Analysis of a nonautonomous eco‐epidemic diffusive model with disease in the prey. (8th December 2017)

• Record Type: Journal Article
• Authors: Pan, Min; Yang, Jing; Lin, Zhigui
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 5(2018)
• Page Start: 1796
• Page End: 1808
• Publication Date: 2017-12-08
• Subjects: disease -- infected prey -- reaction‐diffusion equations -- stability; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4706
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper deals with the behavior of positive solutions to a nonautonomous reaction‐diffusion system with homogeneous Neumann boundary conditions, which describes a two‐species predator‐prey system in which there is an infectious disease in prey. The sufficient condition on the permanence of the prey and the predator is established by combining the comparison principle with the results related to the corresponding ODE system. Some sufficient conditions for the spreading and vanishing of the disease are obtained. The global attractivity is also discussed by constructing a Lyapunov functional. Our results show that the disease is spreading if the transmission rate is suitably large, while if the transmission rate is small, the disease must be vanishing.