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The control of opportunistic infections among HIV infected individuals shouldbe one of the major public health concerns in reducing mortality rate ofindividuals living with HIV/AIDS. In this study a deterministic co-infectionmathematical model is employed to provide a quantification of treatment at eachcontagious stage against Pneumocystis Pneumonia (PCP) among HIV infectedindividuals on ART. The disease-free equilibrium for the HIV/AIDS sub model,PCP sub model and the co-infection model are shown to be locally asymptoticallystable when their associated disease threshold parameter is less than a unity.By use of suitable Lyapunov functions, the endemic equilibrium corresponding toHIV/AIDS and PCP sub models are globally asymptotically stable whenever$\mathcal{R}_{0H}>1$ and $\mathcal{R}_{0P}>1$ respectively. The sensitivityanalysis results implicate that the effective contact rates are the mainmechanisms fueling the proliferation of the two diseases and on the other handtreatment efforts play an important role in reducing the incidence. Numericalsimulations show that treatment of PCP at all contagious stages reduces itsburden on HIV/AIDS patients and dual treatment of the co-infected individualssignificantly reduces the burden of the co-infection.

A Mathematical Model for Co-infection Dynamics of Pneumocystis Pneumonia and HIV/AIDS with Treatment