A control problem in a polluted environment

Due to the importance of remediating polluted environments, many mathematical models have been developed to describe population-toxicant interactions. This article considers the situation where the amount of pollution in the environment is restricted to lie below a certain value M. A model is presented and viewed as a control problem in which the toxicant input into the environment is the controllable variable. An explicit formula is computed for the input function that meets certain restrictions. By analytically studying the dynamics of the population, it is possible to provide conditions on how to set M in order to guarantee survival of the population without a significant reduction of its carrying capacity. Numerical and experimental data are described that support these results.