A co-infection model for Two-Strain Malaria and Cholera with Optimal Control

Omame, D. A.; Egeonu, K. U.; Inyama, S. C.

A mathematical model for two strains of Malaria and Cholera with optimal control is studied and analyzed to assess the impact of treatment controls in reducing the burden of the diseases in a population, in the presence of malaria drug resistance. The model is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the model is proven not to exist. The necessary conditions for the existence of optimal control and the optimality system for the model is established using the Pontryagin's Maximum Principle. Numerical simulations of the optimal control model reveal that malaria drug resistance can greatly influence the co-infection cases averted, even in the presence of treatment controls for co-infected individuals.