Stability analysis of a prey-predator system involving holling`s response using back-stepping regimentation

In this paper, a mathematical model with back-stepping controller is proposed and analyzed to study the prey-predator interaction in which the prey population is infected. Investigation is made of the dynamical complexities of a prey-predator model with susceptible and infected (SI) prey including the non-selective prey harvesting with back-stepping controller. In this work, it has been assumed that in the interaction of susceptible and infected prey populations, predator predates on infected prey only. By constructing a suitable Lyapunov function, global asymptotic stability is established. Comparative analysis has been presented between the system without control and the system with control. Numerical examples are furnished and diagrams are presented which support our results.