Impact of Directed Migration on the Incidence of the Population in the SIS Model

Mathematical model of the spread of an infectious disease, written in the form of a system of nonlinear equations of parabolic type, is considered. The spatial and temporal evolution of the densities of two population groups is studied: susceptible to infection and infected. Mutual transition from one group to another is allowed. The dynamics of densities are determined by migration flows and local interaction. Migration flows are caused by the diffusion of the population across the area and directed migration caused by some stimulus. The modeling is carried out taking into account the mortality of infected people. Computational experiments determined the role of migration factors in epidemiological scenarios.

Keywords

mathematical modelling; epidemic; compartmental model; nonlinear PDEs; taxis.

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