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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.30 No.2

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Dynamics of an Improved SIS Epidemic Model

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2023, v.30 no.2, pp.203-220
https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.203
Reza Memarbashi
Milad Tahavor
Reza, M. , & Milad, T. (2023). Dynamics of an Improved SIS Epidemic Model. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 30(2), 203-220, https://doi.org/https://doi.org/10.7468/jksmeb.2023.30.2.203

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.

keywords
SIS epidemic model, adaptive host behavior, global stability, Bogdanov-Takens bifurcation

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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