Abstract
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.
Highlights
Infectious diseases are a clinically evident illness, and commonly, they have a great influence on the human population
The effect of treatment at each infected compartment was considered for both the submodels and the full model, namely, treatment of pneumonia infection, treatment of acute Human immunodeficiency virus (HIV) infection, treatment of chronic HIV infection, treatment of AIDS patients, treatment of acute HIV/AIDS
We have showed the most sensitive parameters of our model which can be epidemiologically controlled are the HIV/AIDS transmission rate β1 and pneumonia transmission rate β2 so it is reasonable to recommend the use of intervention strategy for HIV/AIDS transmission in making β1 less than 0:00014 and treatment for pneumonia transmission in making β2 less than 0:00006: Numerical simulations were used to compare the endemic scenarios showed by analytical results
Summary
Infectious diseases are a clinically evident illness, and commonly, they have a great influence on the human population. Nwankwo and Okuonghae [19] formulated and analyzed a mathematical model for the transmission dynamics of syphilis and HIV coinfection in a community to assess the impact of treatment of syphilis on the coendemicity of both diseases in a population where treatment for HIV is not readily available (or accessible) but with syphilis treatment sufficiently available Their syphilis-only model and the full coinfection models undergo the phenomenon of backward bifurcation due to syphilis reinfection after recovery from a previous syphilis infection. We applied the center for disease control and prevention (CDC) human immunodeficiency virus (HIV) infection stages and the control measure treatment at each stage of the single infections and coinfection model We have checked this case has never been done before.
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