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Qualitative analysis on an SIS epidemic reaction-diffusion model with mass action infection mechanism and spontaneous infection in a heterogeneous environment

  • * Corresponding author: Chengxia Lei

    * Corresponding author: Chengxia Lei 

This work was partially supported by the National Natural Science Foundation of China (No. 11801232), the Priority Academic Program Development of Jiangsu Higher Education Institution, the Natural Science Foundation of the Jiangsu Province(No. BK20180999), the Foundation of Jiangsu Normal University (17XLR008)

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  • In the recent paper [29], a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with a mass action infection mechanism and linear birth-death growth with no flux boundary condition was studied. It has been recognized that spontaneous infection is an important factor in disease epidemics, in addition to disease transmission [43]. In this paper, we investigate the SIS model in [29] with spontaneous infection. We establish the global boundedness and uniform persistence in the general heterogeneous environment, and derive the global stability of the unique constant endemic equilibrium in the homogeneous environment case. Moreover, we analyze the asymptotic behavior of the endemic equilibrium when the movement (migration) rate of the susceptible or infected population tends to zero. Compared to the case that there is no spontaneous infection, our study suggests that spontaneous infection can enhance persistence of infectious disease, and hence the disease becomes more threatening.

    Mathematics Subject Classification: Primary: 35K57, 35J57, 35B40; Secondary: 92D25.


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