Prey–predator optimal harvesting mathematical model in the presence of toxic prey under interval uncertainty

Abstract

This paper explores a multispecies prey–predator harvesting system based on Lotka–Volterra model with two preys (palatable and toxic prey) and one predator with interval biological parameters. Due to the enhancement in resource availability, prey–predator system becomes destabilized theoretically (the paradox of enrichment). Also, a prey may become toxic for the predator due to a little change in the resource stoichiometry. The presence of toxic prey influences the growth of the predator as well as that of a palatable prey. Thus the dynamics of prey–predator system is significantly affected by the presence of such toxic prey. Again, due to lack of precise numerical data of the biological parameters an interval number based mathematical toxic prey–predator model is developed and then discussed the dynamical behaviour of the model. Then, we observe the existence of different points of equilibrium and also the stabilities at these points of equilibrium of the system are presented. Also, the bionomic equilibrium of the harvesting model has been analysed. Next, the optimal harvest policy is carried out and obtained the solution in the interior equilibrium point using Pontryagin’s maximum principle. All important analytical findings are demonstrated through computer simulation using MATLAB followed by discussions and conclusions.

Keywords

• Prey–predator
• Food toxicity
• Stability
• Optimal harvest policy
• Bionomic equilibrium
• Imprecise parameters