Analysis of prey-predator interaction in the presence of alternative prey and toxici

In this work, a non-linear model has been proposed and analysed for a population to study prey-predator interactions in the presence of alternative prey and toxicity. The model is found to be well posed and solutions exist in a feasible region where equilibrium points are obtained and their stability investigated. It integrates the effect of toxicity in both prey and predator population. The equilibrium points are found to be locally stable and globally asymptotically stable under certain conditions. The model analysis shows that the immense amount of toxin the menace for both populations to go to extinction. The study proves that the higher the prey population size, the lower predator population size leading to its extinction.Finally, with the help of numerical simulations, it is observed that the increase of toxin tends to lower both populations. It is also shown that the toxicity can be controlled.