Qualitative study of an eco-epidemiological model with anti-predator and migration presence

In this work, an environmental and epidemiological model has been formulated and analyzed, where it was assumed that there is a disease in the predator society of an incurable type and does not give the predator immunity that leads to the death of the affected predator in the end. On the other hand, it has been assumed that a healthy predator is only capable of predation according to a functional response ~Holling type -- IV, Also, two types of factors are considered behavior against predation and the group's defence to formulate our proposed model. In addition, immigration was taken into consideration for prey society, mathematically and biologically acceptable equilibrium points for this model were found, as well, these points were studied analytically and numerically to know the effect especially, the emigration and behavior against predation to keep both the two types.