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Estimating the state of the COVID-19 epidemic in France using a model with memory
- Source :
- Royal Society Open Science, Royal Society Open Science, 2021, 8 (3), ⟨10.1098/rsos.202327⟩, Royal Society Open Science, Vol 8, Iss 3 (2021), Royal Society Open Science, The Royal Society, 2021, 8 (3), ⟨10.1098/rsos.202327⟩
- Publication Year :
- 2021
- Publisher :
- HAL CCSD, 2021.
-
Abstract
- International audience; 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.
- Subjects :
- 2019-20 coronavirus outbreak
Coronavirus disease 2019 (COVID-19)
01 natural sciences
law.invention
03 medical and health sciences
Volterra equations
model with memory
law
0101 mathematics
lcsh:Science
Research Articles
030304 developmental biology
0303 health sciences
Multidisciplinary
010102 general mathematics
COVID-19
Intensive care unit
3. Good health
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Geography
Susceptible individual
Hospital admission
Probability distribution
lcsh:Q
State (computer science)
Epidemic model
Mathematics
Demography
Subjects
Details
- Language :
- English
- ISSN :
- 20545703
- Database :
- OpenAIRE
- Journal :
- Royal Society Open Science, Royal Society Open Science, 2021, 8 (3), ⟨10.1098/rsos.202327⟩, Royal Society Open Science, Vol 8, Iss 3 (2021), Royal Society Open Science, The Royal Society, 2021, 8 (3), ⟨10.1098/rsos.202327⟩
- Accession number :
- edsair.doi.dedup.....503e7188f66446bebc9506b41ae468ff