Harvesting effect on Prey--predator system with strong Allee effect in prey and Herd Behaviour in both

Abstract

In this paper, we introduce a prey-predator system with Allee effect in prey where both the prey and predator species are subject to harvesting and they also exhibit herd behaviour. The new idea of this paper is to consider the Allee effect, herd behaviour and harversing together. Herd behaviour may be proved as a buffer against environmental obstacles. On the contrary, Allee effect and harvesting together may wash out the population from the system. So, the optimal harvesting policy is very meaningful for the ecosystem cocerned to our proposed model. Moreover, taking some hypothetical data, a rigorous numerical illustration along with sensitivity analysis of the main parameters are offered here to validate the mathematical findings. This may be considered as a biological relevance of our model system with the real world. Summerisingly, we can say that our model is nothing but a small endeavour aiming the ecological balance in nature.