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In this paper, we introduce a prey-predator model where the susceptible prey becomes infective. We consider the case where the predator will consume the unhealthy prey and at the same time the healthy prey will be harvested. Conditions for the stability of the equilibrium points were obtained. We show when the disease rate is increasing, the trajectories of the general model approach the equilibrium in which all population survive. Also we show that the threshold of harvesting is important because when it approach the size of prey this make the disease increasing so we must start the harvesting so early to control the disease and not become epidemic. [ABSTRACT FROM AUTHOR]

In [1], a delayed three-species intraguild predation (IGP) model was considered. This particular tri-trophic community module includes a predator and its prey which share a common basal resource for their sustenance [3]. Here, it is assumed that in the absence of predation, the growth of the basal resource follows the delayed logistic equation. Without delay time, the IGP model in [1] reduces to the system considered in [7] where it was shown that IGP may induce chaos even if the functional responses are linear. Meanwhile, in [2] the delayed IGP model in [1] was generalized to include harvesting. Under the assumption that the basal resource has some economic value, a constant harvesting term on the basal resource was incorporated. However, both models in [1] and [2] use the delay time as the main parameter. In this research, we studied the delayed IGP model in [1] with the addition of linear harvesting term on each of the three species. The dynamical behavior of this system is examined using the harvesting rates as main parameter. In particular, we give conditions on the existence, stability, and bifurcations of equilibrium solutions of this system. This allows us to better understand the effects of harvesting in terms of the survival or extinction of one or more species in our system. Numerical simulations are carried out to illustrate our results. In fact, we show that the chaotic behavior in [7] unfolds when the harvesting rate parameter is varied. [ABSTRACT FROM AUTHOR]