Complex dynamics of a tri-tropic food chain model with disease in intermediate predator

Abstract

Disease in ecological system can not be ignored. An eco-epidemiological model with disease has a great importance to researchers as well as ecologists. The curiosity of this paper is to observe different dynamical behaviour of prey population for increasing the force of infection and half saturation constant. We have performed local stability analysis around the different biological feasible equilibria and the Hopf bifurcation analysis around the interior equilibrium point. We have derived the ecological as well as disease basic reproduction numbers and studied the community structure of the model system. We pay attention to chaotic dynamics which is produce by low level disease propagation in the intermediate predator. Our numerical simulation reveal that the three species food chain model with low level disease infection in intermediate predator induce chaos. The chaos enters into the stable focus for increasing the force of infection. We have also observed that chaos can be stabilize for increasing the half saturation constant(b1) for prey population. We conclude that the chaotic dynamics can be controlled by changing the force of infection as well as half saturation constant.