The effect of epidemic disease outbreaks on the dynamic behavior of a prey-predator model with Holling type II functional response

Abstract

We formulate and analyze the dynamism of the epidemic problem consisting of the prey-predator interaction with a susceptible–infected–susceptible (SIS) epidemic disease in prey species has been suggested for study in the present work. It is supposed that the disease was spread in two separate ways by direct contact between susceptible prey with infected prey and external sources of infective such as (water, food, contamination environment). The uniqueness and boundedness of the trajectory of this model has been discussed and the existence of all the fixed points (FPs) are determined. The local and global stability (LS and GS) conditions for all of the feasible (EPs) are established. Finally, to confirm the analytic results we solve the model by numerical simulation for different values of parameters and represent them graphically.