@article{Cantin2022, 
author = {Guillaume Cantin and Cristiana J. Silva and Arnaud Banos},
title = {Mathematical analysis of a hybrid model: Impacts of individual behaviors on the spreading of an epidemic},
year = {2022},
journal = {Networks and Heterogeneous Media},
volume = {17},
number = {3},
pages = {333-357},
keywords = {Hybrid model, networks, agent-based model, multi-scale, epidemics},
url = {https://www.sciopen.com/article/10.3934/nhm.2022010},
doi = {10.3934/nhm.2022010},
abstract = {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.}
}