Mathematical modeling and stability analysis of Buruli ulcer in Possum mammals

Abstract

A mathematical model for the understanding of the transmission dynamics of Buruli ulcer in possum mammals is considered. This disease is known to be the neglected tropical disease and its spread can now be seen in Australia. The disease has been identified in some mammals including possum. The present work investigates a mathematical model on the possum epidemic with control analysis. The model basic properties are extensively investigated and the stability analysis is presented with R0. The stability at the steady states show that the model is locally as well as globally asymptotically stable for the two states. Moreover, the proposed model is then reformulated with the inclusion of three control variables. Further, utilizing the Pontryagin's Maximum Principle, obtaining the necessary conditions and the characterization of an optimal problem in order to minimize the Buruli ulcer spread. We present numerical results in details by choosing a set of control combinations in order to determine the best possible and useful strategy for the minimization of infection. Our results indicate that considering all the controls effectively at the same time can possible reduce the infections better in the infective compartments.