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

Xiaoling Li; Guangping Hu; Zhaosheng Feng; Dongliang Li

doi:10.3934/dcdss.2017021

Article Contents

2017, Volume 10, Issue 3: 445-461. Doi: 10.3934/dcdss.2017021

This issue Previous Article State transformations of time-varying delay systems and their applications to state observer design Next Article Almost periodic solution for neutral functional dynamic equations with Stepanov-almost periodic terms on time scales

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

1.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
2.
School of Mathematical and Statistical Sciences, University of Texas-Rio Grande Valley, Edinburg, TX 78539, USA
3.
College of Atmospheric Science, Nanjing University of Information Science and Technology, Nanjing 210044, China

^* Corresponding author: Guangping Hu
^* Corresponding author: Guangping Hu

Received: November 30, 2015

Revised: September 30, 2016

Published: May 2017

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Abstract

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.

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

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