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Global dynamics of a fractional-order SIS epidemic model with media coverage

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Abstract

In this paper, a fractional-order SIS model with generalized transmission function and media coverage is proposed and analyzed. We first obtain the existence, uniqueness, and non-negativeness of solutions. The basic reproduction number \(R_{0}\) is calculated using the next generation matrix method, which serves as a threshold parameter. Precisely, if \(R_0<1\) then the disease-free equilibrium is globally asymptotically stable; if \(R_0>1\) then the endemic equilibrium is globally asymptotically stable. The results are obtained by employing the extension of the Lyapunov Direct Method for Caputo type fractional-order nonlinear systems. Numerical simulations are performed to demonstrate the main theoretic results and reveal the effect of media coverage on disease transmission.

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Notes

  1. A non-negative function f is \(\alpha \)-Barbalat if \(I^{\alpha }f\) bounded implies that f converges to zero, where

    $$\begin{aligned}{} & {} I^{\alpha }f(t)=\frac{1}{\Gamma (\alpha )}\int _0^t (t-s)^{\alpha -1}f(s)ds. \end{aligned}$$

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Funding

This work was supported partially by the Fund of Education Department of Yunnan Province of China (No. 2022J0986), China Scholarship Council (202206990025), the National Natural Science Foundation of China (No. 12071382), and NSERC of Canada (No. RGPIN-2019-05892).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Lihua Dai & Xianning Liu

  2. Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada

    Lihua Dai & Yuming Chen

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  1. Lihua Dai
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  2. Xianning Liu
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Correspondence to Yuming Chen.

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Dai, L., Liu, X. & Chen, Y. Global dynamics of a fractional-order SIS epidemic model with media coverage. Nonlinear Dyn 111, 19513–19526 (2023). https://doi.org/10.1007/s11071-023-08838-4

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