An Optimal Control Analysis of Malaria by Coinfection Model

Malaria and Hepatitis B Virus (HB V) are diseases that poses serious challenges health wise in the world especially in countries that are developing:-Both diseases belong to t the most widespread diseases, and therefore, a major public health concerns in tropical developing countries. In this research, a mathematical model showing dynamics of Co­ infection of Malaria and HBV diseases was developed using ordinary differential equations which consists of 9 compartments. The study covers the model*s futdre solution positivity, model invariant region and disease-free points. The next generation matrix method was used to compute the basic reproduction number, R0, for the coinfection model using and the disease free equilibrium point and was shown to be Locally Asymptotically Stable ifJl0 < 1 and unstable if > 1. Then, the coinfection model was extended to optimal control by incorporating four control interventions. The optimality System was obtained using the Pontryagin’s maximum principle. Simulation of the optimality system was done and five strategies was proposed to qheck the effect of the controls. First, prevention only for both diseases was considered, and the result shows that, applying prevention control has a great impact in bringing down the expansion of malaria, HBV infection, and their coinfection in the specified period of time. Other approaches are prevention effort for malaria and treatment effort for HBV infection, prevention effort for HBV infection and treatment effort for malaria, treatment effort for both diseases, and using all interventions. We obtained that the listed strategies were effective in ,,minimizing the expansion of Malaria HBV coinfeciious population in the specified period of time.