Abstract

In this paper, we proposed and analyzed a realistic compartmental mathematical model on the spread and control of HIV/AIDS-pneumonia coepidemic incorporating pneumonia vaccination and treatment for both infections at each infection stage in a population. The model exhibits six equilibriums: HIV/AIDS only disease-free, pneumonia only disease-free, HIV/AIDS-pneumonia coepidemic disease-free, HIV/AIDS only endemic, pneumonia only endemic, and HIV/AIDS-pneumonia coepidemic endemic equilibriums. The HIV/AIDS only submodel has a globally asymptotically stable disease-free equilibrium if ℛ1 < 1. Using center manifold theory, we have verified that both the pneumonia only submodel and the HIV/AIDS-pneumonia coepidemic model undergo backward bifurcations whenever ℛ2 < 1 and ℛ3 = max{ℛ1, ℛ2} < 1, respectively. Thus, for pneumonia infection and HIV/AIDS-pneumonia coinfection, the requirement of the basic reproduction numbers to be less than one, even though necessary, may not be sufficient to completely eliminate the disease. Our sensitivity analysis results demonstrate that the pneumonia disease transmission rate β2 and the HIV/AIDS transmission rate β1 play an important role to change the qualitative dynamics of HIV/AIDS and pneumonia coinfection. The pneumonia infection transmission rate β2 gives rises to the possibility of backward bifurcation for HIV/AIDS and pneumonia coinfection if ℛ3 = max{ℛ1, ℛ2} < 1, and hence, the existence of multiple endemic equilibria some of which are stable and others are unstable. Using standard data from different literatures, our results show that the complete HIV/AIDS and pneumonia coinfection model reproduction number is ℛ3 = max{ℛ1, ℛ2} = max{1.386, 9.69 } = 9.69 at β1 = 2 and β2 = 0.2 which shows that the disease spreads throughout the community. Finally, our numerical simulations show that pneumonia vaccination and treatment against disease have the effect of decreasing pneumonia and coepidemic disease expansion and reducing the progression rate of HIV infection to the AIDS stage.

Highlights

  • human immunodeficiency virus (HIV)/AIDS remains a major global health problem affecting approximately 70 million people worldwide causing significant morbidity and mortality (WHO, 2018) [1]

  • A realistic compartmental mathematical model on the spread and control of HIV/AIDS-pneumonia coepidemic incorporating pneumonia vaccination and treatment for both infections are available at each stage of the infection in a population constructed and analyzed

  • We have shown the positivity and boundedness of the complete HIV/ AIDS-pneumonia coepidemic model

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Summary

Introduction

HIV/AIDS remains a major global health problem affecting approximately 70 million people worldwide causing significant morbidity and mortality (WHO, 2018) [1]. Mathematical models have been used to investigate the dynamics of single infections and coepidemics, and HIV/AIDS-pneumonia is among the diseases that infect a large number of individuals worldwide [10, 17, 20, 21]. We are motivated by the above studies especially the HIV/AIDS-pneumonia coexistence in the community; in this study, we considered the three center for disease control and prevention (CDC) stages of the HIV infection which are acute HIV infection, chronic HIV infection, and AIDS stage; we presented and analyzed a mathematical model describing the transmission dynamics of HIV/AIDS and pneumonia coinfection in a population where treatment for HIV/AIDS and both vaccination and treatment for pneumonia are available, respectively, in the community. Discussion, conclusion, and recommendation of the study are carried out in Sections 5 and 6, respectively

Mathematical Model Formulation
The Mathematical Model Analysis
Disease-Free Equilibrium Point of the Pneumonia
Local and Global Stability of the Disease-Free Equilibrium Point
Sensitivity and Numerical Analysis
Discussion
Conclusion

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