Dynamics of a predator-prey model incorporating prey refuge, predator infection and harvesting

We investigate the dynamics of a predator-prey model with infectious disease in the predator species. The population is divided into three classes, namely prey, susceptible predator and infective predator. We also consider a prey refuge and predator harvesting in the model. The predation rate and the growth rate due to predation of the infective predator are assumed to be smaller than those of susceptible predator. It is found that the model has five equilibrium points, i.e., the extinction of all population equilibrium, the predator extinction equilibrium, the susceptible predator extinction equilibrium, the infective predator extinction equilibrium and the coexistent equilibrium. The extinction of all population equilibrium is unstable, while other equilibrium points are asymptotically stable with certain condition. Such analytical finding is confirmed by some numerical simulations.