key: cord-0801164-jpdsukne
authors: Domenech de Celles, M.; Casalegno, J.-S.; Lina, B.; Opatowski, L.
title: Influenza may facilitate the spread of SARS-CoV-2
date: 2020-09-09
journal: nan
DOI: 10.1101/2020.09.07.20189779
sha: 67ad36b528602e454ef61d375cfa12c9d5d7a390
doc_id: 801164
cord_uid: jpdsukne

As in past pandemics, co-circulating pathogens may play a role in the epidemiology of coronavirus disease 2019 (COVID-19), caused by the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Here we hypothesized that influenza interacted with SARS-CoV-2 during the early 2020 epidemic of COVID-19 in Europe. We developed a population-based model of SARS-CoV-2 transmission, combined with mortality incidence data in four European countries, to test a range of assumptions about the impact of influenza. We found consistent evidence for a 2-2.5-fold population-level increase in SARS-CoV-2 transmission associated with influenza during the period of co-circulation. These results suggest the need to increase vaccination against influenza, not only to reduce the burden due to influenza viruses, but also to counteract their facilitatory impact on SARS-CoV-2.

time (mean 6.5 days, coefficient of variation 0.58, see Fig. S2 and Ref. [18] ) and of the time from symptom onset to death (mean 17.8 days, coefficient of variation 0. 45 [19] ), under the assumption that 1% of all infections resulted in death [16] . A novel feature of our model was the inclusion of the stringency index, an aggregate measure of the number and of the strictness of non-pharmaceutical control measures (e.g., restrictions on travel, school or work closure, lockdown) implemented by governments in response to COVID-19 ( Fig. 1A and ref. [3] ). Specifically, we mapped the stringency index into a relative reduction in SARS-CoV-2 transmission using a simple linear scaling function, whose slope represented the impact of control measures (see Methods). To assess the potential impact of influenza, we also incorporated renormalized time series of influenza incidence as drivers of SARS-CoV-2 transmission into our model. Fig. 2B ). The results were unequivocal: we found consistent evidence that, during the period of co-circulation, influenza was associated with an average 2-2.5-fold population-level increase in SARS-CoV-2 transmission (Table 1) . After controlling for the impact of influenza, our estimates of the basic reproduction number (R 0 ) ranged from 2 (Italy and Spain) to 3.3 (Belgium). Although the increased transmission associated with influenza early during the SARS-CoV-2 epidemic explained the data significantly better (Table 1) , a model without influenza led to higher R 0 estimates (range 2.5-5, Fig. 2A ), consistent with those of a previous study [16] . Also in line with [16], we found consistent evidence for a marked impact of non-pharmaceutical control measures (Table 1), which were associated with a decrease in SARS-CoV-2 transmission below the reproduction threshold from mid-March to early June 2020 ( Fig. 2A) . Visual inspection of simulations suggested that our model correctly captured the dynamics of COVID-19 mortality in every country (Fig. 2B) . A more detailed model-data comparison of summary statistics confirmed that our model accurately predicted the peak time, the peak number and the total number of deaths, and the death growth exponent [27] , except in Spain where the latter statistic was systematically under-estimated (Table S5 ). Our model-based estimates of the total proportion of individuals infected with SARS-CoV-2 (as of 4 May 2020, Table 1 ) were also comparable with those of a previous modeling study [16] and of a seroprevalence study conducted in early May in Spain [28] . Hence, our model appeared to precisely recapitulate the epidemiology of SARS-CoV-2 morbidity and mortality over a period of ∼4 months.

