Numerical modeling of the epidemic process taking into account time- and place-local contacts of individuals

N. V. Pertsev   ; K. K. Loginov

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 702-728

Résumé

A modification of SEIRS model of the epidemic process taking into account time- and place-local contacts of individuals is developed. The model on the base of a high-dimensional system of differential equations with two delays, supplemented with initial data, is constructed. The correctness of model is studied. Conditions for the asymptotic stability of the trivial equilibrium state, which reflects the solution of the model in which there is no infection, is established. An expression for the infection spread coefficient is obtained. To solve the model numerically, a semi-implicit Euler scheme is used. The results of computational experiments with the model are presented. The significant influence of the heterogeneity of cohorts of susceptible and infectious individuals on the dynamics of the epidemic process is shown. The results of fitting solutions to the original high-dimensional model using its simpler modification are presented.

Détail

Keywords: epidemiology, SEIRS model, infection spread coefficient, differential equations with delay, asymptotic stability, computational experiment.
Mots-clés : semi-implicit Euler scheme

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