Modeling the transmission dynamics of the co-infection of Malaria andTuberculosis with optimal control strategies and cost - bene t analysis

This research focuses on a continuous-time mathematical model to better understand thespread of co-infections involving Malaria and Tuberculosis. The study evaluates optimalcontrol strategies, including regular use of treated bed nets, fumigation, insect repellents,and public awareness campaigns about respiratory protection and co-infection risks. Theobjective is to reduce transmission rates and lessen the overall impact of these diseases onthe population. We applied the Pontryagin maximum principle in discrete time to deter-mine the best control strategies, solving the system through an iterative process. UsingMATLAB's optimization tools and the Runge-Kutta forward-backward sweep method,we ran simulations to show how these strategies a ect di erent groups, both infectedand uninfected. A cost-e ectiveness analysis was also carried out to pinpoint the most efficient measures for reducing the co-infection of Malaria and Tuberculosis, while mini-mizing costs. The ndings suggest that scaling up the use of treated bed nets, fumigation,and public health education can signi cantly curb the spread of these diseases nd theirco-infection within the population.