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Article Dans Une Revue Networks and Heterogeneous Media Année : 2022

Mathematical analysis of a hybrid model: Impacts of individual behaviors on the spreading of an epidemic

Résumé

In this paper, we investigate the well-posedness and dynamics of a class of hybrid models, obtained by coupling a system of ordinary differential equations and an agent-based model. These hybrid models intend to integrate the microscopic dynamics of individual behaviors into the macroscopic evolution of various population dynamics models, and can be applied to a great number of complex problems arising in economics, sociology, geography and epidemiology. Here, in particular, we apply our general framework to the current COVID-19 pandemic. We establish, at a theoretical level, sufficient conditions which lead to particular solutions exhibiting irregular oscillations and interpret those particular solutions as pandemic waves. We perform numerical simulations of a set of relevant scenarios which show how the microscopic processes impact the macroscopic dynamics.
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Dates et versions

hal-03618929 , version 1 (24-03-2022)

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Guillaume Cantin, Cristiana J. Silva, Arnaud Banos. Mathematical analysis of a hybrid model: Impacts of individual behaviors on the spreading of an epidemic. Networks and Heterogeneous Media, 2022, 17 (3), pp.333-357. ⟨10.3934/nhm.2022010⟩. ⟨hal-03618929⟩
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