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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 stages. 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 ( R H and R P ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R P and R H ) 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 R H P 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 max 7 , 17 = 17. 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 β 1 and β 2 , 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. [ABSTRACT FROM AUTHOR]

An improved Susceptible-Infected-Susceptible (SIS) epidemic diffusion model with population migration between two cities is modeled. Global stability conditions for both the disease-free equilibrium and the endemic equilibrium are analyzed and proved. The main contribution of this paper is reflected in epidemic modeling and analysis which considers unequal migration rates, and only susceptible individuals can migrate between the two cities. Numerical simulation shows when the epidemic diffusion system is stable, number of infected individuals in one city can reach zero, while the number of infected individuals in the other city is still positive. On the other hand, decreasing population migration in only one city seems not as effective as improving the recovery rate for controlling the epidemic diffusion. [ABSTRACT FROM AUTHOR]