Spatiotemporal dynamics for an impulsive eco-epidemiological system driven by canine distemper virus

Canine distemper is a highly contagious and incurable viral disease to the family Canidae over the world. The objective of this work is mathematical and computational analysis of an impulsive eco-epidemiological reaction-diffusion system on the interplay of rabbits and foxes driven by canine distemper virus. According to the theory of non-autonomous system, we establish conditions for the prevailing and extinction of canine distemper under impulsive controls. Further, the existence and globally asymptotic stability of a unique positive periodic solution are verified by virtue of Brouwer’s fixed point theorem and auxiliary function. Additionally, three numerical examples are presented to illustrate the theoretical results, and it is found that strong impulsive harvesting control of the infected population leads to the extinction of the infectious disease.