ON THE DYNAMICS MALARIA-DYSENTERY CO-INFECTION MODEL

Abstract

In this paper, a mathematical model for malaria-dysentery co-infection was formulated in order to study and examine its dynamic relationship in the presence of malaria and dysentery preventive and treatment measures. First, analysis of the single infection steady states was done and then the basic reproduction number was obtained. Furthermore, investigation into the existence and stability of equilibria carried out. The single infection models were found to exhibit the possibility of backward bifurcation. Thereafter, the impact of malaria on the dynamics of dysentery is further investigated. Second, incorporating time-dependent controls, using Pontryagin’s Maximum Principle, the necessary conditions for the optimal control of the disease was derived. It is found that malaria infection may be associated with an increased risk of dysentery. Also, that dysentery infection may be associated with an increased risk for malaria. Therefore, to effectively control malaria, the malaria intervention strategies by policy makers must at the same time it also includes effective prevention and control measures for dysentery. Policy makers should take efforts on preventive strategies in combating dysentery and malaria.