A mathematical model for the coinfection of Buruli ulcer and Cholera

Abstract

We propose to study the modeling and analysis of the coinfection of Buruli and cholera. We developed the model based on the literature for the coinfection and its optimal control. First, we analyze the sub-models at their steady states and present its mathematical results. The global stability for the sub-models are investigated for the special case. We show that the sub-models are locally as well as globally asymptotically stable whenever R0 is less or greater than one. Further, the co-infection model is analyzed by computing its R0 and it is proven that the coinfection model is locally asymptotically stable. We study the bifurcation analysis for the coinfection model and determine the conditions for the possible existence of backward bifurcation phenomenon. Moreover, we use five different control variables and obtain the control problem. The details mathematical results involve in the optimality system are shown. We use the Pontryagin’s Maximum Principle to determine the best strategy in controlling both the diseases. Lastly, we perform the numerical experiments using different set of controls for the possible eliminations of infection. We observe from our numerical results that the preventions and treatments are the best controls for the infection minimization.