AN ECO-EPIDEMIOLOGICAL MODEL WITH NON-CONSUMPTIVE PREDATION RISK AND A FATAL DISEASE IN PREY

Apart from direct killing, the non-consumptive risk of the predation process influences the community dynamics of ecological systems. Recent studies reveal that the fear induced in the prey due to predation risk suppresses prey growth as well as increases the death rate. In this work, we investigate an epidemiological predator–prey model where the cost of fear affects the death rate of infected prey. We assume that the predator species feed on susceptible and infected prey and can adopt self-medication. The dynamical behaviour of the system around the steady states is analyzed both analytically and numerically. The global stability of the coexistence equilibrium is discussed in a geometric approach. We determined the basic reproduction number \(\mathcal {R}_0\) ${\mathcal{R}}_0$ such that \(\mathcal {R}_0<1\) ${\mathcal{R}}_0<1$ leads to eradicating the disease from the prey population. Our simulation results show that the strength of fear and the disease fatality rate have a destabilizing role. Above a critical parameter value of fear strength and disease fatality rate, the coexistence equilibrium becomes disease-free and predator-free via a transcritical bifurcation. A parametric region is determined for which the system shows a bistability nature. Our numerical simulation also shows that zero fatality may lead to instability in the coexistence equilibrium state via periodic oscillations. In addition, we also determined some other threshold parameters at which the system becomes disease-free and predator-free.