A Delayed Eco-Epidemiological Model with Weak Allee Effect and Disease in Prey

Abstract

In this paper, we have proposed and analyzed a mathematical model for the eco-epidemiological system with disease in prey population, placing particular emphasis on the effects of an incubation time delay and the influence of weak Allee effect on the growth of the predator population. We investigate basic properties of the proposed model including positivity, boundedness, uniform persistence and the stability of the biologically feasible equilibrium points. Using the time delay as bifurcation parameter, we explore the stability of the interior equilibrium point and observe that Hopf bifurcation can occur when the incubation time delay crosses some threshold value. We have identified the stability regions associated with the extinction of populations, stability of the steady states, and high-periodic oscillations in disease transmission. Analytical findings are supported by numerical illustrations that demonstrate the behavior of the proposed model in different dynamical regimes. Stability criteria for the biologically feasible equilibrium points were obtained and validated with numerical simulations. We found most sensitive system parameters using the PRCC sensitivity analysis. We observe that our model simulation exhibits high-periodic oscillations due to the increasing value of time delay parameter [Formula: see text] and the disease transmission rate [Formula: see text].