Modelling the Spread of Infectious Diseases Taking Into Account a Two-Factor Taxis

The paper studies a mathematical model of a mass infectious disease, written as a system of nonlinear reaction-diffusion-advection equations. The spatiotemporal interaction of two population groups is considered: susceptible to infection and infected. Local interaction determining the mutual transition from one group to another and migration flows caused by diffusion and directed migration are taken into account. The modeling is carried out without taking into account the birth and mortality rates of the population. For spatial approximation of the problem, the finite difference method based on shifted grids was used. Computer experiments were carried out in the MATLAB system. The study established the existence of an analytical solution corresponding to the stationary distribution of both population groups. Using computational experiments, parametric dependencies were established that affect the formation of epidemiological structures and the ratio of the shares of the infected and healthy population.

Keywords

math modeling; epidemic; compartmental model; nonlinear PDEs; taxis.

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