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Dynamics of an Improved SIS Epidemic Model

Reza Memarbashi|Milad Tahavor
한국수학교육학회|2023.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제30권 제2호|pp. 203-220|DOI https://doi.org/10.7468/jksmeb.2023.30.2.203

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참고문헌

키워드

SIS epidemic modeladaptive host behaviorglobal stabilityBogdanov-Takens bifurcation.
주제분류수학

초록

A new modification of the SIS epidemic model incorporating the adaptive host behavior is proposed. Unlike the common situation in most epidemic models, this system has two disease-free equilibrium points, and we were able to prove that as the basic reproduction number approaches the threshold of 1, these two points merge and a Bogdanov-Takens bifurcation of codimension three occurs. The occurrence of this bifurcation is a sign of the complexity of the dynamics of the system near the value 1 of basic reproduction number. Both local and global stability of disease-free and endemic equilibrium point are studied.

Abstract

A new modification of the SIS epidemic model incorporating the adaptive host behavior is proposed. Unlike the common situation in most epidemic models, this system has two disease-free equilibrium points, and we were able to prove that as the basic reproduction number approaches the threshold of 1, these two points merge and a Bogdanov-Takens bifurcation of codimension three occurs. The occurrence of this bifurcation is a sign of the complexity of the dynamics of the system near the value 1 of basic reproduction number. Both local and global stability of disease-free and endemic equilibrium point are studied.

참고문헌 (27)

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