Research ArticleOpen Access

Global analysis of a network-based SIR epidemic model with a saturated treatment function

Xiaodan Wei

College of Computer Science, Dalian Minzu University, Dalian 116600, P. R. China

https://doi.org/10.1142/S1793524523501127Cited by:2 (Source: Crossref)

Abstract

In this paper, we study a network-based SIR epidemic model with a saturated treatment function in which a parameter $α$ is introduced to measure the extent of the effect of the infected being delayed for treatment. Our aim is to present a global analysis and to investigate how the parameter $α$ affects the spreading of diseases. Our main results are as follows: (1) In the case of the threshold value $R_{0} < 1$ , there exist two values of $α$ : $α_{c}$ and $α_{0}$ , such that the disease-free equilibrium is globally asymptotically stable when $α \leq α_{c}$ and multiple endemic equilibria exist when $α \geq α_{0}$ . This means that the parameter $α$ has an essential influence on the spreading of the disease. (2) In the case of the threshold value $R_{0} > 1$ , if the model has only one endemic equilibrium, then the unique endemic equilibrium is globally attractive. In this case, it is also proved that if $α \leq α_{c}$ , then the endemic equilibrium has only one, so is globally attractive. In addition, numerical simulation is performed to illustrate our theoretical results.

Keywords:

AMSC: 34D23, 34D45, 34C60, 82C23, 92B05

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Vol. 17, No. 06

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History

Received 19 June 2023

Revised 24 November 2023

Accepted 19 December 2023

Published: 4 January 2024

Information

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Global analysis of a network-based SIR epidemic model with a saturated treatment function

Abstract

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