperature and absolute humidity data for each week. Finally, this was done both to convert the climate data into a dimensionless form, and to facilitate interpretation of the climate forcing parameters. Because temperature and absolute humidity are highly correlated (Pearson’s r=0.944 over the course of the study period; see Supplementary Fig. 3), we performed a sensitivity analysis to check whether including both variables improved model fit over including temperature alone. We also compared our model to one fit using a sinusoidal forcing term, rather than climate data (see below and Supplementary Table 5).

Sinusoidal forcing. Because Canada covers a large geographic area over which climatic conditions vary considerably, it is unlikely that climatic conditions averaged over the country would meaningfully modulate the force of infection of influenza and RSV. For this reason, when fitting our model to data from Canada, we instead allowed the force of infection for each virus to vary according to a sinusoidal wave, such that:
β i (t) = β^ i (1 + b i cos(2π / 52.25 * (t - φ i))) (2)
where b i represents the extent to which the strength of forcing varies over the year, φ i represents the week during which the force of infection is maximal, and β^ i represents the average force of infection; these parameter values are allowed to differ for influenza (i=1) and RSV (i=2). The division by 52.25 inside the cosine function both accounts for the fact that our data are weekly, and specifies the period (in weeks) of the sinusoidal wave.

Observation model. Due to the prevalence of mild and asymptomatic infections, many cases of influenza and RSV are never reported, and therefore do not show up in empirical datasets. To model the process by which individuals seek healthcare and are tested for specific viral infections, we draw from a binomial distribution at each time point, where the number of trials is equal to the total observed number of tests for respiratory viruses conducted that week, and the probabilities of a positive test for influenza (P 1 (t)) or RSV (P 2 (t)) at time t are:
P i (t) = min(1.0, ρ^ i (t) * H i (t) / ILI(t)) (3)
where:
ρ i (t) = ρ i (1.0 + α cos(2π / 52.25 * (t - φ i))) (4)
Here, H i (t) represents the modeled incidence of virus i at time t, and ILI(t) represents the observed number of ILI cases per all-cause consultation. Notably, while H i (t) is in terms of incidence per total population, the data, ILI(t) are instead in terms of incidence per all-cause consultation. Thus, these terms are not directly comparable. The parameter ρ^ i is a composite parameter accounting for both the rate at which individuals infected with virus i report their illness and are diagnosed with ILI, and for the scaling by Bayes’ Rule necessary to directly compare H i (t) and ILI(t)47 (see Supplementary Text for more details)47,48,85. We account for possible seasonality in reporting and in background consultation rates using a cosine function, such that the exact value of the composite reporting and scaling parameter varies over time, with its value at time t represented by ρ i (t). Thus, 1 + α represents the maximum value of ρ i (t), while φ i represents the week during which the reporting rate is maximal. We divide by 52.25 to account for the fact that our data are weekly, and to impose a period of one year on reporting seasonality. To ensure that the probability of a positive test does not exceed one, we take the minimum of one and of ρ i (t) * H i (t) / ILI(t) at each time point.

Model fitting
For model fitting, parameters are designated as either shared or season-specific (Table 1). Shared parameters (e.g., those describing interaction characteristics or climate forcing) are assumed not to vary by season, and are therefore constrained to take the same value in all seasons; season-specific parameters (e.g., the initial reproductive number or the proportion immune at the start of the season) are allowed to differ by season. By fitting the proportion of infected and immune at the beginning of each individual season, we avoid the need to explicitly account for processes such as the loss of immunity over time or complicated strain dynamics, which can in particular complicate the model fitting process for influenza. Meanwhile, constraining the shared parameters to take the same value in all seasons maximizes the amount of information available for the estimation of these parameters, which include our key parameters of interest. Models were fit to data from each location separately.

All model fitting was accomplished using a maximum likelihood approach to conduct trajectory matching. More specifically, model fitting was performed using a two-step process. In the first step, we obtained reasonable initial estimates for the season-specific parameters by fitting each season of data separately, assuming no interaction, climate forcing, or reporting seasonality. In the second step, we fit the model to all seasons of data for a given location simultaneously, with initial values of the season-specific parameters drawn from the ranges fit in the previous step. By constraining this second step to begin in a relatively good region of the parameter space, we allow for more efficient convergence to the MLE. To ensure convergence to the MLE, multiple rounds of fitting to all seasons simultaneously were performed.

We obtained 95% confidence intervals for all parameter values using parametric bootstrapping24. This method is computationally efficient, and has been shown to perform well for similar work in the past8,61,86. Specifically, we generated 500 sets of synthetic epidemics at the MLE for each location using the stochastic observation model, where each set contained a simulated epidemic for all available seasons, and fit the model to each set of synthetic epidemics. Confidence intervals were obtained by computing the highest posterior density87 of the best-fit estimates over all 500 synthetic epidemics. More specific details on the process used for model fitting and construction of the confidence intervals can be found in the Supplementary Text.

We assessed the quality of model fits by comparing the observed data to data simulated from the model at the MLE. We further confirmed convergence to the MLE by calculating the profile likelihood of θ λ1 25 (Supplementary Fig. 10).

