An optimal control problem for a reaction-diffusion model of invasive species

Last modified: 2014-03-28

#### Abstract

Consider a parabolic system of PDEs that models the dynamics of a population of invasive species, where the normal females and males are taken into consideration. We introduce a "feminized" supermale into the population, with 2Y chromosomes. This is a genetically modified organism. Mating with this mutant produces only males and supermales. The long time behavior is that this will lead to less and less number of normal females in the population, ultimately leading to extinction. This is a way to eradicate a harmful invasive species. These "supermales" and "Feminized supermales" are created by hormone treatments in a laboratory environment, then released into the population. It is done regularly in salmon industry to produce more male offspring.

The model has applications in invasive species control and more recently in bioterrorism control.

We are interested to regard the model as an optimal control problem. Suppose that the "feminized" mutant is released at some rate into the population and this rate is regarded as a control parameter.Our goal is to minimize the female population, maximize the male population, while minimizing the rate of introduction of the "feminized supermales". We prove the existence of an optimal solution and establish some optimality conditions for the above problem.

The model has applications in invasive species control and more recently in bioterrorism control.

We are interested to regard the model as an optimal control problem. Suppose that the "feminized" mutant is released at some rate into the population and this rate is regarded as a control parameter.Our goal is to minimize the female population, maximize the male population, while minimizing the rate of introduction of the "feminized supermales". We prove the existence of an optimal solution and establish some optimality conditions for the above problem.