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Stationary Patterns of a Cross-Diffusion Epidemic Model

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  • Yongli Cai
  • Dongxuan Chi
  • Wenbin Liu
  • Weiming Wang

Abstract

We investigate the complex dynamics of cross-diffusion epidemic model. We first give the conditions of the local and global stability of the nonnegative constant steady states, which indicates that the basic reproduction number determines whether there is an endemic outbreak or not. Furthermore, we prove the existence and nonexistence of the positive nonconstant steady states, which guarantees the existence of the stationary patterns.

Suggested Citation

  • Yongli Cai & Dongxuan Chi & Wenbin Liu & Weiming Wang, 2013. "Stationary Patterns of a Cross-Diffusion Epidemic Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    • Handle: RePEc:hin:jnlaaa:852698
    DOI: 10.1155/2013/852698
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    Cited by:

    1. Victoria Chebotaeva & Paula A. Vasquez, 2023. "Erlang-Distributed SEIR Epidemic Models with Cross-Diffusion," Mathematics, MDPI, vol. 11(9), pages 1-18, May.
    2. Anita Triska & Agus Yodi Gunawan & Nuning Nuraini, 2023. "The Effects of the Susceptible and Infected Cross-Diffusion Terms on Pattern Formations in an SI Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.

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