Simulation study of vaccine impact
In order to assess the potential for vaccination with a live attenuated influenza vaccine (LAIV) to reduce the burden of RSV, we conducted a simulation study. We adapted our SITRxSITR model, described above, to allow for vaccination of individuals who were fully susceptible to influenza, RSV, or both (specifically, those in compartments X SS, X SI, X ST, X SR, X RS, or X RT) with LAIV (Supplementary Equation (2) and Supplementary Fig. 13). To account for the different outbreak dynamics observed in different regions, we ran our simulation study for two scenarios: a “subtropical” scenario, where all model parameters were set to their MLEs obtained when fitting the model to data from Hong Kong, and a “temperate” scenario, where parameters were set to their MLEs based on the data from Canada (Table 1). For consistency, we set the interaction parameters to the values obtained from Hong Kong in both scenarios; results from a sensitivity analysis instead using the values obtained from Canada can be found as Supplementary Fig. 15. Vaccination was assumed to confer either strong (θ λvacc = θ λ1 as inferred based on the Hong Kong data) or moderate (θ λvacc = θ λ1 as inferred based on the Canada data) protection against RSV; in both cases, protection against RSV due to LAIV was assumed to wane at the same rate as protection due to natural infection, again using the value obtained in Hong Kong. Additionally, vaccination conferred imperfect (“leaky”) immunity to influenza32 with a vaccine efficacy of 80%88. For simplicity, we assume that all vaccinated individuals receive the vaccine at a single instantaneous time point.

For each scenario, we simulated the total number of influenza and RSV cases over the course of each season at a range of vaccine coverage levels and timings using our deterministic model. We calculated the influence of LAIV on RSV burden for each simulation as a rate ratio:
RR = AR1 RSV / AR0 RSV (5)
where AR1 RSV represents the RSV attack rate throughout the season in a partially vaccinated population, and AR0 RSV represents the RSV attack rate in a population where no vaccination occurred. Thus, values less than one indicate that LAIV reduced the overall attack rate of RSV for the season, while values greater than one indicate that LAIV led to an increase in the attack rate of RSV. Several sensitivity analyses, where vaccine efficacy and duration were varied, were also conducted (see Supplementary Fig. 16).

Implementation
All analyses were conducted in R version 4.2.389. The model was coded and run using the package pomp90 (version 5.4), and fit using the sbplx algorithm via the package nloptr91,92 (version 2.0.3). All code can be found on GitHub93, as well as on Edmond, the Open Research Data Repository of the Max Planck Society94.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Kramer et al present an interesting modelling study assessing interactions between influenza and\nRSV infections over 5 seasons in Hong Kong. The extensive discussion particularly focusses on\npotential impact of non-specific cross protection, the authors highlighting a remarkable reduction\nin RSV susceptibility following influenza A H1N1 infection that persists for 3–4 months and a\nsimilar impact for the converse effect which lasts around 2–3 months.\nThe manuscript is well written with a detailed introduction and discussion and well thought-through\nmodelling.\nComments:\n1. As the authors note, this work is not the first to model these interactions. Waterlow et al PLoS\nComput Biol (June 2022) reported mathematical modelling based on 11 years of Vietnamese data,\nconcluding that there was a short lived (10 day) period of cross-protection. However, they\nconcluded that absence of either pathogen was not to the detriment of the other, and that\nvaccination against either pathogen is unlikely to have a major effect on the burden of disease\ncaused by the other. The important differences between this and the current study are described\non lines 313-333. The current study would be strengthened and of broader applicability if they\nwere able to access other datasets and validate predictions in other contexts.\n2. The discussion is very extensive but well written, running to almost 10 pages. Throughout the\nmanuscript there is some scope to merge some sentences and sections to improve readability\n(lines 62–65, for example). If the Editors were to ask for a reduction in word count, where would\nthe authors be prepared to compromise?\n3. While aspects of the models are mostly explained well for a non-specialist audience a concise\nsummary (or visual abstract) of the dominant parameters that drive predictions (in addition to the\nprovided table) would enhance immediate understanding for many readers.\n4. Comparisons of predictions of model with observed values over the season and seasons should\nbe included. Currently, only a comparison of predicted versus observed cases is included. Even\nwhen only considering total case numbers the models seem to show poor performance with a wide\nrange in predicting RSV case numbers. The authors comment that this may be due to the weaker\nseasonality of RSV, which raises questions over the accuracy of results presented and whether the\napproaches used are suitable for modelling epidemics that do not have simple large and seasonal\npeaks. Again, application of the model developed by the authors to other parts of the globe would\nbe of great interest.\n5. The authors excluded modelling of interactions with H3N2 on account of its multi-peak\ncomplexity. How many cases of H3N2 occurred during the study period and (assuming these would\nalso provide non-specific protection) how major might be the effect of this omission? The authors\nthemselves point this out as a limitation of (in their own words) “simple models”, can more\ncomplex models be used to assess this?\n6. The model estimates concerning the different effects of humidity and temperature on influenza\nA and B seems questionable: is this more likely a shortcoming of the models and data than a real\neffect?\n7. Why are the ranges of immunity estimates so wide (line 188)? Again, is this a case of pushing\nthe model beyond what the data can accurately inform. The range of 0% to 71% for RSV when fit\nalongside flu B is particularly notable, though other ranges are similarly wide, making it hard to\ninterpret.\n8. In the Discussion, the authors refer to several viral and bacterial pathogens that have significant\ninteractions with influenza, i.e., rhinovirus and pneumococcus. How frequent were these infections\nduring the study period, do the authors have access to such data, and might omission of other\ncommon infections in the model terms not undermine the accuracy of modelling results?