On studying the spread model of the HIV/AIDS epidemic

A. I. Shashkin^a, M. V. Polovinkina^b, I. P. Polovinkin<sup>ac

a</sup> Voronezh State University, Voronezh, Russia
^b Voronezh State University of Engineering Technologies, Voronezh, Russia
^c Belgorod State National Research University (BelGU), Belgorod, Russia

Abstract: The aim of this work is to study sufficient conditions for the asymptotic stability of the stationary solution of the initial-boundary value problem for a system of nonlinear partial differential equations describing the growth and spread of the HIV/AIDS epidemic. The above-mentioned model takes into account not only the factors taken into account by classical models, but also includes migration processes.

Keywords: system of nonlinear partial differential equations, initial-boundary value problem, stationary solution, mathematical modeling, spread model of the HIV/AIDS epidemic, migration processes.

UDC: 517.444, 517.957.7, 517.951.9, 51-7

DOI: 10.22363/2413-3639-2024-70-4-691-701