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Analysis on a diffusive SEI epidemic model with/without immigration of infected hosts

  • * Corresponding author: Guanghui Zhang

    * Corresponding author: Guanghui Zhang 
C. Lei is partially supported by NSF of China (No. 11671175, 11801232), the Priority Academic Program Development of Jiangsu Higher Education Institutions, the Natural Science Foundation of the Jiangsu Province (No. BK20180999) and the Foundation of Jiangsu Normal University (No. 17XLR008). G. Zhang is partially supported by NSF of China (No. 11501225) and the Fundamental Research Funds for the Central Universities (No. 5003011008). Y. Zhang is partially supported by NSF of China (No. 11701415)
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  • In this paper, we study a reaction-diffusion SEI epidemic model with/without immigration of infected hosts. Our results show that if there is no immigration for the infected (exposed) individuals, the model admits a threshold behaviour in terms of the basic reproduction number, and if the system includes the immigration, the disease always persists. In each case, we explore the global attractivity of the equilibrium via Lyapunov functions in the case of spatially homogeneous environment, and investigate the asymptotic behavior of the endemic equilibrium (when it exists) with respect to the small migration rate of the susceptible, exposed or infected population in the case of spatially heterogeneous environment. Our results suggest that the strategy of controlling the migration rate of population can not eradicate the disease, and the disease transmission risk will be underestimated if the immigration of infected hosts is ignored.

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

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