\n9. The authors exclude seasons with under 2000 influenza cases, with the justification that virus-\nvirus interaction would be minimal. How was this 2000 case figure chosen, how does it compare to\nthe average number of cases and, most importantly, why can fitting not be performed for these\nbelow 2000 case seasons to provide evidence of minimal interaction during times of lower\ninfluenza?\n10. Although not mentioned in the title, the authors give prominence to the potential impact of\nLAIV in some parts of the manuscript. While this is an interesting and potentially important point\nand a nice use of the model, there appears to be no actual data on LAIV to support the argument.\nThe authors have instead simply applied a proportion of the live infection effect to model LAIV.\nThere are several unknowns surrounding this approach. We suggest that the LAIV section and the\nresulting conclusions (especially those in the Abstract) should be caveated and scaled back.", "reviewer_2": "The manuscript “Characterizing the epidemiological interactions between influenza and respiratory\nsyncytial viruses and their implications for epidemic control” describes an attempt to infer\ninteraction between flu and RSV from population level syndromic respiratory surveillance in Hong\nKong using mathematical modelling. With the arrival of a number of potential RSV prevention\nstrategies and a drive to enhance influenza vaccination coverage in the wake of the SARS-CoV-2\npandemic a better understanding on such potential interaction could prove very important to\nanticipate ecological knock-on effects.\nWhile the topic is important, I do have a number of concerns that in sum make it difficult for me to\nrecommend this work for publication. The main ones are\n- There seems not a great deal of appreciation that the type of data available for this work is really\nnot ideal to make inference on the causal relationship of flu and RSV infections and that even with\nthe best of models one needs to cautious in its interpretation. As a result, much of the discussion\nand conclusions seems over-confident as to how much this study adds to the overall evidence base\n– in particular since this work proposes a strength of interaction that by far exceeds any of the\nprevious estimates be it from time series, mouse models or others.\n- The data analysed is partly selected post-hoc. Only seasons with >2000 flu cases are included\nwhich is arbitrary and should be avoided but more importantly H3 is excluded because its seasonal\npattern could not be easily modelled. However, H3 is particularly interesting as its circulation\nseems to overlap much with that of RSV making the hypothesis of competitive exclusion difficult\nunless one proposes that H3 would behave completely different from other flu strains\n- The interaction of RSV with either influenza B or H1 are considered in isolation. Flu B and H1 in\nthe considered setting and time frame share relatively similar seasonality and thus it is little\nsurprise that both models come to similar conclusions: both flu B and H1 exert strong competitive\npressure on RSV and with this observed RSV seasonality can be well replicated in either model.\nThe logical flaw in this is that if indeed H3 does compete strongly with RSV and substantially\nreduces RSV transmission, then this will need to be accounted for in the fluB-RSV model because\notherwise the effect will be double counted.\nI do have several additional concerns, questions and comments that I have listed in no particular\norder below:\n• General:\no This modelling study uses data from Hong Kong. However there is no mention of any input from\nHong Kong on the interpretation of the data. Collaborating with local experts often helps limiting\nthe scope for misinterpretation and in this case should have also allowed for potentially useful\ninformation, eg information on how many samples were infected with both flu and RSV at the\nsame time and the age of the cases. I very much encourage the authors to consider this approach\nin the future but realise that for the current work it is too late.\no It is a very difficult project to infer individual level effects on infection from population level\nobservations on disease. So, one needs to be careful and generally sceptical in its conduct and\ninterpretation which is the basic approach for my review.\n• Introduction:\no Several studies have also suggested that RSV-flu confection enhances severity! Need to better\nbalance the reporting of the evidence here.\no Both Pfizer and GSK have announced that in phase 3 trials their candidates met the primary\nendpoints and thus while true that there is currently no vaccine licensed this will likely change in\nthe imminent future making it highly unlikely that LAIV will be trialled for RSV prevention - so the\nauthors should temper respective statement on the potential importance of LAIV for RSV\nprevention given that those gains from LAIV are largely hypothetical.\no I wouldn’t call mentioned modelling study inconclusive; it was able to exclude a large part of the\npotential parameter space and found support in the data for two potential regions of interest.\n• Results\no The clear seasonality for flu is not true for H3 so you will need to clarify that you are only talking\nabout H1 and B and that this is not true for H3.\no Before you throw everything into the model it would be interesting to see some more straight\nforward data analyses. Eg your modelling results would suggest that flu and RSV incidence are\nnegatively correlated. This may be masked by seasonality but worth a look what the data says\ndirectly\no “the effect of RSV on influenza B appears to be unidentifiable” I would re-phrase this as “no\nevidence for …”\no It is hardly a surprise that the model fit will be slightly better when an additional parameter is\nfitted. So, you will need to strengthen your argument if you want to include both temp and\nhumidity in the main model despite their strong correlation, at least a DIC would be more\nmeaningful than a straight up comparison of goodness of fit\n• Methods\no Why remove seasons with fewer than 2,000 flu cases? This seems arbitrary and also an\nunnecessary loss of available data. I would think this data should be included in the inference. Or\nat the very least I would need to see some sensitivity analysis on this.\no Similarly, one needs to be careful about excluding H3N2 because of the shape of the epidemics.\nUnless there is a clear biological reason for why interaction with or the epidemiology of H3N2\nwould be different this would seem to be epidemiological cherry picking; particularly so since H3\nconstitutes the majority of all flu cases and thus, unless a very different effect on RSV it should\nhave a large impact on RSV and the other inferences. Also H3 seems to circulate much more in the\nRSV season than the other flu variants.