Modelling the Effects of Pollution on a Population and a Resource in a Polluted Environment

Abstract

A model for the effect of pollution on an animal population partially dependent on a plant resource is examined. Using a system of ordinary differential equations, the model tracks and relates changes in an animal population and its internal pollution levels, a plant population and its internal pollution levels, and the overall environmental pollution level. The model system is analysed using standard mathematical techniques, including the direct Lyapunov method and numerical simulations. Criteria for the stability of the system are found and numerically tested. Three inequalities are sufficient to establish global stability, and a parameter range exists in which these criteria are satisfied. The stability criteria dictate that the system will be globally stable provided that the removal rate of the pollution from the environment, the intrinsic growth rate of the plant population, and the rate the animal population relieves itself of its pollution are all sufficiently large.