What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases?

Quentin Griette; Jacques Demongeot; Pierre Magal; Quentin Griette; Jacques Demongeot; Pierre Magal

doi:10.3934/mbe.2022025

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 1: 537-594. doi: 10.3934/mbe.2022025

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What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases?

1.
Université de Bordeaux, IMB, UMR 5251, Talence F-33400, France CNRS, IMB, UMR 5251, Talence F-33400, France
2.
Université Grenoble Alpes, AGEIS EA7407, La Tronche F-38700, France

Academic Editor：Hiroshi Nishiura

Received: 22 September 2021 Accepted: 05 November 2021 Published: 17 November 2021

The COVID-19 outbreak, which started in late December 2019 and rapidly spread around the world, has been accompanied by an unprecedented release of data on reported cases. Our objective is to offer a fresh look at these data by coupling a phenomenological description to the epidemiological dynamics. We use a phenomenological model to describe and regularize the reported cases data. This phenomenological model is combined with an epidemic model having a time-dependent transmission rate. The time-dependent rate of transmission involves changes in social interactions between people as well as changes in host-pathogen interactions. Our method is applied to cumulative data of reported cases for eight different geographic areas. In the eight geographic areas considered, successive epidemic waves are matched with a phenomenological model and are connected to each other. We find a single epidemic model that coincides with the best fit to the data of the phenomenological model. By reconstructing the transmission rate from the data, we can understand the contributions of the changes in social interactions (contacts between individuals) on the one hand and the contributions of the epidemiological dynamics on the other hand. Our study provides a new method to compute the instantaneous reproduction number that turns out to stay below $ 3.5 $ from the early beginning of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important factor in understanding the epidemic wave dynamics for COVID-19. The instantaneous reproduction number stays below $ 3.5 $, which implies that it is sufficient to vaccinate $ 71\% $ of the population in each state or country considered in our study. Therefore, assuming the vaccines will remain efficient against the new variants and adjusting for higher confidence, it is sufficient to vaccinate $ 75-80\% $ to eliminate COVID-19 in each state or country.
- SARS-CoV-2,
- social changes,
- transmission rate,
- identification of parameters
Citation: Quentin Griette, Jacques Demongeot, Pierre Magal. What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases?[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 537-594. doi: 10.3934/mbe.2022025

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Abstract

The COVID-19 outbreak, which started in late December 2019 and rapidly spread around the world, has been accompanied by an unprecedented release of data on reported cases. Our objective is to offer a fresh look at these data by coupling a phenomenological description to the epidemiological dynamics. We use a phenomenological model to describe and regularize the reported cases data. This phenomenological model is combined with an epidemic model having a time-dependent transmission rate. The time-dependent rate of transmission involves changes in social interactions between people as well as changes in host-pathogen interactions. Our method is applied to cumulative data of reported cases for eight different geographic areas. In the eight geographic areas considered, successive epidemic waves are matched with a phenomenological model and are connected to each other. We find a single epidemic model that coincides with the best fit to the data of the phenomenological model. By reconstructing the transmission rate from the data, we can understand the contributions of the changes in social interactions (contacts between individuals) on the one hand and the contributions of the epidemiological dynamics on the other hand. Our study provides a new method to compute the instantaneous reproduction number that turns out to stay below $ 3.5 $ from the early beginning of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important factor in understanding the epidemic wave dynamics for COVID-19. The instantaneous reproduction number stays below $ 3.5 $, which implies that it is sufficient to vaccinate $ 71\% $ of the population in each state or country considered in our study. Therefore, assuming the vaccines will remain efficient against the new variants and adjusting for higher confidence, it is sufficient to vaccinate $ 75-80\% $ to eliminate COVID-19 in each state or country.

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