\no The data description should be improved. E.g. it is unclear to the reader what would trigger a\ntest for RSV and for flu in the outpatient clinics? E.g. is there mandatory testing for all ILI cases in\nthe country, is this sentinel surveillance, is the tested proportion of ILI cases dependent on the\nseason, are all samples tested for both flu and RSV, if not what determines this,…?\no This seasonal forcing function that translates mean temperature and absolute humidity into\nchanges in the FOI would be good to visualise for at least the fitted nu parameters. Also, assuming\nthat flu and RSV are driven by exactly the same weather determinants is not unreasonable but\nquite a strong assumption. In the worst case the model will need to trade off this seasonal forcing\nby artificially (?) using other parameters (like competition) to reproduce the observed difference in\nseasonality. Thus It would be good to look at the sensitivity of this assumption eg by using a\nsinusoidal curve allowing for differences in phase for the two pathogens\no It is not clear whether the cosine seasonal reporting rate is needed for HongKong; ideally this\nshould be clarified with local expertise on the the way surveillance is conducted\no In eqn 2 do you really mean cos(cos()) or is this a typo? Also in Eqn 2 is this meant to be 1.0\ntimes pi or something else? Actually, there are a couple of things here that I don’t understand. Are\npi(t) and pi - are they the same? In the para below you refer to phi in another way to the phi in\nthe equation. The 52.25 is unmotivated (scaling to weekly I guess).\no\no Why would the reproduction number vary by season? I agree that the net R will vary due to\ndifferent immunity but that is captured separately. I may be missing something here but I would\nthis that the R0 should be estimated as a joined parameter across seasons\no Is the susceptibility to infection at the start of the season estimated independently from the\nattack rate of the previous season? I could see why this may be necessary for the fitting to be\ntractable but it should be highlighted as a limitation.\no Why 99% CI’s? That’s untypical. Please provide a rationale or stick to typical reporting of 95%\no The fitting process is odd. Please elaborate why no more usual MCMC inference approach is\nused. Also, I am pretty sceptical that this method is indeed making sure that not just a local\nmaximum is captured given the complexity of a 47 dimensional parameter space. More information\nis needed on the fitting – ie how many fitting attemps did you do with how many and how different\nstarting values and did they indeed all come to the same conclusion? Also I would like to see a\nsensitivity analysis where the authors fix the interaction effect to 1, ie no effect, and then run the\notherwise same inference pipeline. Is the model still able to fit and how much worse is the MLE? I\nsee what you have done with the profile LL and Figure S8, but I think a sense check of no\ninteraction and the rest of the parameters fitted would be interesting.\no the model does not have age groups. You do some discussion around that but need to add that\nAR for flu is typically highest in School age whereas for RSV in v young kids and infants - hence\nthe overlap may be less than included in this model.\no The covid pandemic has shown that RSV seasonality is quite easily disrupted. This in turn implies\nthat any observed seasonality is to a great extent driven by the build up and loss of immunity. It\nshould be discussed how the absence of this in this model could influence results.\no I am struggling to understand the approach to incorporating the data. The authors provide a\nnumber of equations, but these are convoluted, and I am unsure whether they indeed add up to\nsomething meaningful. Particularly I am not seeing any plain English justification to why the data\non proportion of consultations that are flu/rsv is a helpful quantity. The model will use infection\nincidence and a typical approach is that modelled infection incidence should be the same as\nobserved ILI incidence times P(reported ILI | infection). The latter may be seasonal, similar to\nwhat you seem to estimate with te cosine function. Given that we have no clue what else was\ncausing GP consultations during that time period I am struggling to understand what the\nproportion of consultations that we diagnosed as ILI would add to our understanding to the flu/rsv\nepidemiology and hence why to include this in the fitting. Please expand on that.\no The proportion immunity against reinfection at the beginning of a RSV is suspiciously high given\nthat most estimates find immunity against reinfection to only last for <1y; ie most should be\nsusceptible again the next year.\n• Discussion\no The discussion of the Waterloo paper needs some balancing. I don’t think it is entirely clear\nwhich of the two approaches is the more robust one. Waterlow had info on co-infection and\nestimated separately the interaction of infection and of severity which is ignored in this work -\nwould be good to discuss this a little. I don’t think it is fair to call the assumption that everyone\nwas susceptible at the beginning of the RSV season “arbitrary” - I think only citing 37 as a counter\nargument is not a fair reflection of all available evidence. See my earlier comments re the use of\ntemperature and humidity as seasonality predictors - I think this argument for bias can really go\neither way. Finally, the reason why Waterlow assumed symmetric of interaction was that RSV\nalways preceded flu and hence the interaction in the other direction could not be independently\nassessed. Long story short: please provide a more balanced discussion of relative strength and\nweaknesses\no The authors suggest that more data from other settings is needed to make more robust\ninference. The data from the Waterlow paper is published. It would be interesting to see if the\ndifferent model s indeed come to different conclusions from the same data or whether the\ndifference is in the data. But this is probably for another paper.\no As Re = R0*(1-immune), how is it possible in this model to estimate both simultaneously from\nsyndromic surveillance data? Can you show the correlation plots for these as well please? Also, I\ndon’t quite understand why R0 should vary between seasons - can you please elaborate on this?