Stability Analysis of an Eco-Epidemiological Model with Time Delay and Holling Type-III Functional Response (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, an eco-epidemiological model with diseases in thepredator and Holling type-III functional response is analyzed. A time delaydue to the gestation of the predator is considered in this model. By analyzingthe corresponding characteristic equations, the local stability of each of feasibleequilibria and the existence of Hopf bifurcations at the disease-free equilibriumand the endemic-coexistence equilibrium are established respectively. By usingLyapunov functionals and LaSalle’s invariance principle, sufficient conditionsare obtained for the global stability of the predator-extinction equilibrium, thedisease-free equilibrium and the endemic-coexistence equilibrium respectively.Finally, numerical simulations are performed to illustrate the theoretical results.