Study of a Prey-Predator Dynamics Under the Simultaneous Effect of Toxicant and Disease

A mathematical model is proposed to study the simultaneous effects of toxicant and infectious disease on Lotka-Volterra prey-redator system. It is considered in the model that only the prey population is being affected by disease and toxicant both, and the susceptible and infected prey populations are being predated by predator. All the feasible equilibrium of the model are obtained and the condition for the existence of interior equilibrium point is also been determined. The criteria for both local stability and instability involving ecotoxicological and epidemiological parameters are derived. The global stability of the interior equilibrium point is discussed using Lyapunov's direct method. The results are compared with the case when environmental toxicant is absent. Moreover, threshold conditions depending upon toxicant, disease and predation related parameters for the non-linear stability of the model is determined. Finally, the numerical verifications of analytic results are carried out.