Abstract
The effect of diseases in ecological system is an important issue from mathematical and experimental point of view. A mathematical model for the susceptible Tilapia population, infected Tilapia population and their predator Pelican birds population is proposed and its essential mathematical features are analyzed. A threshold phenomenon, ‘basic reproductive ratio R 0’ of epidemic theory is defined. Local and global stability of the system around the biological feasible equilibria is presented. Conditions for persistence of the system are worked out. It is observed that if the level of the search rate of predator is low, the system around the positive interior equilibrium is stable. But the instability sets in with the increase of search rate level of predator. We conclude that for sustainability of Tilapia on Pelicans in the Salton sea, reduction of Tilapia population in a considerable amount is required. Numerical examples and computer simulations are also presented to validate our analytical findings.
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