Qualitative Analysis and Control of Predator Switching on an Eco-Epidemiological Model with Prey Refuge and Harvesting

In this paper, an eco-epidemiological model has been studied where disease of prey population is modelled by a Susceptible–Infected (SI) scheme. Prey switching strategy is adopted by predator population when they are provided with two types of prey, susceptible and infected prey. However switching may happen due to several reasons such as shortage of preferable prey or risk in hunting the plentiful prey. In this work, we have proposed a prey–predator system with a particular type of switching functional response where a predator feeds on susceptible and infected prey but it switches from one type of prey to another when a particular prey population becomes lower. Both the species are supposed to be commercially viable and undergo constant non-selective harvesting. The stability aspects of the switching models around the infection-free state from a local as well as a global perspective has been investigated. Our aim is to study the role of harvesting and refuge of susceptible population on the dynamics of disease propagation and/or annihilation of an epidemiological model under consideration of switching phenomena. Numerical simulations are done to demonstrate our analytical results.