HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation

In the paper, we have considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia coinfection in a human population at different infection stage s. Our model revealed that the disease-free equilibrium points of the HIV/AIDS and pneumonia submodels are both locally and globally asymptotically stable whenever the associated basic reproduction numbers ( and ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( and ) are greater than unity. The full HIV/AIDS-pneumonia coinfection model has both locally and globally asymptotically stable disease-free equilibrium points whenever the basic reproduction number of the coinfection model is less than unity. Using standard values of parameters collected from different kinds of literature, we found that the numerical values of the basic reproduction numbers of the HIV/AIDS-only submodel and pneumonia-only submodel are 17 and 7, respectively, and the basic reproduction number of the HIV/AIDS-pneumonia coinfection model is . Applying sensitive analysis, we identified the most influential parameters to change the behavior of the solution of the considered coinfection dynamical system are the HIV/AIDS and pneumonia transmission rates and , respectively . The coinfection model was numerically simulated to investigate the stability of the coinfection endemic equilibrium point, the impacts of transmission rates, and treatment strategies for HIV/AIDS-only, pneumonia-only, and HIV/AIDS-pneumonia coinfected individuals. Finally, we observed that numerical simulations indicate that treatment against infection at every stage lowers the rate of infection or disease prevalence.