TY - JOUR

T1 - Estimates for solutions in one epidemic model with infinite distributed delay

AU - Skvortsova, Maria A.

N1 - Skvortsova, M.A. Estimates for solutions in one epidemic model with infinite distributed delay. Comput Math Model (2026). https://doi.org/10.1007/s10598-025-09664-6 The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).

PY - 2026/1/21

Y1 - 2026/1/21

N2 - 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.

AB - 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.

KW - Asymptotic stability

KW - Attraction set

KW - Delay differential equations

KW - Epidemic model

KW - Equilibrium point

KW - Estimates for solutions

KW - Infinite distributed delay

KW - Lyapunov–Krasovskii functional

UR - https://www.scopus.com/pages/publications/105028299904

UR - https://www.mendeley.com/catalogue/939ac87b-9675-3c84-9c4d-73b7d9e3ca1e/

U2 - 10.1007/s10598-025-09664-6

DO - 10.1007/s10598-025-09664-6

M3 - Article

JO - Computational Mathematics and Modeling

JF - Computational Mathematics and Modeling

SN - 1046-283X

ER -