Global dynamics and bifurcations in a SIRS epidemic model with a nonmonotone incidence rate and a piecewise-smooth treatment rate Article Swipe

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YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.3934/dcdsb.2021195

In this paper, we analyze a SIRS epidemic model with a nonmonotone incidence rate and a piecewise-smooth treatment rate. The nonmonotone incidence rate describes the "psychological effect": when the number of the infected individuals (denoted by ) exceeds a certain level, the incidence rate is a decreasing function with respect to . The piecewise-smooth treatment rate describes the situation where the community has limited medical resources, treatment rises linearly with until the treatment capacity is reached, after which constant treatment (i.e., the maximum treatment) is taken.Our analysis indicates that there exists a critical value for the infective level at which the health care system reaches its capacity such that:(i) When , the transmission dynamics of the model is determined by the basic reproduction number : separates disease persistence from disease eradication. (ii) When , the model exhibits very rich dynamics and bifurcations, such as multiple endemic equilibria, periodic orbits, homoclinic orbits, Bogdanov-Takens bifurcations, and subcritical Hopf bifurcation.

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Type: article
Language: en
Landing Page: https://doi.org/10.3934/dcdsb.2021195
OA Status: diamond
Cited By: 5
References: 27
Related Works: 10
OpenAlex ID: https://openalex.org/W3190599174

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DOI: https://doi.org/10.3934/dcdsb.2021195

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Title: Global dynamics and bifurcations in a SIRS epidemic model with a nonmonotone incidence rate and a piecewise-smooth treatment rate

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Type: article

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Language: en

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Publication year: 2021

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Publication date: 2021-08-13

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Authors: Qin Pan, Jicai Huang, Qihua Huang

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Landing page: https://doi.org/10.3934/dcdsb.2021195

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Concepts: Mathematics, Incidence (geometry), Piecewise, Combinatorics, Arithmetic, Geometry, Mathematical analysis

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Cited by: 5

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