In this paper, we introduce a predator-prey with susceptible and infected prey model. The model includes the harvesting of infected prey. We assume that the predator avoids the infected prey. The susceptible prey becomes infected when they are in contact with infected prey and recover to be susceptible again. We find the equilibrium points and the conditions for their existence and stability. We also show the non-existence of periodic solutions. Numerical simulations explain the effect of the parameters on the behaviour of the three classes of populations. The simulations also give the region of the solution and guarantees that all solutions of the system lie within the region.

In this paper, a mathematical model consisting of the prey-predator model, prey is at risk of disease then become as susceptible and infected, while predator with different stage structure: immature and mature predator, the infected prey is at risk recover and harvest. The function of disease is proportionality function. At the beginning, the reasons of studying stage structure and the dynamic of nontrivial subsystems that may be lead to coexistence of these types of spices explain and by using Maple software, Jacobean matrix, Routh-Hurwitz criterion, Bendixson-Dulac criterion and Lyapunov function to prove the existence, periodic solution, local and global stability. We concluded that the survival for two preys are possible through the non-periodic solution due to the Bendixson-Dulac criterion, also the immature predator neither attack preys nor yield offspring's and die when the mature predator extinction, the global stability conditions for the original system be stretch of global stability conditions for subsystems. Finally, Mathematica software employs to describe some results in numerical simulation   http://dx.doi.org/10.25130/tjps.25.2020.040

In this paper, the dynamic of prey predator model was discussed when the relationship between them is functional response type III. In addition, when prey exposure to the disease as nonlinear function. Also the infected prey exposed to harvest as a nonlinear and as linear function. The bounded and positive solutions, periodic, conditions of equilibrium points and the stability were we discussed Some results were illustrated in numerical simulations, and show we can use the linear function of harvesting to control on the dices   http://dx.doi.org/10.25130/tjps.24.2019.079