Fuzzy optimal harvesting of a prey-predator model in the presence of toxicity with prey refuge under imprecise parameters

The objective of this paper is to investigate the dynamic behaviors of a prey-predator model incorporating the effect of toxic substances with prey refuge under imprecise parameters. We handle these biological parameters in model by using interval numbers. The existence together with stability of biological equilibria are obtained. We also analyze the existence conditions of the bionomic equilibria. The optimal harvesting strategy is explored by taking into account instantaneous annual discount rate under fuzzy conditions. Three numeric examples are performed to illustrate our analytical findings.