Stability Analysis of Predator-Prey System with Consuming Resource and Disease in Predator Species

The present study is concerned with formulating a predator-prey eco-epidemiological mathematical model assuming that an infection exists in the predator species. The two classes of predator species (susceptible and infected) compete for the same sources available in the environment with the predation option. It is assumed that the disease does not spread vertically. The proposed model is analyzed for the stability of the coexistence of the predators and prey. The fixed points are carried out, and the coexisting fixed point is studied in detail by constructing the Lyapunov function. The movement of species in search of food or protection in their habitat has a significant influence, examined through diffusion. The ecological influences of self-diffusion on the population density of both species are studied. It is theoretically proved that all the under consideration species can coexist in the same environment. The coexistence fixed point is discussed for both diffusive and non-diffusive cases. Moreover, a numerical scheme is constructed for solving time-dependent partial differential equations. The stability of the scheme is given, and it is applied for solving presently modified eco-epidemiological mathematical model with and without diffusion. The comparison of the constructed scheme with two exiting schemes, Backward in Time and Central in Space (BTCS) and Crank Nicolson, is also given in the form of plots. Finally, we run a computer simulation to determine the effectiveness of the proposed numerical scheme. For readers' convenience, a computational code for the proposed discrete model scheme may be made available upon request.