Analysis of a prey-predator model with an epidemic disease in predators

In this paper, a Prey-Predator model with an epidemic disease in predators, a Holling type II functional response, and a saturated incidence rate is studied. The system's equilibria and the basic reproduction number of the model, R_۰, are obtained. If R_۰<۱, the disease-free equilibrium is locally asymptotically stable, and if R_۰>۱, the positive equilibrium is locally asymptotically stable. We studied the transcritical bifurcation using the Sotomayor theorem. As the infection rate increases, the system's asymptotic behavior near the disease-free equilibrium approaches that of the positive equilibrium, and the system undergoes a transcritical bifurcation. We examined the sensitivity index for the basic reproduction number R_۰. Finally, we perform numerical simulations to support our theoretical results.

کلیدواژه ها:

Prey-predator model ، Saturated incidence rate ، Stability ، Transcritical bifurcation ، Holling functional response type II