Model of predator-prey for interaction between agrotis segetum and Zea mays

In this study, a predator-prey model constructed to describe the interaction between Agrotis segetum as predator and Zea mays as prey, when Agrotis segetum infected with a disease. Agrotis segetum granulovirus which sprayed on the Zea mays makes Agrotis segetum get infected. In the end, the infected Agrotis segetum will die within six to twelve days. A four-dimensional mathematical model of ordinary nonlinear differential equations is formed by dividing the population into susceptible and infected predator (Agrotis segetum) population, susceptible and infected prey (Zea mays) population. The infection process is modelled with the Holling Type II response function. Local stability for the extinction and coexistence of equilibrium points is analyzed using the linearization method with the Jacobian matrix. From the model, there are three equilibrium points, all of them are stable with conditions. Numerical simulations are given to show how the disease in Agrotis segetum can influence the final size of Zea mays.