Abstract
In the present article, we make an attempt to investigate the effect of two time delays, logistic delay and gestation delay, on an eco-epidemiological model. In the proposed model, strong Allee effect is considered in the growth term of the prey population. We incorporate two time lags and inspect elementary mathematical characteristic of the proposed model such as boundedness, uniform persistence, stability and Hopf-bifurcation for all possible combinations of both delays at the interior equilibrium point of the system. We observe that increase in gestation delay leads to chaotic solutions through the limit cycle. We also observe that the Allee effect play a major role in controlling the chaos. We execute several numerical simulations to illustrate the proposed mathematical model and our analytical findings.