\no I think the authors will need to temper their conclusion on the RSV influenza interaction - this\nstudy is one piece of evidence and I do not believe that it would necessarily be so robust as to\nd\ndisregard conflicting evidence.", "reviewer_3": "This is an interesting, well conceived, well written, and compelling article that examines time\nseries of epidemiological observations for evidence of interaction between influenza and respiratory\nsyncytial virus (RSV) at the scale of a whole population. This is a timely topic and the implications\nof the paper are potentially very important. In particular, the authors adduce evidence for\nimmunological interaction among these circulating pathogens with appreciable effects at the\npopulation scale. This in turn suggests that the use of live attenuated influenza vaccines may be\neffective in suppressing RSV, though this will depend on the recent past history of prevalence in\nboth pathogens. The paper explains these dependencies in some detail and thereby offers some\ninitial guidance toward the design of possible vaccination strategies and supporting surveillance\nefforts. It is therefore likely to be of broad interest in the vaccinology and public health\ncommunities, as well as for the broader public.\nAlthough the evidence for the existence of these effects, as presented, is compelling, there are\nnevertheless improvements that can be made both to clarify the presentation and to solidify the\nconclusions. I detail these in the following.\nl 88: Please say more about the “inconclusive results” of the earlier study based on data from\nVietnam. The reader naturally wonders at this point what these results were. Of course, it would\ndistract from the presentation to say too much here, but some indication of what was not\nconcluded in the earlier study is called for. See also below.\nll 104ff: It is concerning that the authors exclude A(H3N2) data from consideration. The\njustification given—that the models cannot handle multiple peaks per season—exacerbates rather\nthan assuages this concern. I miss some discussion of what aspects of the modeling approach put\nthe consideration of multiple peaks beyond its ken.\nl 106: Why is 2000 cases chosen as the threshold for including a season? What would the\nconsequences of altering this threshold be?\nl 124: Why do the authors choose to use a deterministic model? What would the consequences of\nincluding stochasticity be? To be clear, I think it would be unreasonable to re-analyze the data\nusing a stochastic model. However, the authors have sufficient experience with stochastic models\nthat they should be able to speak to the question of what the consequences of the assumption of\ndeterministic dynamics are likely to be. Perhaps this is best addressed in the Discussion section.\nll 141–151: The authors point out several parameters that are unidentifiable given the data they\nhave. It would be interesting to have some idea as to why the data are silent about these\nparameters when they are not with respect to others. For example, can the authors say something\nabout features absent in the data that would help to identify these parameters were they present?\nConversely, can we begin to understand which features in the data contribute to the identification of\nthose parameters that are identifiable?\nll 188–193: How is the observed evidence in favor of variability in start-of-season population\nimmunity to be interpreted? Is this evidence for long-lived immunity coupled with antigenic\nevolution, as we have by now come to expect? If not, is it inconsistent with this? If so, would it be\npossible and perhaps better to model this immunity dynamically instead of via extra parameters?\nMore generally, why do the authors choose to introduce start-of-season parameters instead of the\nmore usual dynamical approach in which all parameters of the model are either constants and\ninitial conditions?\nll 322–324: Similarly, in this passage, the choice to make the fraction of the population susceptible\nat the beginning of the season is presented as an alternative to Waterlow’s decision to make this a\nconstant. Of course, it is an alternative, and a more reasonable one, but it is not the only\nalternative, nor is it the most intuitive one. Why do the authors take this approach?\nOne way to address this would be to discuss the observed differences in season-specific\nparameters from one season to the next (Supp Fig 3) and to plot these against estimates of the\ntotal number of within-season infections. In other words, how does the estimate of S at the\nbeginning of a season depend on the total number of infections in the preceding season?\nll 195ff & Fig 3: The R^2 values quoted amount to a comparison of the model’s predictions relative\nto those of a model in which the cases are constant through time. It would be informative to\nsimilarly present a comparison with a more descriptive model, such as one which captures the\naverage seasonality.\nSupp Fig 6: The profile likelihoods could be solidified. More exploration is clearly needed at very\nlow values of these parameters and it may be necessary, for example, to use a logarithmic\nhorizontal scale. Also, a proper profile likelihood plot should have a vertical scale showing at most\n10 or 20 log units—at least if the Wilks theorem applies—since one log unit of resolution is then\nmeaningful. Finally, the variability in the estimates for the Influenza B-RSV interaction cast doubt\non the identification of the MLE.\nMinor remarks\nl 48: I believe “host cell” should be hyphenated here.\nl 50: It would be better not to begin two successive paragraphs with the same word.\nl 76ff: As written, this sentence is awkward. I suggest recasting as “It is, as usual, unclear whether\nand how results from studies in animal models are applicable to human populations. Moreover,\nseemingly intuitive study designs, …”\nl 78: What is meant by “phase differences”? Is this meant to describe differences in the timing of\nepidemic peaks between different infections? As it stands, this is unclear.\nl 81: It is unclear what is meant by the “large number of components” needed to characterize\ninteractions. Please clarify.\nll 82–83: Mathematical models are useful not only because they can express complex and\nnonlinear dynamics and account for various mechanisms, but because they establish logical\nlinkages between these things and observable data.\nl 137: The point estimate is reported to 3 significant figures, but the uncertainty does not support\nthis. Perhaps a formulation like “…reduction in susceptibility persists for roughly 100 days (point\nestimate 111 d, 95% CI 96–127 d)…” would be better. There are other instances of similarly\noverprecise statements.\nl 148: Given that the duration of potential effect of RSV on Influenza B is not identifiable, it is not\nsurprising that the magnitude is similarly unidentified. Indeed, it would be strange if it were\notherwise, no?