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.
Citation: Guillaume Cantin, Cristiana J. Silva, Arnaud Banos. Mathematical analysis of a hybrid model: Impacts of individual behaviors on the spreading of an epidemic[J]. Networks and Heterogeneous Media, 2022, 17(3): 333-357. doi: 10.3934/nhm.2022010
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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Figures(7) / Tables(3)
Guillaume Cantin, Cristiana J. Silva, Arnaud Banos. Mathematical analysis of a hybrid model: Impacts of individual behaviors on the spreading of an epidemic[J]. Networks and Heterogeneous Media, 2022, 17(3): 333-357. doi: 10.3934/nhm.2022010
Timeline of the hybrid model
Social network generated over a finite set of agents, by running a Newman–Watts-Strogatz graph generation algorithm: each vertex represents an agent, and each edge models a social connection between two agents. Different colors correspond to the different epidemic sub-classes of the population. In such a social network, each agent can observe the types and the behaviors of its neighbors and can make decisions with respect to its observations
Basic reproduction number
Local stability condition of the endemic equilibrium
Model
A geographical network with 5 regions and the main connections. Individual displacements from one region to another occur along these connections
Numerical simulations of the hybrid model (8)-(13), for four relevant scenarios. Each sub-figure shows the number
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