article · PLoS ONE
HIV/AIDS and COVID-19 co-infection presents severe public health and socio-economic challenges globally. A mathematical model examines the transmission dynamics of this co-infection by incorporating protection and treatment interventions for infected populations. Mathematical evaluations establish the non-negativity and boundedness of system solutions, steady states, and conditions where backward bifurcation occurs when the effective reproduction number is below unity. Using optimal control theory, necessary conditions were derived to evaluate time-dependent disease control strategies. Numerical simulations confirm that the model converges to an endemic equilibrium when the effective reproduction number exceeds one. Furthermore, applying all available protection and treatment strategies simultaneously proves to be the most effective approach to drastically reducing co-infection transmission within a community.
Managing overlapping epidemics is a complex challenge for healthcare systems worldwide. By mathematically evaluating how HIV/AIDS and COVID-19 spread together, this research demonstrates the necessity of comprehensive intervention strategies. It highlights that isolated measures are insufficient, showing public health decision-makers that concurrent prevention and treatment efforts are critical to bringing dual infections under control.
The model provides theoretical insights that could inform public health planning frameworks and epidemiological decision-support tools for healthcare authorities. However, the work represents early-stage theoretical and numerical research. The abstract does not indicate an immediate commercialisation pathway, deployed software product, or direct clinical application.
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HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV/AIDS and COVID-19 co-infection in the community under consideration of the study.
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DOI: 10.1371/journal.pone.0284759
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