To verify the robustness of our results, we conducted three additional analyses (see Supplementary   Results ). First, we estimated an extended model in which influenza was allowed to modulate the lethality, 4 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189779 doi: medRxiv preprint in addition to the transmission, of SARS-CoV-2 (Table S2) . Compared with the base model, we found little support for such a model in Belgium, Italy, and Norway (log-likelihood difference [∆ log L] in the range 0.0-0.4, likelihood ratio test P-value in the range 0.37-1.00). In Spain, however, the parameter estimates suggested that influenza was associated with both increased transmission and lethality, but the statistical evidence was weak (∆ log L = 3.2, P = 0.01). Second, we estimated another model, in which the reduction of SARS-CoV-2 transmission was allowed to scale non-linearly with the stringency index (Table S3) . We found little statistical evidence that such a model outperformed the simple linear scaling function in Belgium, Norway, and Spain (∆ log L ∈ [0.1, 1.5], P ∈ [0.08, 0.65]). In Italy, however, we found strong evidence (∆ log L = 21.3, P < 10 −3 ) for super-linear scaling at low values of the stringency index (Fig. S3) , although our estimate of the impact of influenza was unchanged. This result may reflect the impact of the early lockdown in part of Lombardy, which preceded the one in Italy as a whole by a few weeks [29] . Third, to take into account potential spatial effects in the transmission dynamics of SARS-CoV-2 in Italy and in Spain [29, 28], we relaxed the assumption of homogeneous mixing (Table S4 and Refs. [30, 31] ). In Italy (∆ log L = 26.1, P < 10 −3 ), but not in Spain (∆ log L = 0.0, P = 1), we found evidence that the force of infection scaled sub-linearly with SARS-CoV-2 infection prevalence. This result may be explained by the progressive spread of SARS-CoV-2 from northern to southern regions of Italy [29] . Crucially, however, our estimate of the impact of influenza was unchanged in both countries. In addition, we found that our parameter estimates varied little when testing alternative hypotheses about the fixed value of the average generation time, of the onset-to-death time, and of the infection fatality ratio (Table S6 ). In sum, our main result about the impact of influenza remained robust to a variety of alternative assumptions regarding the epidemiological traits of SARS-CoV-2 and the modeled impact of control measures.

Our model makes at least two testable predictions. First, even though our results did not allow to distinguish between higher transmissibility or higher susceptibility in individuals co-infected with influenza and SARS-CoV-2, previous experimental work suggests that the latter mechanism may operate, as a result of up-regulation of the ACE2 receptor caused by influenza infection [14] . Hence, we predict that a recent influenza infection should be an independent risk factor for subsequent SARS-CoV-2 infection. Estimates of the frequency of co-detection of influenza and SARS-CoV-2 by polymerase chain reaction (PCR) testing in nasopharyngeal swabs were highly variable in previous studies (range 0-60% [6, 32] ). Although the marked seasonality of influenza in temperate regions likely explains in part the low frequency found in some studies [32], we propose that differences in the natural history of influenza and SARS-CoV-2 infections also lead to a systematic under-estimation of co-infection. Specifically, because the incubation period of SARS-CoV-2 infection (estimated to average 5.7 days [33]) exceeds that of influenza (A, 1.4 days or B, 0.6 days [34]), it is likely that, by the time SARS-CoV-2 infection becomes detectable, influenza no longer is. To make that 5 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted September 9, 2020. . statement more precise, we calculated the probability of detectability of a co-infection, with influenza first then SARS-CoV-2 (Table S7 ). Assuming that influenza is detectable by PCR up to 4-5 days after [35] , and SARS-CoV-2 from 2-4 days before [36] , symptom onset, we find that a large, 30-50% of co-infections may not be detectable at all. These results may help explain the low frequency of co-detection found in some studies [37] , and suggest that the time window of co-detectability may be too short to adequately infer the association between influenza and SARS-CoV-2 using PCR testing. Serological studies comparing the prevalence of antibodies against influenza in SARS-CoV-2 cases and non-cases may therefore be required to test the prediction that influenza is a risk factor for SARS-CoV-2 infection. Second, we predict that individuals vaccinated against influenza should be at lower risk of SARS-CoV-2 infection than those unvaccinated. The findings of a negative association between influenza vaccine coverage and COVID-19 mortality in ecological studies (in Italy [38] and in other countries [39] ) and of a lower risk of SARS-CoV-2 infection in influenza vaccinees in a US prospective study [40] are consistent with our prediction, but further epidemiological investigations are needed. Importantly, our results can explain these findings as the direct effect of influenza vaccines on influenza infection, instead of indirect effects on non-influenza pathogens (e.g., as a result of trained immunity) [41] .

