Fear Effect on a Modified Leslie-Gower Predator-Prey Model with Disease Transmission in Prey Population

A model that represents the effect of fear on predator-prey interaction with disease transmission in the prey population is considered in this research. The modified Leslie-Gower predator-prey model is adopted here. The prey population is classified into susceptible and infected classes. The fear of prey to the presence of predators reduces the growth rate of susceptible prey as well as the rate of interaction among the prey population. These phenomena are represented by two fear parameters in the model. The first acts as the inhibitor of the growth of susceptible prey, while the second plays as the inhibitor of disease transmission. The existence and local stability of each equilibrium is investigated analytically. It is shown that fear controls the local stability of the two of six equilibrium points, the disease-free and the interior equilibrium point. Furthermore, it is shown that the model undergoes a Hopf bifurcation driven by the fear rate. Some numerical simulations are conducted to illustrate the analytical results.