Backward bifurcation, oscillations and chaos in an eco-epidemiological model with fear effect. (1st January 2019)

• Record Type: Journal Article
• Authors: Sha, Amar; Samanta, Sudip; Martcheva, Maia; Chattopadhyay, Joydev
• Is Part Of: Journal of biological dynamics. Volume 13(2019)Supplement 1
• Page Start: 301
• Page End: 327
• Publication Date: 2019-01-01
• Subjects: Eco-epidemiological model -- fear factor -- stability -- bi-stability -- Hopf bifurcation -- backward bifurcation -- Chaos -- Lyapunov exponent; 92D30; Biology -- Mathematical models -- Periodicals; 570.15118
• DOI: 10.1080/17513758.2019.1593525
• Languages: English
• ISSNs: 1751-3758

Abstract

Abstract : This paper considers an eco-epidemiological model with disease in the prey population. The disease in the prey divides the total prey population into two subclasses, susceptible prey and infected prey. The model also incorporates fear of predator that reduces the growth rate of the prey population. Furthermore, fear of predator lowers the activity of the prey population, which reduces the disease transmission. The model is well-posed with bounded solutions. It has an extinction equilibrium, susceptible prey equilibrium, susceptible prey-predator equilibrium, and coexistence equilibria. Conditions for local stability of equilibria are established. The model exhibits fear- induced backward bifurcation and bistability. Extensive numerical simulations show the presence of oscillations and occurrence of chaos due to fear induced lower disease transmission in the prey population.