Optimal Control Analysis of the Dynamical Spread of Malaria/Cholera Co-Infection

In this paper, a fourteen (14) non-linear compartmental model is presented to study the transmission dynamics of Malaria/Cholera co-infection in a population at any point in time. The model is rigorously analyzed to gain insight into the dynamical features of Malaria/Cholera co-infection in order to know the effect of each control and which of the diseases should be treated before the other when all the controls are to be implemented. Optimal control analysis was carried out with different control strategies, Malaria Prevention (Mosquitoes treated bed net (µ1)), Malaria Treatment (µ2), Malaria-Cholera Prevention (µ3), Cholera Prevention (µ4), Cholera Treatment (µ5) and Boosting of Immune System (µ6) were introduced as the control strategy for the spread of Malaria-Cholera Co-infection and also, optimal control theory is applied to give an optimality system which we used to minimize the number of infected individuals and propose the most suitable control strategy for the spread of malaria/cholera co-infection. It is shown that the model has a diseases free equilibrium which is globally asymptotically stable (GAS). Also, there exists a unique endemic equilibrium point which is locally stable whenever the associated threshold is less than unity i.e Ro<1 and become unstable whenever the associated threshold quantity exceeds unity i.e Ro>1. It was also shown that there exists a solution for the optimality system. Numerical Simulation was performed using Differential Transformation Method (DTM). From the result, it was observed that the prevention control and treatment control strategies were more efficient in reducing the number of malaria/cholera infected individuals as compared to other control strategies.