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Global stability of a diffusive HCV infections epidemic model with nonlinear incidence

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Abstract

In this paper, we study a diffusive HCV infections epidemic model with nonlinear incidence rate and analyze the stability of the two kinds of equilibria. By constructing various Lyapunov functions, we prove that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number \(R_{0}< 1\) and the endemic equilibrium is globally asymptotically stable when the basic reproduction number \(R_{0} >1\). Finally, some numerical simulations are given to confirm the theoretical analysis. The results show that when other parameters are the same, the linear infection rate and the non-linear infection rate have different effects on disease spread.

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Acknowledgements

This work is supported by the Natural Science Foundation of China (11672074), and the Natural Science Foundation of Fujian Province (2018J01655).

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Authors and Affiliations

  1. College of Mathematics and Informatics, Fujian Normal University, Fuzhou, 350117, Fujian, People’s Republic of China

    Ruyan Su & Wensheng Yang

  2. FJKLMAA and Center for Applied Mathematics of Fujian province (FJNU), Fuzhou, 350117, Fujian, People’s Republic of China

    Wensheng Yang

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  1. Ruyan Su
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  2. Wensheng Yang
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Correspondence to Wensheng Yang.

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Su, R., Yang, W. Global stability of a diffusive HCV infections epidemic model with nonlinear incidence. J. Appl. Math. Comput. 68, 2685–2697 (2022). https://doi.org/10.1007/s12190-021-01637-3

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