Influence of dispersal on the dynamics of an eco-epidemiological two-patch predator–prey model in deterministic and stochastic environment with ratio-dependent functional responses

Abstract

An eco-epidemiological predator–prey system containing two separate prey patches has been assessed in this paper with disease in prey population involving ratio-dependent functional responses and incidence rates. The model dynamics is studied by employing environmental perturbations to develop more genuine as well as realistic dynamics. This comprehensive study offers analytical insights into the positivity and uniform boundedness of the model system. Through numerical investigations, the study reveals the occurrence of local bifurcations, bistable regions, hysteresis phenomena, and parametric regions where saddle-node and transcritical bifurcation curves exist. Utilizing appropriate Lyapunov functions, it is demonstrated that a unique globally positive solution emerges from positive initial values. It has also been proved that the suggested model is stochastically ultimate bounded. Afterward, certain sufficient criteria illustrate the extermination of disease and persistence in mean. Notably, stochastic perturbations are shown to potentially impede disease propagation, suggesting strategies for dynamically controlling the spread of the illness. Additionally, the study derives a set of requirements for the existence of an ergodic stationary distribution. Numerous numerical simulations, conducted using MATLAB and MATCONT, effectively illustrate the theoretical findings.