Our study has a number of important limitations. First, for simplicity and as in other studies [15, 17, 16], our model was not age-structured, even though many aspects of COVID-19 and of influenza epidemiologylike disease severity and lethality-vary markedly with age [19] . The susceptibility to SARS-CoV-2 infection was also found to increase with age [42] , a finding potentially explained by lower baseline expression of the ACE2 receptor in children [43] . Another testable prediction of our model, therefore, is that influenza should be associated with a transient increase in susceptibility to SARS-CoV-2 infection, commensurate with the variations of influenza incidence over age. Second, we modeled the impact of non-pharmaceutical control measures using a simple, linear function scaling the stringency index to the reduction of SARS-CoV-2 transmission. Even though this simple hypothesis provided a more parsimonious fit (except in Italy), that result may be specific to Europe, where control measures gradually increased in number and in intensity ( Fig. 1A) . In general, the association is likely non-linear (e.g., if a high-impact intervention like a lockdown is implemented early on), and we therefore recommend testing a variety of scaling functions. Third, we did not specifically model fully asymptomatic cases, which may represent a large fraction of SARS-CoV-2 infections [17]. The omission of asymptomatic infections may lead to biased R 0 estimates if their duration significantly differs from that of symptomatic infections [44] . A previous study, however, estimated that the duration of both types of infection is comparable [17] , such that our estimates should be robust in more complex model structures. Finally, we assessed only the impact of influenza, because of its high prevalence and period of overlap with SARS-CoV-2 in early 2020 in Europe and of the availability of high-quality 6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189779 doi: medRxiv preprint data [22] . Nevertheless, other respiratory viruses, like RSV and rhinoviruses, may also interact with SARS-CoV-2 and should be considered [14] , especially if SARS-CoV-2 continues to spread widely during new seasons in temperate regions of the Northern hemisphere.

In conclusion, our results suggest that influenza virus infection increases the transmission of SARS-CoV-2 and facilitated its spread during the early 2020 epidemic of COVID-19 in Europe. Hence, an increase in the uptake of influenza vaccines may be called for, not only to reduce hospitalizations due to influenza infections [32, 45] , but also to reduce their downstream impact on SARS-CoV-2 transmission and on COVID-19 mortality. More generally, taking into account the microbial environment of SARS-CoV-2 may be essential, not only to better understand its epidemiology, but also to enhance current and future infection control strategies.

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The copyright holder for this preprint this version posted September 9, 2020. Fig. S1 for a time plot of the latter two variables). The vertical dashed lines delimitate the period of overlap between SARS-CoV-2 and influenza, defined as the period between the assumed start date of SARS-CoV-2 community transmission and 6 weeks after the epidemic peak of influenza [46] . In each country, the time series displayed were incorporated as covariates, which modulated the transmission rate of SARS-CoV-2 in our model (see Methods). In B, the y-axis values differ for each panel.

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The copyright holder for this preprint this version posted September 9, 2020. . Table 1 ) in each country. The dotted black line represents the effective reproduction number estimated from a model without influenza (i.e., with the influenza impact parameter fixed to 0 and the other parameters estimated from the data). The horizontal grey line is at R e = 1. B: time plot of the simulated and observed numbers of daily deaths caused by SARS-CoV-2. In each panel, the light grey lines represent 1,000 model simulations, with one simulation highlighted in dark grey; the black line represents the actual death counts. In A and B, the x -axis and the y-axis values differ for each panel.

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The copyright holder for this preprint this version posted September 9, 2020. Table 1 : Model parameter estimates in Belgium, Italy, Norway, and Spain. For the proportion infected as of May 4, the numbers between parentheses represent a 95% prediction interval, based on 1,000 simulations at the maximum likelihood estimate. For the other parameters, they represent an approximate 95% confidence interval, calculated using either the profile likelihood [47] (parameter e β F ) or a parametric bootstrap (other parameters). SE: standard error, calculated using 5 replicate particle filters, each with 20,000 particles, at the maximum likelihood estimate.

