Estimating the impact of influenza on the epidemiological dynamics of SARS-CoV-2

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). In particular, experimental evidence indicates that influenza infection can up-regulate the expression of ACE2—the receptor of SARS-CoV-2 in human cells—and facilitate SARS-CoV-2 infection. Here we hypothesized that influenza impacted the epidemiology of SARS-CoV-2 during the early 2020 epidemic of COVID-19 in Europe. To test this hypothesis, we developed a population-based model of SARS-CoV-2 transmission and of COVID-19 mortality, which simultaneously incorporated the impact of non-pharmaceutical control measures and of influenza on the epidemiological dynamics of SARS-CoV-2. Using statistical inference methods based on iterated filtering, we confronted this model with mortality incidence data in four European countries (Belgium, Italy, Norway, and Spain) to systematically test a range of assumptions about the impact of influenza. We found consistent evidence for a 1.8–3.4-fold (uncertainty range across countries: 1.1 to 5.0) average population-level increase in SARS-CoV-2 transmission associated with influenza during the period of co-circulation. These estimates remained robust to a variety of alternative assumptions regarding the epidemiological traits of SARS-CoV-2 and the modeled impact of control measures. Although further confirmatory evidence is required, our results suggest that influenza could facilitate the spread and hamper effective control of SARS-CoV-2. More generally, they highlight the possible role of co-circulating pathogens in the epidemiology of COVID-19.


S2 Supplementary results
Log-likelihood profiles of F The log-likelihood profiles for the impact of influenza (parameter F ) are plotted in Fig. S3 Table 2).
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 S-5 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: 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 such that the base model with linear scaling is nested within this more general model. The corresponding parameter estimates are presented in Table S1, and further discussed in the main text.

Quantity
Belgium  for the stringency index. ⇤ Log-likelihood difference (P-value from a log-likelihood ratio test) with the base model presented in Table 2. The confidence intervals represent approximate 95% multivariate confidence intervals, calculated from the 100 MIF runs as the range of parameters within 1 2 ⇥ p=0.95,df=n ✓ units from the maximum log-likelihood (n ✓ = 6: number of parameters estimated).
Model with unexplained trend in transmission rate To assess the robustness of our results to potential confounding bias, we considered an extended model that included an exponential trend in the transmission rate: where the trend parameter ⌧ was estimated from the data, in addition to the other parameters. The corresponding parameter estimates are presented in Table S2 and discussed in the main text.  Table S2: Parameter estimates of an extended model with a trend in transmission. ⇤ Log-likelihood difference (P-value from a log-likelihood ratio test) with the base model presented in Table 2. The confidence intervals represent approximate 95% multivariate confidence intervals, calculated from the 100 MIF runs as the range of parameters within 1 2 ⇥ p=0.95,df=n ✓ units from the maximum log-likelihood (n ✓ = 6: number of parameters estimated).
Additional sensitivity analyses To verify the robustness of our results, we conducted a number of additional sensitivity analyses. Specifically, we modified the value of 3 fixed model parameters (infection fatality ratio, average onset-to-death time, and average generation time) and we repeated the estimations as before. As shown in Table S3, the estimate of the impact of influenza on SARS-CoV-2 transmission remained consistently above 0 for all scenarios tested. The table also reports the estimates of the model with no impact of influenza on SARS-CoV-2 transmission ( F = 0).

Model
Belgium Italy Norway Spain  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 [Wood, 2010, King et al. , 2016). Specifically, we considered the following probes: S-7 • 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 [Maier & Brockmann, 2020], we assumed that, until the peak time, the daily number of deaths grew algebraically, i.e., D(t) / t ↵ . We then estimated the growth exponent ↵ using a log-log linear regression model.
The observed and simulated probe values are plotted in Fig. S5 and discussed in the main text.  and of SARS-CoV-2 detection start times, assuming that SARS-CoV-2 could be detected from 2 to 4 days before symptom onset [Tindale et al. , 2020]. In each simulation, we calculated the probability of detecting a co-detection 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 S4 and discussed in the main text.  Table S4: Probability of detecting a co-infection with influenza and SARS-CoV-2. The results are based on sample size of 10 5 ; replicate simulations gave identical results, such that the estimates may be considered exact. S-10