article · Journal of Biological Dynamics
A mathematical framework uses ordinary differential equations to model the dynamics of co-infection between pneumonia and HIV/AIDS alongside optimal control strategies. Both individual infections and combined co-infections undergo qualitative analysis, including the calculation of effective reproduction numbers. Stability analysis demonstrates global stability for disease-free equilibrium states under specific mathematical criteria. In addition, the analysis reveals that pneumonia mono-infection and pneumonia-HIV co-infection can display backward bifurcation even when the effective reproduction number remains below unity, indicating that reducing transmission below standard thresholds may not be sufficient on its own to eliminate the disease. Numerical simulations evaluate system behaviours and assess multiple optimal control strategies, identifying targeted interventions designed to minimise transmission and potentially eradicate dual infections within a community.
Understanding how pneumonia and HIV/AIDS interact within populations is vital for designing effective public health responses. The presence of backward bifurcation indicates that standard disease control measures may fail even when transmission indicators appear favourable. Identifying optimal intervention combinations provides mathematical evidence that can guide healthcare planning and resource deployment to reduce the burden of severe co-infections.
The model provides early-stage theoretical frameworks that could inform public health decision-support tools or epidemiological planning software for health authorities and policymakers. As theoretical and computational research based on differential equations, the work remains at an early stage, requiring empirical data integration and field testing before direct application in real-world intervention planning or healthcare resource allocation.
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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.
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DOI: 10.1080/17513758.2023.2288873
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