The thesis mainly studies the optimal harvesting problem of several types of structural

population models. This thesis consists of four chapters. The fifirst chapter mainly introduces the historical background and the recent development of the problems to be studied as well as the main contents of the dissertation, and gives some lemmas which will be used in proving the main results.

   In Chapter 2, we study a predator-prey model for fifishery resource with reserve area and age structure:

where the variables x and y are the biomass densities of the prey fish species inside the unreserved and reserved areas, respectively. The variables z and w are the biomass densities of predator fish species  inside the unreserved and reserved areas, respectively. Fishing in the reserved area is strictly prohibited. The corresponding optimal harvesting problem  is considered, where the objective functional represents the total economic benefits obtained from the harvesting process. Firstly, the existence and uniqueness of the solution of the model are proved by means of the fixed point theorem. Then, the optimality conditions for achieving the optimal harvesting policy are given by solving the extremum point of the cost functional. Furthermore, the existence of a unique optimal harvesting strategy is demonstrated with the use of Ekeland's Principle. Finally, the numerical simulations indicate that the creation of marine reserves is indeed conducive to the recovery of fishery resources, increasing fish abundance and protecting biodiversity as well as ecosystem structure.

where J denotes the density of juvenile individuals and A stands for the number of adult population. The corresponding optimal harvesting problem  is considered. Firstly, we  prove the existence and uniqueness of generalized solution of the model while the optimal harvesting effort is discontinuous. Then, we demonstrate the existence of the optimal harvesting policy. Furthermore, we derive the maximum principle describing the optimal control by searching the extremum point of the cost functional. Finally, the dynamical behavior of the population is simulated by solving the corresponding optimality system numerically with an algorithm based on the method of backward Euler implicit finite-difference approximation.