URL
https://royalsocietypublishing.org/doi/10.1098/rsos.202327
Type d’article
Article peer-reviewed
Thème
Infectiologie
Que retenir de cet article, en 1-2 phrases ?
The authors use a SEIR model to identify key epidemiological parameters of the COVID-19 epidemics in France between March 2020 and December 2020. The key feature of this study is the assumption of very general distributions of durations of the exposed (E) and infected (I) phases, and the authors provide explicit estimates of relevant parameters such as R0.
Objectifs de l’étude / Questions abordées
Most SEIR models are implemented as ODEs, which can be obtained as limits of Markovian processes. This implies that the duration of the exposed and the infected phases are implicitly assumed to be exponentially distributed. Here the authors use Volterra-type integral equations to describe the time course of the epidemics, given that distributions of exposed and infectious durations are known. The exposed duration is assumed to be between 2 and 4 days, while the infected phase duration has a bimodal distribution (between 3 and 4 days or between 8 and 12 days), accounting whether the individual has been isolated or not.
Méthode
Given the disease duration, the authors derive formulas to estimate the infection rate λ and the basal reproduction number R0. The infection rate is given by the (asymptotic) growth rate ρ of the number of infected individuals at the beginning of the epidemics, divided by the expected fraction of infected individuals within the non-susceptible population. R0 is given by the product between the infection rate and the expected duration of the infected phase. The authors show numerically that for a given R0 and infection duration, there can be different growth rates ρ, depending on the shape of the distribution of durations. The estimation method applies also to situations where there is a change in the infection rate, e.g. during lockdown phases, using piecewise approximations to the linear Volterra equations.
Résultats principaux
Using Santé Publique France data, the authors obtained estimates on infection doubling times and R0 before and during the first and second lockdowns for different French regions (Ile-de-France, Grand Est, Auvergne-Rhône-Alpes, Provence-Alpes-Côte-d’Azur).
Estimates for the delay between infection and admission to hospital or to ICU, or between infection and death were also obtained.
Different scenarios were explored to estimate the ratio of cumulative infections for the different regions. For instance, using a fatality ratio of 0.5%, more than 20% of the population was infected in Ile-de-France at the end of 2020.
Commentaire / brève évaluation, limites, ouvertures possibles
Unlike other papers that use nonlinear regression to estimate unknown parameters, an explicit dependence between unknown and known parameters is derived. Epidemiological models with memory have already been used in the context of the current COVID-19 epidemics. Notably, fixed phase durations lead to delay differential equations, and time-since-infection structure lead to Kermack-McKendrick models. Estimates on R0 and time to hospital admission and deaths are consistent with other estimates obtained with different methodologies (see Table 2 and 3). Models with memory are non-Markovian, meaning that their solutions depend also on the past, which is often unknown at the beginning of an epidemics. This limitation is also a strength because transient dynamics induced by changes in public health measures can be more fully taken into account. This can prove useful for short-term projections when introducing or removing restrictions, instead of the conventional “we need to wait for two weeks to see an effect”. Among simplifications made in the model, no population age structure was assumed. Exposed and infectious periods and time to hospital admission should likely depend on the age of individuals, as well as on other co-morbidity factors.