| In this thesis, a model for the effect of pollution on an animal population partially dependent on a plant resource is examined. The model is an extension of previous mathematical models for populations living in polluted environments. 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, as well as the overall environmental pollution level. The model system is analysed using standard mathematical techniques, including the direct Liapunov method and numerical simulations, to assess the impact of varying levels of pollution on population survival. Criteria for the stability of the system are found, and numerically tested. A biological interpretation of the stability criteria is also given. It was found three inequalities are sufficient to establish global stability and that a parameter range exists in which these criteria are satisfied. This indicates real world applicability of the model and stability criteria. 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.;Key words. Mathematical Model, Ordinary Differential Equations, Pollution, Populations, Dynamics. |
