Eur. Phys. J. Plus (2022) 137: 528
https://doi.org/10.1140/epjp/s13360-022-02751-2

Regular Article

Effects of fear, refuge and hunting cooperation in a seasonally forced eco-epidemic model with selective predation

¹ Department of Basic Science and Humanities, Indian Institute of Information Technology, 813210, Bhagalpur, India
² Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

^b pktiwari.math@iiitbh.ac.in

Received: 31 January 2022
Accepted: 21 April 2022
Published online: 2 May 2022

Abstract

In ecological systems, the fear of predation risk may assert privilege to the prey species by restricting their exposure to potential predators, and also impose costs by constraining the exploration of optimal resources. In this paper, an eco-epidemic model of the predator–prey system is investigated by considering disease in prey population and selective behavior of predator; the cost of fear is taken as affecting the reproduction and intraspecies competition of vulnerable prey population, and also lowers the disease transmission; the predators are assumed to cooperate with each other for the hunting while the susceptible/infected prey population takes refuge. Numerical observations of the system demonstrate that the cost of fear causing a reduction in the birth rate of susceptible prey has a destabilizing role, whereas the levels of fear responsible for the increase in the intraspecies competition of susceptible prey and eradication of the disease prevalence have the capacity to stabilize an otherwise unstable system. The intensity of disease prevalence potentially affects the dynamics of the ecosystem by altering its stability around the infection-free state and the coexistence of prey and predator species. However, refuge taken by the susceptible/infected prey has the potential to restore the stability of the system. Moreover, the chaotic nature of the system is observed if the preference of predators for susceptible prey or hunting cooperation of predators exceeds a fixed value. We also investigate the dynamics of the system by letting some of the model parameters to vary with time. Our numerical results for the seasonally forced system showcase different dynamical features including periodic solutions, higher periodic solutions, bursting patterns, and chaos.