Global Stability of a Delayed Eco-Epidemiological Model with Holling Type III Functional Response
In this paper, we consider an eco-epidemiological model with Holling type III functional response and a time delay representing the gestation period of the predator. In the model, it is assumed that the predator population suffers a transmissible disease. By means of Lyapunov functionals and Laselle’s invariance principle, sufficient conditions are obtained for the global stability of the endemic coexistence of the system.
KeywordsEco-epidemiological model Delay Laselle’s invariance principle Global stability
- 1.Beretta, E., Hara, T., Ma, W., Takeuchi, Y.: Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonlinear Anal. 47, 4017–4115 (2001)Google Scholar
- 9.Bairagi, N.: Direction and stability of bifurcating periodic solution in a delay-induced eco-epidemiological system. Int. J. Differ. Equ. 1–25 (2011)Google Scholar
- 14.Holling, C.S.: The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Entomol. Soc. Can. 45, 3–60 (1965)Google Scholar