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Global dynamics of a vector-borne disease model with infection ages and general incidence rates

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Abstract

A vector-borne disease model with general incidence rates is proposed and investigated in this paper, where both vector and host are stratified by infection ages in the form of a hyperbolic system of partial differential equations coupled with ordinary differential equations. The existence, uniqueness, nonnegativeness, and boundedness of solution of the model are studied for biologically reasonable purpose. Furthermore, a global threshold dynamics of the system is established by constructing suitable Lyapunov functionals, which is determined by the basic reproduction number \(\mathcal {R}_0\): the infection-free equilibrium is globally asymptotically stable when \(\mathcal {R}_0<1\) while the endemic equilibrium is globally asymptotically stable when \(\mathcal {R}_0>1\).

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Acknowledgements

X. Wang is supported by NSFC (no. 11771374), the CSC (201508410281), the Nanhu Scholar Program for Young Scholars of Xinyang Normal University, the Program for Science and Technology Innovation Talents in Universities of Henan Province (17HASTIT011), the Universities Young Teachers Program of Henan Province (2014GGJS-093). Y. Chen is supported by NSERC. S. Liu is supported by NSFC (no. 11471089).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China

    Xia Wang

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

    Yuming Chen

  3. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Shengqiang Liu

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  1. Xia Wang
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  2. Yuming Chen
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Correspondence to Xia Wang.

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Communicated by Geraldo Diniz.

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Wang, X., Chen, Y. & Liu, S. Global dynamics of a vector-borne disease model with infection ages and general incidence rates. Comp. Appl. Math. 37, 4055–4080 (2018). https://doi.org/10.1007/s40314-017-0560-8

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