Mathematical Modelling and Optimal Controls for Controlling Pneumonia-HIV Co-Infection

Abstract

Bacterial infections like Pneumonia have emerged as an important cause of morbidity and mortality in individuals infected with HIV giving rise to their co-infection. There are mathematical models that describe; the co-dynamics, treatment and protection mechanisms of Pneumonia and HIV infections. Therefore, this research is aimed at determining optimal control treatments through developing a deterministic mathematical model Pneumonia-HIV co-infection incorporating the use of anti-pneumonia and ART treatment interventions as controls. The uncontrolled pneumonia-HIV co-infection is presented with its analysis. Finally, the optimal control theory for Pneumonia-HIV co-infection model is derived analytically by applying the Pontryagin's Maximum Principle.