Mathematical Analysis of the Role of Treatment and Vaccination in the Management of the HIV/AIDS and Pneumococcal Pneumonia Co-Infection

Concomitant infections by two or more pathogens are on upsurge and among these is the interplay between HIV/AIDS and pneumococcal pneumonia infections. A mathematical co-infection model that fronts vaccination and treatment against pneumococcal pneumonia and antiretroviral therapy for HIV/AIDS in the management of the co-infection burden is presented. The model is also extended to include optimal control plans, in line with protection, early detection, and treatment of both HIV/AIDS and pneumococcal pneumonia. Co-infection model analysis manifests that the solutions are positive and bounded, and the disease equilibria stabilities are established in reference to the computed effective reproduction numbers. Sensitivity analysis indicated that infection rate parameters are by far the most influential in the co-infection escalation, whereas treatment and vaccination associated parameters have inhibiting effect towards the co-infection. Numerical simulations reveal that treatment and vaccination interventions are important in co-infection reduction but not sufficient for co-infection elimination. Further analysis indicates that, in addition to treatment and vaccination, adopting all optimal control plans can be a concrete start to co-infection elimination.