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SUMMARYRatio-dependent models set up a challenging issue for their rich dynamics incomparison to preydependent 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 di erential equations describing the time evolution of susceptible and infected Tilapia ÿsh population and their predator, the Pelican. Existence and stability analysis of di erent equilibria of the system lead to di erent 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.

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A predator-prey model with disease in the prey population is proposed and analysed. The mode of disease transmission plays an important role in such dynamics. Keeping this factor in mind, we observe the dynamics of such a system for simple mass action incidence and standard incidence. Our observations indicate that the phenomenon of rarity or non-occurrence of chaos in our proposed model is well defined if the mode of disease transmission follows standard incidence. Moreover, using the method of Latin hypercube sampling, we show that the region of stability increases if the disease transmission follows the standard incidence law.