Study of dynamical behaviors of harvested stage-structured predator–prey fishery model with fear effect on prey under interval uncertainty

Abstract

The lack of clarity in many parameters used in ecological models is due to the constant changes in nature. The fundamental predator–prey model discussed in this article takes into account several ecological parameters as parametric-functional interval numbers. It discusses the dynamic characteristics of the model within the context of an uncertain environment. To account for this uncertainty, the model incorporates the concepts of bionomic equilibria and maximum sustainable yield (MSY). The article explores the optimal harvesting policy by applying Pontryagin’s maximum principle in an imprecise and uncertain environment. The proposed imprecise model formulation includes two additional variables: the influence of fear on prey population growth rate and the harvesting of prey and juvenile predator populations. The system of interval differential equations governs the interactions between these imprecise species, allowing for mathematical analysis of the proposed system. The aim of this study is to evaluate the robustness of an imprecise prey–predator model within an unpredictable environment. The article concludes by presenting rigorous numerical simulations that support all the analytical findings.