OPTIMAL MANAGEMENT OF A SINGLE-SPECIES FISH POPULATION IN THE PRESENCE OF INVASIVE ALIEN SPECIES

Abstract

Alien invasive species significantly impact the growth rate and yield of native fish populations in harvesting systems. Reducing invasive species is expected to alleviate pressure on native fish, enhancing both their stock and overall harvest yield. This thesis investigates the dynamics of native fish and invasive species, optimal harvesting, and the allocation of effort towards invasive species removal within an ecosystem. Using a deterministic mathematical model, we establish the existence, uniqueness, positivity, and boundedness of solutions. We characterize non-negative steady states and analyze their local and global stability. The maximum sustainable yield is determined, and the optimal harvesting strategy is derived using Pontryagin’s Maximum Principle. Findings indicate that excessive harvesting can lead to system collapse, while moderate harvesting enables optimal effort allocation, maximizing both yield and net profit. Numerical simulations illustrate these results