A co-infection model for two-strain Malaria and Cholera with optimal control

A mathematical model for two strain-Malaria and Cholera with optimal control is developed and analyzed to assess the impact of malaria drug resistance on treatment controls in a population where the two diseases co-exist. Using the Centre Manifold Theory, the model is shown to undergo backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the model is shown 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.