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A diffusive dengue disease model with nonlocal delayed transmission

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  • Xu, Zhiting
  • Zhao, Yingying

Abstract

In this paper, we derive a nonlocal delayed and diffusive dengue transmission model with a spatial domain being bounded as well as unbounded. We first address the well-posedness to the initial-value problem for the model. In the case of a bounded spatial domain, we establish the threshold dynamics for the spatially heterogeneous system in terms of the basic reproduction number R0. Also, a set of sufficient conditions is further obtained for the global attractivity of the endemic steady state where all the parameters are spatially independent. In the case of an unbounded spatial domain, and when the coefficients are all constants, we show that there exist traveling wave solutions of the model. Numerical simulations are performed to illustrate our main analytic results.

Suggested Citation

  • Xu, Zhiting & Zhao, Yingying, 2015. "A diffusive dengue disease model with nonlocal delayed transmission," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 808-829.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:808-829
    DOI: 10.1016/j.amc.2015.08.079
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    References listed on IDEAS

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    1. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
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    Cited by:

    1. Wang, Wei & Ma, Wanbiao, 2018. "Hepatitis C virus infection is blocked by HMGB1: A new nonlocal and time-delayed reaction–diffusion model," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 633-653.
    2. Chen, Zhenwu & Xu, Zhiting, 2019. "A delayed diffusive influenza model with two-strain and two vaccinations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 439-453.

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