Dynamics and optimal harvesting of prey–predator in a polluted environment in the presence of scavenger and pollution control

Abstract

This paper is concerned with the dynamics and optimal harvesting of a prey–predator system in a polluted environment in the presence of scavengers and pollution control. Toxicants, released from external sources and the dead bodies of prey and predators, pollute the environment, which affects the growth of both prey and predators, resulting in a decline in the economic revenue from harvest. We assume that scavengers reduce pollution by consuming dead bodies. Further, we consider pollution reduction through depollution efforts as an alternative to enhancing revenue. We propose and analyze a prey–predator–pollutant model and study the optimal harvesting problem. We investigate the persistence of the ecosystem, and we solve the optimal harvest problem using Pontryagin’s maximum principle. The results indicate that uncontrolled prey harvesting and a high rate of pollution drive the system toward the extinction of both species. A moderate amount of pollution and the reasonable harvest efforts allow the system to persist. The optimal harvest strategy highlights that investing in pollution reduction enhances the persistence of the system as well as economic revenue. Numerical examples demonstrate the significant outcomes of the study.