Dynamical behaviour of infected predator–prey eco-epidemics with harvesting effort

Abstract

This investigation accounts for a predator–prey system where the predator community is affected by infectious disease and also subjected to harvest. The model considers the behavioural change in susceptible predators due to the crowding effect of infected predators. The dynamical characteristics are studied encompassing asymptotic stability of the existing equilibrium points and bifurcation analysis. A sufficient parametric condition for global stability of the interior equilibrium point is investigated using a geometric approach. The system undergoes a Hopf-bifurcation around interior equilibrium point considering disease transmission rate as a bifurcation parameter. An optimal control problem is formulated by considering a time-dependent fishing effort as a control variable. The objective of this optimal control problem is to maximize the present value of the economic revenue obtained by fishing. Finally, several numerical simulations are conducted to visualize our analytical results.