A Non-linear Model of a Fishery Resource for Analyzing the Effects of Toxic Substances

The goal of the proposed model is to investigate and analyze the qualitative behaviour of predator-prey fishery resource in an aquatic ecosystem by a non-linear mathematical model in which prey and predator species are contaminated by the toxic substances released by each of the species. In this model the species are subjected to bio-economic combined harvesting and obey the logistic growth rate function. Bio-economic harvesting of prey-predator species in presence of harmful toxic substances released by them is analyzed here by using modified catch rate function. Boundedness of the proposed model is examined here. Biological and bionomic steady states of the proposed model are derived. The conditions for local behaviour, instability and global behaviour of the steady states are exhibited in this paper. Optimal harvesting policy with the help of Pontryagin’s maximal principle and finally, numerical exmples are illustrated to verify theoretical observations obtained from proposed model.