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The copyright holder for this preprint this version posted September 9, 2020. [23] Belgian institute for health (Sciensano), access date: 6 July 2020;. Available from: https://epistat. wiv-isp.be/Covid/.

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The copyright holder for this preprint this version posted September 9, 2020. Data and materials availability All data and R codes will be made available via a Dryad digital repository and are available upon request of the reviewers.

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Data Stringency index data Country-level time series of the stringency index were available from the Oxford COVID-19 Government Response Tracker, developed at the University of Oxford and described elsewhere [3] .

Briefly, the stringency index provides an aggregate measure of the number and of the strictness of nonpharmaceutical control measures implemented by governments in response to the COVID-19 epidemic. The stringency index is defined as the average of 9 normalized ordinal variables, which quantify the strength (e.g., recommended or required) and the scope (e.g., targeted or general) of closure and containment measures (8 variables) and of health measures (1 variable). The resulting index allows to quantify the strength of control measures in a systematic way, on a scale ranging from 0 (no interventions) to 100 (maximum number and maximal intensity of control measures). Of note, however, the stringency index does not quantify the impact of control measures, which likely varied across countries [16] . In formulating our model, we therefore modeled the relationship between the stringency index and the relative reduction in SARS-CoV-2 transmission using a non-decreasing function, whose parameters represented the impact of control measures and were estimated from the data.

Influenza incidence data Virological data on the weekly numbers of samples tested and of samples positive to any influenza virus were available from the FluNet database, compiled by the WHO (Fig. S1A ).

Parallel syndromic data on the weekly incidence rate of influenza-like illnesses (ILI) were available from the FluID database, also compiled by the WHO (Fig. S1B) . Those data were deemed high-quality and used in a previous study on influenza forecasting in the countries considered here [22] . The weekly incidence rate of influenza was then calculated as the product of ILI incidence and of the fraction of samples positive to any influenza virus (Fig. 1B) . Because the magnitude of influenza incidence thus calculated varied markedly across countries (e.g., as a result of different surveillance systems and case definitions), we rescaled each time series by its average during the period of co-circulation of influenza and SARS-CoV-2 (Fig. 1B) . The resulting time series was therefore dimensionless and equalled 1 when influenza equalled its average value during that period.

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The copyright holder for this preprint this version posted September 9, 2020. 

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The copyright holder for this preprint this version posted September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189779 doi: medRxiv preprint Following a previous study [16] , and to avoid a possible bias caused by the dominance of deaths due to non-locally acquired infections early in the epidemic, we included observed deaths from the date after which the cumulative observed death count exceeded 10. Data points before that date were treated as missing and were assigned a conditional log-likelihood of 0, such that they did not contribute to the overall log-likelihood.

The data were not further pre-processed, except in Italy, where a negative death count was reported on 24

June 2020 and was treated as missing and also assigned a log-likelihood of 0.

Model formulation We formulated a variant of the standard Susceptible-Exposed-Infected-Recovered transmission model [48] , using the method of stages to allow for a realistic distribution of the latent, infectious, and onset-to-death periods [49, 50] . Specifically, we assumed that the latent and infectious periods were Erlang-distributed with shape parameter 2 and mean 1/σ = 4 days and 1/γ = 5 days, respectively [17] . The resulting generation time T g (i.e., the time from infection of a primary case to transmission to a secondary case) had a mean of 6.5 days and a coefficient of variation of 0.58 (see Fig. S2 for the full distribution and the details of the calculation), consistent with empirical observations and with the values fixed in a previous modeling study [18, 16] . To model the impact of the gradual implementation of non-pharmaceutical control measures (e.g., border closure, school closure, lockdown), we mapped the stringency index (denoted by s(t)) to the time-varying relative reduction in transmission of SARS-CoV-2 (denoted by r β (t)). Specifically, we used the following simple linear scaling function, with saturation:

