Optimal control strategies on HIV/AIDS and pneumonia co-infection with mathematical modelling approach

Abstract

In this paper, a compartmental model on the co-infection of pneumonia and HIV/AIDS with optimal control strategies was formulated using the system of ordinary differential equations. Using qualitative methods, we have analysed the mono-infection and HIV/AIDS and pneumonia co-infection models. We have computed effective reproduction numbers by applying the next-generation matrix method, applying Castillo Chavez criteria the models disease-free equilibrium points global stabilities were shown, while we have used the Centre manifold criteria to determine that the pneumonia infection and pneumonia and HIV/AIDS co-infection exhibit the phenomenon of backward bifurcation whenever the corresponding effective reproduction number is less than unity. We carried out the numerical simulations to investigate the behaviour of the co-infection model solutions. Furthermore, we have investigated various optimal control strategies to predict the best control strategy to minimize and possibly to eradicate the HIV/AIDS and pneumonia co-infection from the community.

KEYWORDS:

• HIV/AIDS
• pneumonia
• co-infection
• vaccination
• protection

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34H05
• 92-10

Acknowledgments

The authors thank Mr. Sitotaw Eshete for his valuable Wi-Fi contribution.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Authors’ contributions

All authors have read and approved the final manuscript.

Math Classification

92-10 Mathematical modelling or simulation for problems pertaining to biology.

Data availability statement

Data used to support the findings of this study are included in the article.

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.