Spread of a disease and its effect on population dynamics in an eco-epidemiological system

• We try to understand how disease spread and its effect on population dynamics.
• We study the dynamical behavior of the model to explore the possibility of chaos.
• We identify backward Hopf-bifurcation when μ1μ1 is treated as bifurcation parameter.
• We show period doubling route to chaos when r is treated as bifurcation parameter.
• We discuss the implications of this result for disease eradication and its control.

In this paper, an eco-epidemiological model with simple law of mass action and modified Holling type II functional response has been proposed and analyzed to understand how a disease may spread among natural populations. The proposed model is a modification of the model presented by Upadhyay et al. (2008) [1]. Existence of the equilibria and their stability analysis (linear and nonlinear) has been studied. The dynamical transitions in the model have been studied by identifying the existence of backward Hopf-bifurcations and demonstrated the period-doubling route to chaos when the death rate of predator (μ1) and the growth rate of susceptible prey population (r) are treated as bifurcation parameters. Our studies show that the system exhibits deterministic chaos when some control parameters attain their critical values. Chaotic dynamics is depicted using the 2D parameter scans and bifurcation analysis. Possible implications of the results for disease eradication or its control are discussed.