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Journal of Applied Nonlinear Dynamics 14(3) (2025) 615--643 | DOI:10.5890/JAND.2025.09.009

Abhijit Jana, Sankar Kumar Roy

Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, India

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Abstract

In this study, we first design an eco-epidemiological model in the presence of a contagious disease in prey population. Prey population following logistic law of growth is classified into two groups: susceptible and infected. The impacts of anti-predatory behaviour for the fear effects of predators are duly investigated. Assumptions are made that the fear effects are capable of reducing prey reproduction rate and alleviating disease transmission rate by lowering prey activity. Additionally, we consider Allee effects, wherein the growth rate of the susceptible prey population is diminished by the fear effects. Hunting cooperation of predator is also incorporated in the proposed model. The model is then transformed into a delayed eco-epidemiological model by accounting for gestation time required to reproduce a new member of the predator family. Equilibrium points and corresponding existence criteria are calculated, and local behaviours of the non-delayed model are analyzed. The delayed model is examined for Hopf bifurcation with time delay as a bifurcating parameter. All the probable directions and the stability of bifurcating periodic solutions are also studied. The effects of herd behaviour, fear, Allee effects, hunting cooperation, and other biological parameters are demonstrated through extensive numerical simulations. Meanwhile, we uncover that predators can control the spread of the disease within the prey population until a certain threshold in the disease transmission rate. They achieve this by consuming infected individuals from the ecosystem. Beyond direct participation, predator also crucially contribute to disease control through fear. Their presence separates strong prey from infected individuals, minimizing the likelihood of direct contact.

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