Optimal Harvesting of a Stochastic Logistic Model with Time Delay

Abstract

This note is concerned with the optimal harvesting of a stochastic logistic model with time delay. The classical optimal harvesting question of this type of model is difficult because it is very difficult to obtain the explicit solution of the corresponding delay Fokker-Planck equation. The main aim of this note was to find a new approach to overcome this problem. In this note, using the ergodic method, sufficient and necessary criteria for the existence of optimal harvesting policy of our model are obtained. At the same time, the optimal harvesting effort and the maximum of harvesting yield are given. This method provides a new approach to study the optimal harvesting problem of stochastic population models, which can be also applied to investigate stochastic multi-species models.

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