\nll 165, 171: “[C]ontribute significantly” is not the right language in this context. It would be better\nto say that temperature and absolute humidity both “modulate transmission”. Similarly, in l 171,\ntemperature and humidity cannot be spoken of as “drivers” of transmission, but rather as\n“modulators”.\nl 180–181: The mathematical symbols have not yet been defined and use unfamiliar notation. In\nparticular, notation such as R20\nis annoyingly idiosyncratic. It would be preferable to write $R_{20}$.\nMake sure all mathematical symbols are defined in the text as they are first used (e.g., l 148, ll\n180–181).\nl 285–286: It would be better to say “…we found evidence for an interaction effect….”\nll 351–352: “…we expect that all influenza (sub)types will be influenced by climate to some\nextent.” Indeed, this is consistent with your findings, as would be worth reminding us here.\nll 428–429: “…a previous modeling study found that the impact of influenza on susceptibility to\nRSV could not be inferred using data from Vietnam.” The reader naturally wonders why the earlier\nstudy failed. Some explanation, or even speculation, would be appreciated here.\nll 446–448: “This suggests that homogeneous models are sufficient to capture the broad\ncharacteristics of this interaction, even when the underlying transmission dynamics vary by age\ngroup….” Unless I am mistaken, this will not be true in general. Indeed, if the coupling between\nage groups is weak, there may be substantial differences between the predictions of an age-\nstructured and a homogeneous model. As written, this conclusion appears more general than I\nbelieve the authors may intend.\nl 596: There appears to be a typo in Eqn 2."}, "author_response": "We would like to thank all of the reviewers for their detailed and helpful comments. Before\nresponding to each reviewer’s individual comments, we want to highlight the major changes we have\nmade to the manuscript:\n1. We now fit the model to data from Canada, in addition to data from Hong Kong, in order to\ntest whether our results were consistent in various locations. We found that these data\nappear to be consistent with a weaker but similarly long-lasting interaction effect than the\ndata in Hong Kong. These results are now incorporated into our main text; furthermore, we\ndiscuss possible reasons for the differing results in both locations, as well as potential future\nanalyses for identifying a consensus (lines 314-326). Parameter estimates for both locations\ncan be found in Table 1, which is copied and pasted below this list for convenience.\n2. Because of the observed challenges when fitting the model to data on influenza B and RSV,\nincluding the fact that our main outcome of interest was not identifiable using only these\ndata, we have elected to combine influenza A(H1N1) and influenza B in Hong Kong, and to\nrun our fitting procedure on this combined influenza data and RSV, rather than fitting\nindividual influenza subtypes separately. Broadly, the new results are consistent with our\noriginal results, and many parameters are more precisely fit, likely due to the greater amount\nof data we consider at once.\n3. In light of the recent approval of vaccines against RSV for older adults and pregnant people,\nwe have reframed the section of our manuscript on the use of LAIV to focus on the potential\ntradeoffs of widespread LAIV use, rather than on LAIV as a potential RSV control measure.\nSpecifically, we explore, broadly, which scenarios are more likely to lead to an increase in RSV\nburden, and which are more likely to lead to a decrease. Additionally, we emphasize that, in\nthe absence of concrete information concerning the impact of LAIV on RSV susceptibility in\nhumans, this analysis is meant to highlight general trends on the expected impact of LAIV\nuse, and not to predict the exact quantitative impact in any specific scenario.\n4. We have conducted several additional sensitivity analyses to test the robustness of the model\nfits to several assumptions we have made. Specifically, we tested a sinusoidally-forced model\nin Hong Kong, and attempted to account for the circulation of influenza H3N2 and of\nrhinovirus. Encouragingly, we find that the estimated values of the shared parameters\nobtained in these sensitivity analyses were similar to those reported in the main text.\nFurthermore, we assessed the importance of including the interaction effect and the extent\nof existing immunity to RSV in our model by fitting models with no interaction effect and\nwhere the model population was fully susceptible to RSV at the beginning of each season\n(as in Waterlow et al. 2022). Both of these models were found to fit the data significantly worse\nthan our main model.\n[... Table 1 omitted for brevity ...]\nReviewer #1 (Remarks to the Author):\nKramer et al present an interesting modelling study assessing interactions between influenza and\nRSV infections over 5 seasons in Hong Kong. The extensive discussion particularly focusses on\npotential impact of non-specific cross protection, the authors highlighting a remarkable reduction in\nRSV susceptibility following influenza A H1N1 infection that persists for 3–4 months and a similar\nimpact for the converse effect which lasts around 2–3 months.\nThe manuscript is well written with a detailed introduction and discussion and well thought-through\nmodelling.\nThank you for your supportive comments.\nComments:\n1. As the authors note, this work is not the first to model these interactions. Waterlow et al PLoS\nComput Biol (June 2022) reported mathematical modelling based on 11 years of Vietnamese data,\nconcluding that there was a short lived (10 day) period of cross-protection. However, they concluded\nthat absence of either pathogen was not to the detriment of the other, and that vaccination against\neither pathogen is unlikely to have a major effect on the burden of disease caused by the other. The\nimportant differences between this and the current study are described on lines 313-333. The\ncurrent study would be strengthened and of broader applicability if they were able to access other\ndatasets and validate predictions in other contexts.\nWe agree that our work would be significantly strengthened by applying our fitting procedure to\ndata from a variety of locations. Applying our model as-is to the data from Vietnam specifically is not\npossible, as our model makes use of syndromic data (e.g., ILI data), and it is unclear whether these\ndata are available from Vietnam (see also our response to Reviewer 2’s second point regarding our\nDiscussion). However, as mentioned above, we were able to find publicly-available data on influenza\nand RSV circulation, including ILI data, from Canada, and include the results of fitting our model to\nthese data in the revised manuscript. These data were consistent with a weaker interaction than the\ndata in Hong Kong, but with a similar duration (see point 1 in the numbered list at the beginning of\nthis document).