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Qualitative analysis of reaction-diffusion host pathogen model with saturation incidence
  • Shuang Jian,
  • Yiming Liu,
  • Jianguo Gao
Shuang Jian
North Minzu University
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Yiming Liu
North Minzu University
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Jianguo Gao
North Minzu University

Corresponding Author:[email protected]

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Abstract

This paper studies the model of host pathogen with saturation and spatial heterogeneity. In the study of infectious diseases, the rate of saturation and spatial heterogeneity is an important factor affecting the spread of disease. First, since the solution semiflow of the model lacks of compactness, we prove the well-posedness of the model by verifying the smoothness of the semiflow. Then the basic reproduction number $R_0$ is determined, and its threshold effect is proved: when $R_0<1$, the system is globally asymptotically at the disease-free equilibrium; when $R_0>1$, we give the solution of the system that not only is uniformly persistent but also has a positive steady state. In addition, we analyze that the critical condition of $R_0=1$, that is, the global asymptotic stability of the disease free steady state remains true. The conclusions obtained in this paper can play a certain supporting role in the prevention and treatment of infectious diseases.