Stability Regions and Bifurcation Analysis of a Delayed Predator-Prey Model Caused from Gestation Period

Abstract

We consider a saturated predator-prey system with delayed time. The system is motivated by natural disease management using the interactions between the original and the treated species populations, such as Aedes aegypti and Wolbachia mosquitoes, fertile and infertile pests as a pesticide’s effect, uninfected and infected cancer cells by an oncolytic virus, and so forth. The delayed time shows the gestation effect of the treated populations where the impact on the stability of the unique positive equilibrium point of the system will be studied. We obtain the exact formula of the equilibrium point where it is asymptotically stable for the nondelay case. The stability region of the nonzero solution is given in parameter space following the Pontryagin criteria. Furthermore, some conditions, such that for delay case this solution is conditionally stable, are also provided in this study.