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.
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.