A ratio-dependent eco-epidemiological model of the Salton sea

Abstract

Ratio-dependent models set up a challenging issue for their rich dynamics incomparison to prey-dependent models. Little attention has been paid so far to describe the importance of transmissible disease in ecological situation by considering ratio-dependent models. In this paper, by assuming the predator response function as ratio-dependent, we consider a model of a system of three non-linear differential equations describing the time evolution of susceptible and infected Tilapia fish population and their predator, the Pelican. Existence and stability analysis of different equilibria of the system lead to different realistic thresholds in terms of system parameters. The condition for extinction of the species is also worked out. Our analytical and numerical studies may be helpful to chalk out suitable control strategies for minimizing the extinction of the Pelicans. We also suggest that supply of alternative food source for predator population may be used as a possible solution to save the predator from their extinction.