Here the parameter b quantifies how fast the transmission rate of SARS-CoV-2 decreases as the stringency index increases. Hence, this parameter can be interpreted as a measure of the impact of non-pharmaceutical control measures on SARS-CoV-2 transmission. The deterministic variant of the model was represented by the following set of differential equations:Ṡ

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The force of infection (that is, the per capita rate at which susceptible individuals contract infection [48] ), λ(t), was modeled as:

where R 0 represents the basic reproduction number of SARS-CoV-2, R e (t) the time-varying effective reproduction number, N the population size (assumed constant during the study period), and F (t) the renormalized time series of influenza incidence, incorporated as a covariate into the model (Fig. 1) . With this formulation, the parameter β F quantifies the impact of influenza on SARS-CoV-2 transmission: β F > 0 if influenza increases transmission, β F < 0 if influenza decreases transmission, and β F = 0 if influenza has no impact on transmission (null hypothesis). More specifically, the average incidence of influenza during the period of co-circulation with SARS-CoV-2 corresponds to F (t) = 1, such that e β F represents the average relative variation of SARS-CoV-2 transmission associated with influenza (null hypothesis: e β F = 1).

In the main text and in the following text, we report the estimates of e β F to facilitate the interpretation of the impact of influenza. In writing equation (2), we implicitly assume that the impact of influenza on SARS-CoV-2 transmission, if any, is short-lived and does not extend long after influenza infection.

Finally, we incorporated an observation model that related the dynamics of SARS-CoV-2 infection to that of COVID-19 mortality, taking into account the fact that only a fraction of infections results in death and that, among those, death occurs some time after symptom onset [19, 33, 16] . We assumed an average duration of pre-symptomatic of 2.5 days, resulting in an average incubation duration of 6.5 days, in broad agreement with previous empirical studies [36, 33] . Hence, individuals in the first infected state (I 1 ) were considered pre-symptomatic, and the onset of symptoms was assumed to coincide with the transition from

The onset-to-death time was then assumed to be Erlang distributed with shape parameter 5 and mean 1/κ = 17.8 days (coefficient of variation of 0.45), the value estimated in a previous epidemiological study [19] . In sensitivity analysis, we also tested a mean onset-to-death time of 1/κ = 13 days, the lower S-4 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 9, 2020. . bound estimated in a meta-analysis [33] . According to previous studies, the infection fatality ratio (IFR) typically ranges from 0.5% to 1% [51, 19] . We fixed the IFR to µ = 0.01 in the base model, but we considered an alternative value of 0.005 in a sensitivity analysis. Given those assumptions, the observation model was modeled by the following set of ordinary differential equations:

Here D M is the simulated number of daily deaths, modeled as an accumulator variable and reset to 0 

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The copyright holder for this preprint this version posted September 9, 2020. Figure S2 : Model-based distribution of the generation time. For our model, the density function of the generation time is given by [53, 54] :

The resulting distribution is bell-shaped, with mean σ −1 + γ −1 2 = 6.5 days and coefficient of variation 0.58.

The following five parameters were estimated from the data:

1. The basic reproduction number, R 0 . According to a previous meta-analysis [55] , this parameter was searched in the interval 2-10. 4. The initial number of individuals exposed to SARS-CoV-2, E 1 (0) (search interval: 0-10 4 ).

5. The over-dispersion in death reporting, k D (search interval: R + ).

A summary list of fixed and estimated model parameters is presented in Table S1 All parameters were transformed to be estimated on an unconstrained scale, using a log transformation for positive parameters and the extended logistic function f (θ) = log θ−a b−θ for parameters constrained in the interval [a, b]. The maximum iterated filtering algorithm (MIF2 [20]), implemented in the R package pomp [21, 56] , was used to estimate model parameters. The estimation was completed in several steps, S-6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189779 doi: medRxiv preprint starting with trajectory matching to identify good starting parameters for MIF2, followed by 100 independent runs of MIF2 to locate the maximum likelihood estimate (MLE). The profile likelihood was calculated to verify the convergence of MIF2 and to derive an approximate 95% confidence interval for the parameter β F [47] . For the other parameters, a parametric bootstrap was used to calculate approximate 95% confidence intervals, by re-estimating the parameters for each of 200 synthetic datasets simulated at the MLE [57, 58] .

