Estimating the state of the COVID-19 epidemic in France using a model with memory

Abstract

In this paper, we use a deterministic epidemic model with memory to estimate the state of the COVID-19 epidemic in France, from early March until mid-December 2020. Our model is in the SEIR class, which means that when a susceptible individual (S) becomes infected, he/she is first exposed (E), i.e. not yet contagious. Then he/she becomes infectious (I) for a certain length of time, during which he/she may infect susceptible individuals around him/her, and finally becomes removed (R), that is, either immune or dead. The specificity of our model is that it assumes a very general probability distribution for the pair of exposed and infectious periods. The law of large numbers limit of such a model is a model with memory (the future evolution of the model depends not only upon its present state, but also upon its past). We present theoretical results linking the (unobserved) parameters of the model to various quantities which are more easily measured during the early stages of an epidemic. We then apply these results to estimate the state of the COVID-19 epidemic in France, using available information on the infection fatality ratio and on the distribution of the exposed and infectious periods. Using the hospital data published daily by Santé Publique France, we gather some information on the delay between infection and hospital admission, intensive care unit (ICU) admission and hospital deaths, and on the proportion of people who have been infected up to the end of 2020.

The stochastic dynamics of early epidemics: probability of establishment, initial growth rate, and infection cluster size at first detection

“…A constant infectiousness over the duration of an individual’s infection leads to the predominantly used framework of ordinary differential equations (ODEs), while non-constant infectiousness can be captured by a partial differential equation. In addition to the added biological realism, a time-varying infectiousness of infected individuals can also properly capture the dynamical consequences of abrupt changes in transmission rate [ 6 , 8 ]. This is not possible with an ODE framework [ 9 ].…”

Dynamic Analysis of a Stochastic SEQIR Model and Application in the COVID-19 Pandemic

“…We also set the range of α, which represents the rate of exposure to infection according to [32]. Because the average recovery period in France is approximately 13.6 days [33], the parameter η is set to 1/13.6 ≈ 0.0735. According to [34], we take the average recovery period in Italy as 13.15 days; thus, in this case, we set the parameter η � 1/13.15 ≈ 0.076. e recovery rate of the UK, β, b 1 , b 2 , and c are estimated by the least square method.…”

Estimating data-driven COVID-19 mitigation strategies for safe university reopening

“…Whereas most epidemic models have been developed based on Markovian processes with transition times following exponential distributions. Such unrealistic assumptions could impair the accuracy of model predictions, and non-Markovian models that accept arbitrary distributions for the transition times of the individual between different compartments have started to draw attention from scholars [17][18][19].…”