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Traveling Wave Solutions for a Delayed SIRS Infectious Disease Model with Nonlocal Diffusion and Nonlinear Incidence

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  • Xiaohong Tian
  • Rui Xu

Abstract

A delayed SIRS infectious disease model with nonlocal diffusion and nonlinear incidence is investigated. By constructing a pair of upper‐lower solutions and using Schauder′s fixed point theorem, we derive the existence of a traveling wave solution connecting the disease‐free steady state and the endemic steady state.

Suggested Citation

  • Xiaohong Tian & Rui Xu, 2014. "Traveling Wave Solutions for a Delayed SIRS Infectious Disease Model with Nonlocal Diffusion and Nonlinear Incidence," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:795320
    DOI: 10.1155/2014/795320
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    References listed on IDEAS

    as
    1. Xu, Rui & Ma, Zhien, 2009. "Stability of a delayed SIRS epidemic model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2319-2325.
    2. Paul Fife, 2003. "Some Nonclassical Trends in Parabolic and Parabolic-like Evolutions," Springer Books, in: Markus Kirkilionis & Susanne Krömker & Rolf Rannacher & Friedrich Tomi (ed.), Trends in Nonlinear Analysis, chapter 3, pages 153-191, Springer.
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