Using population approach to model COVID-19 epidemics in France: estimating the burden of SARS-Cov-2 and the effects of non-pharmaceutical interventions.
Mélanie Prague, Boris Hejblum, Philippe Moireau, Rodolphe Thiébaut, Annabelle Collin
Université de Bordeaux, Inria, Inserm U1219, Vaccine research institute, France.
Objectives: The COVID-19 disease is an ongoing pandemics of coronavirus infection caused by SARS-CoV-2. Governments are taking a wide range of non-pharmaceutical interventions (NPIs) in response to the COVID-19 outbreak. These measures include interventions as stringent as strict lockdown to school closings, bars and restaurants closings, curfews and barrier gesture such as masks wearing and social distanciation. Hale et al. [1] built a stringency index that helps understanding how strong the measures over time were. However, this indicator does not allow to distinguish the effectiveness of each NPI, which is crucial to inform future preparedness response plans. Other approach such as Haug et al. [2] evaluate the effectiveness of various NPIs using regression methods on effective reproduction number in multiple countries. We preferably work at a country level so that the effect is not confounded by the various behaviors and adherence of the population. Finally, existing methods does not account for vaccination roll out, introduction of variants and the importance of weather [3]. We propose an approach which focusses on French data and combines estimation of epidemics dynamics models and estimation of NPIs effectiveness. The objective is twofold (i) develop a methodology based on population approach which allow to understand the effect of time-varying covariates on dynamical markers and (ii) inform which combination of NPIs could be as effective and less drastic than others.
Methods: We developed a multi-level model of the French COVID-19 epidemic at the regional level. We rely on a global extended Susceptible-Exposed-Infectious-Recovered (SEIR) model as a simplified representation of the average epidemic process, with the addition of region-specific random effects. The epidemics is modeled with a mechanistic model which is a non-linear mixed effects model. Using a two-step approach based on population Kalman filters [4], we non-parametrically inferred the relationship between transmission rate and NPIs introduction. We estimated the effect of non-pharmaceutical interventions adjusting for weather, vaccination and apparition of more transmissible variants. The proposed novel methodology, consisting in using population approach for epidemic models, allows to compare with satisfactory efficiency the effects of NPIs and derive informative parameters such as region-specific effective reproductive numbers and attack rates.
Results: Using hospitalization data from the SIVIC database over a period of one year (March 2020 to 2021), we demonstrated a non-null effect of all NPIs in reducing the transmission rate. First lockdown from March 17th to May 11th (78% [74%; 82%] reduction) was more efficient than second lockdown from October 30th to December 15th (54% [49%; 57%] reduction). Barrier gesture (46% [44%; 48%] reduction), and curfews at 6PM or 8PM with no statistically different effect (28% [25%; 31%] reduction for curfews at 8PM) were more effective than bars and restaurants closings (10% [8%; 13%] reduction), and school closings (7% [5%; 8%] reduction). We also demonstrated that the weather has a strong impact on spread of the epidemics: summer conditions decrease by 22% [21%; 24%] the transmission rate, winter conditions increase it by 10% [9%; 11%] . We find that variants are likely to increase the transmission by about 22% [15%; 28%] (consistent with [5]). Finally, we calculated the basic reproduction number (R0= 3.10 [2.95; 3.26], consistent with [6]) and the time-varying effective reproduction numbers. Attack rates is 25% [16%; 24%] of the French population infected as of March 28th 2021 (consistent with [7]).
Conclusions: There are two methodological novelties in this work: (i) using population approach for epidemics modeling (ii) the use of population Kalman filters to methodologically validate a relationship between outcome and time-varying covariates. Moreover, the use of mechanistic modeling has been shown to accurately estimate causal effect of treatment in observational studies [8], our similar setting here guarantees the interpretability of our estimates. From an epidemiological point of view, direct extension of our results allows to run (possibly region-specific) « what-if » scenario for future NPIs.
References:
[1] Thomas Hale, Noam Angrist, Rafael Goldszmidt , Beatriz Kira , Anna Petherick, Toby Phillips, Samuel Webster, Emily Cameron-Blake, Laura Hallas, Saptarshi Majumdar, and Helen Tatlow. (2021). “A global panel database of pandemic policies (Oxford COVID-19 Government Response Tracker).” Nature Human Behaviour. https://doi.org/10.1038/s41562-021-01079-8
[2] Haug, N., Geyrhofer, L., Londei, A., Dervic, E., Desvars-Larrive, A., Loreto, V., ... & Klimek, P. (2020). Ranking the effectiveness of worldwide COVID-19 government interventions. Nature human behaviour, 4(12), 1303-1312. https://doi.org/10.1038/s41562-020-01009-0
[3] Bukhari, Q., & Jameel, Y. (2020). Will coronavirus pandemic diminish by summer?. Https://doi.org/10.2139/ssrn.3556998
[4] Collin, A., Prague, M., & Moireau, P. (2020). Estimation for dynamical systems using a population-based Kalman filter-Applications to pharmacokinetics models. Submitted. https://hal.inria.fr/hal-02869347
[5] Davies, N. G., Abbott, S., Barnard, R. C., Jarvis, C. I., Kucharski, A. J., Munday, J. D., ... & Edmunds, W. J. (2021). Estimated transmissibility and impact of SARS-CoV-2 lineage B. 1.1. 7 in England. Science, 372(6538).
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[7] Nathanaël Hozé, Juliette Paireau, Nathanaël Lapidus, Cécile Tran Kiem, Henrik Salje, Gianluca Severi, Mathilde Touvier, Prof Marie Zins, Prof Xavier de Lamballerie, Daniel Lévy-Bruhl, Fabrice Carrat, Simon Cauchemez Monitoring the proportion of the population infected by SARS-CoV-2 using age-stratified hospitalisation and serological data: a modelling study, Lancet Public Health (2021) https://doi.org/10.1016/S2468-2667(21)00064-5
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