[Pre-print] Mathematical model of marine protected areas

Abstract

We consider two regions with a fish population that is dispersing between the two areas, and fishing takes place only in region 2, with region 1 established as no-fishing zone. Marine protected areas (MPAs) have been promoted as conservation and fishery management tools, and at present, there are over 1300 MPAs in the world. A new mathematical model of an MPA that reflects the complexity of the natural setting is presented. The resulting model of an age-structured fish population belongs to a class of non-linear systems of differential equations with delay. New easily verifiable sufficient conditions for the existence, boundedness, permanence and stability of the positive internal steady-state solutions are obtained. From the point of view of fishery managers, the existence of stable solutions is necessary for planning harvesting strategies and sustaining the fishing grounds. Numerical simulations illustrate qualitative behaviour of the model, including stability switches.