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Estimates for solutions in one epidemic model with infinite distributed delay.

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Title: Estimates for solutions in one epidemic model with infinite distributed delay.
Authors: Skvortsova, Maria A.1,2 (AUTHOR) sm-18-nsu@yandex.ru
Source: Computational Mathematics & Modeling. Jun2026, Vol. 37 Issue 2, p240-256. 17p.
Subjects: Differential equations, Lyapunov functions, Global asymptotic stability, Communicable diseases, At-risk people, Epidemiological models
Abstract: 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. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mathematics & Modeling is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computational Mathematics & Modeling is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10598-025-09664-6
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      – Code: eng
        Text: English
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      – SubjectFull: Differential equations
        Type: general
      – SubjectFull: Lyapunov functions
        Type: general
      – SubjectFull: Global asymptotic stability
        Type: general
      – SubjectFull: Communicable diseases
        Type: general
      – SubjectFull: At-risk people
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      – SubjectFull: Epidemiological models
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      – TitleFull: Estimates for solutions in one epidemic model with infinite distributed delay.
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              Text: Jun2026
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