Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1849-1860.

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Analysis of a Reaction-Diffusion Epidemic Model with Horizontal Transmission and Environmental Transmission

Zhenxiang Hu,Linfei Nie*()   

  1. School of Mathematics and System Sciences, Xinjiang University, Urumqi 830017
  • Received:2022-01-07 Online:2022-12-26 Published:2022-12-16
  • Contact: Linfei Nie;
  • Supported by:
    the NSFC(11961066);the Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01E12);the Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01C070)


In this paper, a reaction-diffusion epidemic model with horizontal transmission and environmental transmission is proposed. The well posedness of this model is investigated, including the global existence and uniform boundedness of the solution. Furthermore, the basic reproduction number ${\mathcal R}_{0}$ is defined by the spectral radius of the next generation operator. The threshold dynamics of the model is studied by using monotone dynamical systems theory and uniform persistence theory.

Key words: Reaction-diffusion model, Environmental transmission and horizontal transmission, Standard incidence, Basic reproduction number, Uniform persistence

CLC Number: 

  • O175.21