Meaning Fixed value or estimation range Comment/Source 

R + E 1 (0) Initial no exposed 0-10 4 Initial condition Table S1 : List of model parameters.

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Model with impact of influenza on both transmission and lethality To test the hypothesis that influenza increases COVID-19 lethality, in addition to SARS-CoV-2 transmission, we extended our base model so that influenza was also allowed to modulate the IFR. Specifically, we replaced the constant IFR µ by the time-varying parameter:

where µ F ∈ R quantifies the impact of influenza on COVID-19 mortality and was estimated from the data.

The results are presented in Table S2 and are discussed in the main text.

Belgium Model with non-linear function mapping the stringency index to the relative reduction in transmission Although we assumed a simple linear scaling in our base model, it can also be hypothesized that the reduction of SARS-CoV-2 transmission scales non-linearly with the stringency index. For example, super-linear scaling for low values of the stringency index may occur if a potentially high-impact intervention (e.g., lockdown) is implemented early on, such that a modest increase in the stringency index results in a marked decrease in SARS-CoV-2 transmission. Conversely, sub-linear scaling may also be plausible if potentially low-impact interventions (e.g., border closure) are implemented first. To test those hypotheses, we considered an alternative, non-linear scaling function of the form:

where f (x) = (1+e −x ) −1 is the logistic function. Here the extra parameter b 2 controls the slope at the origin, with b 2 < 1 representing super-linear scaling at low values of the stringency index, and b 2 > 1 super-linear S-8

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The copyright holder for this preprint this version posted September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189779 doi: medRxiv preprint scaling. For b 2 = 1, r β (t) = min(1, b × s(t) 100 ), such that the base model with linear scaling is nested within this more general model. The corresponding parameter estimates are presented in Table S3 ; the scaling function estimated in Italy is also plotted in Fig. S3 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 9, 2020. .

where the mixing coefficient α ≥ 0 was estimated from the data. Given that I1+I2 N < 1, α > 1 represents sub-linear scaling and α < 1 super-linear scaling. The results of those experiments are presented in Table S4 and further discussed in the main text.

Italy

570 120 α 1.07 1.00 Table S4 : Point parameter estimates of an extended model with inhomogeneous mixing. * Loglikelihood difference (P-value) with the base model presented in Table 1 .

Model fit to data summary statistics To evaluate the model fit in more detail, we examined the modeldata agreement on a number of statistics that summarized important aspects of the mortality data-that is, probes [59, 21] ). Specifically, we considered the following probes:

• Peak time (in days relative to the start of the study period).

• Peak daily number of deaths.

• Total number of deaths.

• Epidemic growth exponent. According to a previous study [27] , we assumed that, until the peak time, the daily number of deaths grew algebraically, i.e., D(t) ∝ t α . We then estimated the growth exponent α using a log-log linear regression model.

The observed and simulated probe values are summarized in Table S5 and discussed in the main text.

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The copyright holder for this preprint this version posted September 9, 2020. Table S5 : Model-data comparison on probes. The values highlighted in red indicate model-based probes that did not enclose the observed data probe value.

Sensitivity analyses To verify the robustness of our results, we conducted a number of sensitivity analyses. Specifically, we modified the value of 3 fixed model parameters (infection fatality ratio, average onset-todeath time, and average generation time) and we repeated the estimations as before. As shown in Table S6 , the estimate of the impact of influenza on SARS-CoV-2 transmission (e β F ) remained consistently above 1 for all scenarios tested. Probability that an influenza-SARS-CoV-2 co-infection is detectable To calculate the probability that a co-infection with influenza then SARS-CoV-2 can be be detected, we ran a simulation study. Assuming that influenza infection occurred first, we first generated a sample of influenza incubation periods from a log-Normal distribution with median 1.4 days and dispersion 1.51, based on the results of a previous review [34] .

