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A periodic and diffusive predator-prey model with disease in the prey

  • * Corresponding author: Guangping Hu

    * Corresponding author: Guangping Hu 
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  • In this paper, we are concerned with a time periodic and diffusivepredator-prey model with disease transmission in the prey. Firstwe consider a $ SI $ model when the predator species is absent. Byintroducing the basic reproduction number for the $ SI $ model, weshow the sufficient conditions for the persistence and extinctionof the disease. When the presence of the predator is taken intoaccount, a number of sufficient conditions for the co-existence ofthe prey and predator species, the global extinction of predatorspecies and the global extinction of both the prey and predatorspecies are given.

    Mathematics Subject Classification: Primary: 35K57, 35B40; Secondary: 92D25, 92D30.


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