Stability Analysis and Optimal Measure for Controlling Eco-Epidemiological Dynamics of Prey-Predator Model

An eco-epidemiological model representing the interactions between prey and predator populations affected by a disease in an ecosystem is presented. The model is governed by a five-dimensional nonlinear system of ordinary differential equations coupling both ecological and epidemiological features of interacting populations. The well-posedness of the model is established with respect to positivity and boundedness of solutions. Conditions for asymptotic stability of different equilibrium points are extensively investigated to determine the existence and coexistence of prey and predator species using local linearization and Lyapunov functions techniques. Additionally, the analysis of the model is extended to assess the effects of three time-dependent control functions, such as disease prevention, treatment and alternative resource for predator, on the population dynamics of the prey-predator coexistence in the system.