\n2. The discussion is very extensive but well written, running to almost 10 pages. Throughout the\nmanuscript there is some scope to merge some sentences and sections to improve readability\n(lines 62–65, for example). If the Editors were to ask for a reduction in word count, where would\nthe authors be prepared to compromise?\nThank you for pointing out lines 62-65, which were unintentionally redundant. We have condensed\nthese sentences, and have gone through the manuscript and attempted to condense in other\nlocations as well.\nWe have tried to be as comprehensive as possible for the initial submission, but understand that the\ndiscussion might need to be condensed. In this case, we would continue to discuss the key results on\nthe strength and duration of interaction, as well as the potential impacts of LAIV, in detail, while\ntruncating the discussion of additional results, such as the role of climate forcing and the inferred\nseason-specific parameters. Our discussion of the broader significance of this work as it relates to the\nstudy of pathogen-pathogen interactions and the use of mathematical models to characterize\ninteractions (lines 419-445) could also be reduced.\nWe also note that, because the interaction parameters were not always identifiable when we\nmodeled subtypes of influenza separately, we have elected to combine influenza A(H1N1) and B in\nthe revised manuscript. This has led to many sections of the manuscript already being shortened.\n3. While aspects of the models are mostly explained well for a non-specialist audience a concise\nsummary (or visual abstract) of the dominant parameters that drive predictions (in addition to the\nprovided table) would enhance immediate understanding for many readers.\nWe have added two panels to Fig. 2 (Fig. 2b-c), in which we show how varying values of the\ninteraction strength and duration parameters influence epidemic trajectories. We hope that this will\nhelp readers to obtain a more intuitive feel for the meaning of these key model parameters.\n4. Comparisons of predictions of model with observed values over the season and seasons should be\nincluded. Currently, only a comparison of predicted versus observed cases is included. Even when\nonly considering total case numbers the models seem to show poor performance with a wide range\nin predicting RSV case numbers. The authors comment that this may be due to the weaker\nseasonality of RSV, which raises questions over the accuracy of results presented and whether the\napproaches used are suitable for modelling epidemics that do not have simple large and seasonal\npeaks. Again, application of the model developed by the authors to other parts of the globe would\nbe of great interest.\nIn order to hopefully partially address your concern, we now compare basic epidemic metrics,\nspecifically peak timing, peak intensity, and observed attack rates, between simulated and observed\noutbreaks. Specifically, we generated 100 simulations of each seasonal outbreak at the MLE, then\ncalculated the percentage of simulations that reproduced the observed peak timing within 2 weeks,\nand the percentage of simulations that reproduced peak intensity and attack rate within 25%. Results\ncan be found in Supplementary Table 4. Specifically, we found that total attack rates in particular are\ncaptured with high accuracy in both locations. Peak intensity is also frequently captured accurately,\nalthough accuracy suffers in seasons with weaker signal. Simulations of influenza are typically also\naccurate at capturing the timing of the observed peak; in many seasons, 100% of simulations\ncorrectly replicated the observed peak timing). RSV simulations, on the other hand, often fail to\ncapture the true peak timing, particularly in Hong Kong. However, this metric is not particularly\nmeaningful for outbreaks where case counts remain fairly consistent throughout the season, as with\nmost RSV outbreaks in our Hong Kong dataset. Thus, although the model cannot always closely\nreproduce the observed cases from week to week, the model at the MLE does accurately reproduce\noverall epidemic patterns. This is encouraging, as capturing the general transmission patterns of\nboth viruses is likely more important than whether the model can closely predict the exact weekly\ncase counts for all weeks.\nFinally, as you say, application of the model to other locations is important. Regarding this, please\nsee the first point in the numbered list at the beginning of the response letter. In particular,\noutbreaks of RSV in Canada show much clearer seasonality than RSV outbreaks in Hong Kong, and\nthe resulting model fit to the RSV data in Canada is therefore much higher (Fig. 3d). The inconsistent\nresults between locations concerning the strength of the interaction effect of influenza on RSV could,\nlike you say, be due to the weaker seasonality of RSV in Hong Kong. Indeed, we now note that it could\nbe difficult to obtain consistent estimates of interaction characteristics by fitting individual locations\nin isolation, and emphasize the importance of fitting to data from several regions (lines 318-326).\n5. The authors excluded modelling of interactions with H3N2 on account of its multi-peak\ncomplexity. How many cases of H3N2 occurred during the study period and (assuming these would\nalso provide non-specific protection) how major might be the effect of this omission? The authors\nthemselves point this out as a limitation of (in their own words) “simple models”, can more complex\nmodels be used to assess this?\nThe number of H3N2 cases over the study period in Hong Kong is shown in Supplementary Fig. 2.\nNotably, the amount of H3N2 circulation varied widely from season to season. To determine whether\nignoring H3N2 was likely to substantially alter our results, we refit our model for only the two\nseasons where minimal circulation of H3N2 occurred, 2017-18 and 2018-19. We found that the\ninferred values for the strength and duration of the interaction were similar for the two analyses,\nalthough the inferred duration of the effect of RSV on influenza wr\n6. The model estimates concerning the different effects of humidity and temperature on influenza A\nand B seems questionable: is this more likely a shortcoming of the models and data than a real\neffect?