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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access A

A note on the Lyapunov functions for SIR and SIRS epidemic model

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pp. 285–288Vol. 26Issue 2March 2023DOI: 10.47974/JIM-1486XML
Received:
05 Jan 2021
Accepted:
05 Dec 2021
Published Online:
01 Mar 2023
Article type:
A
Language:
EN
Article no.:
JIM-1486
Pages:
285–288

Abstract

O’Regan et al [Journal of Applied Mathematics Letters. 23 (2010) , pp. 446-448] constructed a function as a Lyapunov function for getting stability of endemic equilibrium of a mathematical model for an epidemic. In this paper, we prove the introduced function does not satisfy some of the conditions of Lyapunov function. At last, we correct the introduced function which can help us to reach the aims in stability.

Keywords

Subject Classifications

(2010) 37B2534D2392D30

References

[1] K. T. Alligood, T. D. Sauer and J. A. Yorke, CHAOS: An Introduction to Dynamical Systems, Springer-Verlag New York, 1996.
[2] W. O. Kermack, A.G. McKendrick Contributions to the mathematical theory of epidemics, Proc. Roy. Soc. A 115 (1927), 700-721.
[3] A. M. Lyapunov, The General Problem of the Stability of Motion, Taylor and Francis, London, 1992.
[4] S. M O’Regan, T. C. Kelly, A. Korobeinikov, M. J. A. O’Callaghan, A. V. Pokrovskii, Lyapunov functions for SIR and SIRS epidemic models, Appl. Math. Lett. 23 (2010), 446-448.
[5] N. Sharma, R. Singh, R. Pathak, Modeling of media impact with stability analysis and optimal solution of SEIRS epidemic model, Journal of Interdisciplinary Mathematics, 22 (2019), 1123-1156.
[6] R. Shi, X. Jiang, L. Chen, The effect of impulsive vaccination on an SIR epidemic model, Applied Mathematics and Computation, 212 (2009), 305-311.

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