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Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices

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  • Liao, Shu
  • Wang, Jin

Abstract

In this paper, we study the global dynamics of a class of mathematical epidemiological models formulated by systems of differential equations. These models involve both human population and environmental component(s) and constitute high-dimensional nonlinear autonomous systems, for which the global asymptotic stability of the endemic equilibria has been a major challenge in analyzing the dynamics. By incorporating the theory of Volterra–Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis and obtain new results on some three- and four-dimensional model systems. In addition, we conduct numerical simulation to verify the analytical results.

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  • Liao, Shu & Wang, Jin, 2012. "Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 966-977.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:7:p:966-977
    DOI: 10.1016/j.chaos.2012.03.009
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    1. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
    2. D. Scott Merrell & Susan M. Butler & Firdausi Qadri & Nadia A. Dolganov & Ahsfaqul Alam & Mitchell B. Cohen & Stephen B. Calderwood & Gary K. Schoolnik & Andrew Camilli, 2002. "Host-induced epidemic spread of the cholera bacterium," Nature, Nature, vol. 417(6889), pages 642-645, June.
    3. Tewa, Jean Jules & Dimi, Jean Luc & Bowong, Samuel, 2009. "Lyapunov functions for a dengue disease transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 936-941.
    4. Li, Guihua & Wang, Wendi & Jin, Zhen, 2006. "Global stability of an SEIR epidemic model with constant immigration," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 1012-1019.
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    Cited by:

    1. Xueyong Zhou, 2022. "Dynamical Analysis of a Stochastic Cholera Epidemic Model," Mathematics, MDPI, vol. 10(16), pages 1-19, August.
    2. Pengcheng Shao & Stanford Shateyi, 2021. "Stability Analysis of SEIRS Epidemic Model with Nonlinear Incidence Rate Function," Mathematics, MDPI, vol. 9(21), pages 1-15, October.

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