\nYes, this seems more likely to indicate that these particular data do not allow these parameters to be\naccurately inferred, rather than that the effect of climate on influenza varies substantially by\nsubtype. There could also be difficulty in estimating these parameters due to the high correlation\nbetween temperature and humidity. However, as we noted, the majority of the past experimental\nwork we found focusing on climate forcing of influenza has been conducted on influenza A, not\ninfluenza B. It is possible that further research would indeed reveal that the climate drivers of\ninfluenza B are different.\nAs mentioned in the numbered list at the beginning of this document, we now combine data on\ninfluenza A(H1N1) and influenza B in Hong Kong, rather than fitting the two subtypes separately. This\nhelps to increase our chances of precisely estimating our parameters of interest, as there is more\ndata being incorporated and more signal in the data season-to-season. In this case, the results for\nclimate forcing are more consistent with the original A(H1N1)-RSV results. As further support for our\nfindings concerning the seasonal pattern of climate forcing (Supplementary Fig. 8), we found a very\nsimilar pattern of forcing when fitting a model where transmission was forced using a sinusoidal\nwave, rather than using climate data explicitly.\n7. Why are the ranges of immunity estimates so wide (line 188)? Again, is this a case of pushing\nthe model beyond what the data can accurately inform. The range of 0% to 71% for RSV when fit\nalongside flu B is particularly notable, though other ranges are similarly wide, making it hard to\ninterpret.\nBecause the season-specific parameters are being fit on the basis of individual seasons, it is likely\nthat they are less precisely and accurately fit than the shared parameters, which are able to take\ninformation from multiple seasons of data simultaneously. Since our main goal was to estimate the\ninteraction parameters, we elected to keep the additional features of the model relatively simple to\navoid having to fit an unreasonably large number of parameters, but this decision of course comes\nwith tradeoffs. Given the simplicity of the model, it is possible that the fit values of the reproductive\nnumbers and the proportion of the population immune are accounting for other features of a\npopulation that may help drive outbreak dynamics that are not explicitly modeled here. For example,\nthe proportion immune may account for widespread partial immunity, or year-to-year differences in\ncontact patterns in the population. While it is therefore encouraging that the ranges of fit values are\nbroadly realistic, the exact fit values of these parameters may not be as reliable as those of the\nparameters that are shared between seasons, which are able to take much more data into account\nwhen being estimated. We have now included more discussion of the difficulty of inferring these\nseason-specific parameters (lines 376-386).\n8. In the Discussion, the authors refer to several viral and bacterial pathogens that have significant\ninteractions with influenza, i.e., rhinovirus and pneumococcus. How frequent were these infections\nduring the study period, do the authors have access to such data, and might omission of other\ncommon infections in the model terms not undermine the accuracy of modelling results?\nOur dataset included information on rhinovirus incidence. While there is overlap of influenza and\nrhinovirus circulation, influenza outbreaks tended to peak between outbreaks of rhinovirus in both\nHong Kong and Canada (see new Supplementary Fig. 19). Because of the extent of overlap in the\ncirculation of these pathogens, it is possible that ignoring rhinovirus could bias our results, a point\nthat we now make in our limitations (lines 490-491).\nThat said, we have now run a sensitivity analysis in Hong Kong where we allow rhinovirus incidence\nto modulate the force of infection of influenza. Specifically, the force of infection of influenza was\nmultiplied by 𝑒−𝛽𝑟ℎ𝑖𝑛𝑜𝑖𝑛𝑐𝑟ℎ𝑖𝑛𝑜, where 𝑖𝑛𝑐 represents the extent of rhinovirus transmission at time\n𝑟ℎ𝑖𝑛𝑜\nt, defined as the proportion of tests positive for rhinovirus multiplied by the ILI rate per consultation\nat time t, standardized to have a mean of 0 and variance of 1, and β is a parameter determining\nrhino\nthe extent to which circulating rhinovirus restricts influenza transmissibility. We found that the\nmaximum likelihood estimates of the shared parameters obtained using this model are very similar\nto those values obtained in the main text (see Supplementary Fig. 20). We now mention this\nsensitivity analysis in lines 486-493.\nAlthough it is likely that an interaction exists between influenza and pneumococcus, the evidence\nsuggests that the interaction is unidirectional. In other words, although influenza may increase the\nrate of pneumococcal acquisition and progression to invasive disease (Domenech de Cellès et al.\n(2019), PNAS), there is no evidence for an impact of pneumococcus on influenza transmission or\nseverity. For this reason, we do not expect ignoring pneumococcus incidence to bias our results.\n9. The authors exclude seasons with under 2000 influenza cases, with the justification that virus-\nvirus interaction would be minimal. How was this 2000 case figure chosen, how does it compare to\nthe average number of cases and, most importantly, why can fitting not be performed for these\nbelow 2000 case seasons to provide evidence of minimal interaction during times of lower\ninfluenza?\nThe other reviewers had the same feedback. We have now removed this restriction, and its mention\nin the paper, and re-run the model to provide updated parameter estimates.\n10. Although not mentioned in the title, the authors give prominence to the potential impact of\nLAIV in some parts of the manuscript. While this is an interesting and potentially important point\nand a nice use of the model, there appears to be no actual data on LAIV to support the argument. The\nauthors have instead simply applied a proportion of the live infection effect to model LAIV. There are\nseveral unknowns surrounding this approach. We suggest that the LAIV section and the resulting\nconclusions (especially those in the Abstract) should be caveated and scaled back.\nWe have now emphasized the lack of empirical data in our discussion of these results, and have\nnoted that the reader should focus on the qualitative, rather than the exact quantitative, results from\nthis analysis (lines 401-408; see also point 3 in our numbered list of major revisions at the beginning\nof the response letter). We have also edited the wording in the abstract to emphasize that these\nresults are based on an assumption about the effect of LAIV on susceptibility to RSV.\nReviewer #2 (Remarks to the Author):\n[... Response to Reviewer 2 omitted for brevity ...]\nReviewer #3 (Remarks to the Author):\n[... Response to Reviewer 3 omitted for brevity ...]"}]

Decision letter