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<p>In the paper we consider an epidemic model described by a&#xa0;system of differential equations with infinite distributed delay. The model consists of three equations, each of which describes changes in the numbers of susceptible individuals, infected individuals, and recovered individuals, respectively. The asymptotic stability of equilibrium points is studied, which correspond to the case of complete recovery of individuals and the case when infected individuals are always present in the system. Estimates for the initial numbers of individuals are indicated, in which they fully recover, or the number of infected individuals tends to a&#xa0;constant value. Estimates for solutions to the system are established, that characterize the rate of infection or the rate of recovery of the entire group of individuals. The results are obtained using Lyapunov–Krasovskii functionals.</p>

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Estimates for solutions in one epidemic model with infinite distributed delay

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Maria A. Skvortsova

摘要

In the paper we consider an epidemic model described by a system of differential equations with infinite distributed delay. The model consists of three equations, each of which describes changes in the numbers of susceptible individuals, infected individuals, and recovered individuals, respectively. The asymptotic stability of equilibrium points is studied, which correspond to the case of complete recovery of individuals and the case when infected individuals are always present in the system. Estimates for the initial numbers of individuals are indicated, in which they fully recover, or the number of infected individuals tends to a constant value. Estimates for solutions to the system are established, that characterize the rate of infection or the rate of recovery of the entire group of individuals. The results are obtained using Lyapunov–Krasovskii functionals.