Dynamics of harvested predator-prey system with disease in predator and prey in refuge

In this paper, a mathematical model of predator prey incorporating harvesting and disease in the predator and prey in refuge are developed and discussed. The harvesting of susceptible and infective predator is assumed to obey the Holling functional responses of type II and type I, respectively. According to the analysis, there exist five equilibrium points. The local stability property of each equilibrium point is presented. The analytical finding is then confirmed by some numerical simulations. Furthermore, we also investigate the effects of predator harvesting and prey refuge in the proposed model. It is found numerically that harvesting of susceptible predator using Holling functional responses type II can maintain the existence of all populations, and harvesting of infected predator can be used as a biological control to prevent the spread of the disease. Moreover, the prey in refuge can avoid the extinction of prey population.