Mathematical modeling and optimal control strategies of Buruli ulcer in possum mammals

Buruli is a neglected tropical disease that can now be found in many countries including developed countries like Australia. It is a skin disorder that usually occurs in the arms and legs. The disease has been identified in a number of mammals, particularly possum. Adequate eradication and control programs are needed to minimize infection and its spread to less developed countries before it becomes an epidemic. In this work, a SIR type possum epidemic model is proposed. The properties of the model are thoroughly studied and obtained its stability results. We determine the stability of the model at its fixed points and show that the model is locally and globally asymptomatically stable. The stability of the disease-free case is shown for $ \mathcal{R}_0 1$. We further extend the model using the control variables and obtain an optimal control system and using the optimal control theory to characterize the necessary condition for controlling the spread of Buruli ulcer (BU). The model results are plotted to determine the best strategies for disease elimination. Numerical simulation has shown that the useful strategy consists in implementing all suggested controls.