We then generated a sample of detection periods, assuming that influenza could be shed (and therefore detected) up to 4-5 days after symptom onset [35] . Second, we generated a sample of SARS-CoV-2 infection times, uniformly between the time of infection and the end time of detectability of influenza. Finally, we S-11 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted September 9, 2020. . https://doi.org/10.1101/2020.09.07.20189779 doi: medRxiv preprint generated a sample of SARS-CoV-2 incubation periods (from a Gamma distribution with mean 5.7 days [33] and coefficient of variation 0.86 [16] ) and of SARS-CoV-2 detection start times, assuming that SARS-CoV-2 could be detected from 2 to 4 days before symptom onset [36] . In each simulation, we calculated the probability that co-detection can be detected as the fraction of the sample for which the maximal detection time of influenza exceeded the minimal detection time of SARS-CoV-2. The results are presented in Table S7 and discussed in the main text. Table S7 : Probability that an influenza-SARS-CoV-2 co-infection can be detected. The results are based on sample size of 10 5 ; replicate simulations gave identical results, such that the estimates may be considered exact.

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A Novel Coronavirus from Patients with Pneumonia in China

Novel Coronavirus (COVID-19) Cases Data

Oxford covid-19 government response tracker

Blavatnik School of Government Working Paper

Factors associated with COVID-19-related death using OpenSAFELY

Predominant role of bacterial pneumonia as a cause of death in pandemic influenza: implications for pandemic influenza preparedness

Use of seasonal influenza and pneumococcal polysaccharide vaccines in older adults to reduce COVID-19 mortality

A systematic approach to virus-virus interactions

Influenza interaction with cocirculating pathogens and its impact on surveillance, pathogenesis, and epidemic profile: A key role for mathematical modelling

Investigating Viral Interference Between Influenza A Virus and Human Respiratory Syncytial Virus in a Ferret Model of Infection

Impact of the 2009 influenza A(H1N1) pandemic wave on the pattern of hibernal respiratory virus epidemics

Time lines of infection and disease in human influenza: a review of volunteer challenge studies

Evidence for transmission of COVID-19 prior to symptom onset

Rates of Co-infection Between SARS-CoV-2 and Other Respiratory Pathogens

Epidemiological evidence for association between higher influenza vaccine uptake in the elderly and lower COVID-19 deaths in Italy

Correlation of Influenza Vaccination and the COVID-19 Severity. Available at SSRN 3572814

Individualizing Risk Prediction for Positive Coronavirus Disease 2019 Testing: Results from 11,672 Patients

The possible beneficial adjuvant effect of influenza vaccine to minimize the severity of COVID-19. Med Hypotheses

Age-dependent effects in the transmission and control of COVID-19 epidemics

Nasal Gene Expression of Angiotensin-Converting Enzyme 2 in Children and Adults

The time scale of asymptomatic transmission affects estimates of epidemic potential in the COVID-19 outbreak

The impact of influenza vaccination on the COVID-19 pandemic? Evidence and lessons for public health policies

Characterizing and Comparing the Seasonality of Influenza-Like Illnesses and Invasive Pneumococcal Diseases Using Seasonal Waveforms

Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood

Modeling infectious diseases in humans and animals

Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods

Appropriate models for the management of infectious diseases

Estimating the burden of SARS-CoV-2 in France

Avoidable errors in the modelling of outbreaks of emerging pathogens, with special reference to Ebola

Explaining rapid reinfections in multiple-wave influenza outbreaks: Tristan da Cunha 1971 epidemic as a case study

A note on generation times in epidemic models

Estimate of the Basic Reproduction Number for COVID-19: A Systematic Review and Meta-analysis

R: A Language and Environment for Statistical Computing

The impact of past vaccination coverage and immunity on pertussis resurgence

Unraveling the seasonal epidemiology of pneumococcus

Statistical inference for noisy nonlinear ecological dynamic systems

Acknowledgements We thank Arturo Zychlinsky and Klaus Osterrieder for helpful comments on the