Optimal harvesting and stability of predator prey model with Monod-Haldane predation response function and stage structure for predator

Abstract

This article deals with growth rate predator prey population model with stage structure for predator. The predator population is divided into two stages, mature and immature predator. Predation functional response in the model follows the Monod-Haldane type. Under consideration that the population is a valuable stock, the mature predator and prey population are then harvested with constant effort. This model is then analysed by found the equilibrium point and stabilities. There exists four equilibrium points and stability analysed is focused only for interior point. The stable interior point is related to the maximum profit problem. From the analyses we found that there exists a condition for the effort of harvesting so that the interior point is still stable and also obtained maximum profit.