An Age-stratified Mathematical Model for Human Immunodeficiency Virus and Tuberculosis Co-infection with Optimal Control

One significant risk factor that is considered to contribute to Kenya’s TB burden is HIV. TB is one of the most common opportunistic infections associated with HIV, and HIV infection increases the risk of developing active TB disease in individuals with latent TB infection. Due to their compromised immune systems, increased susceptibility to TB infection and latent TB reactivation, people with HIV have a higher probability of attaining TB. This study develops an age-stratified mathematical model with optimal control for co-infection of HIV and TB. The model’s reproduction number, as well as the equilibrium of endemic and disease-free states have been computed. Least Squares technique of minimization has be used to determine the model parameters. HIV antiretroviral therapy treatment adherence and tuberculosis treatment have been considered for optimization. Runge-Kutta 𝒪(<i>h</i><sup>4</sup>) has been used to solve the system differential equations for its high accuracy and flexibility. Results from the numerical simulations show that ART adherence is the best intervention to control the co-infection in its earlier stages (HIV and latent TB). TB treatment is the best intervention for those affected with the coinfection on the later stage (HIV and active TB). Considering viral load suppression and TB prevention, viral load suppression is most effective for children and TB prevention is most effective for adults. The results of this research can be used by the Ministry of Health (MOH) for emphasis on most effective interventions as well as a basis study tool that can be recreated for other co-infections.