Optimal control analysis of pneumonia and HIV/AIDS co-infection model

Abstract

A Pneumonia and HIV/AIDS deterministic co-infection model is constructed and utilized to assess how the dynamics of Pneumonia and HIV/AIDS impact on each other. In order to summarize the analysis of Pneumonia and HIV/AIDS co-infection model, the analysis of Pneumonia and HIV/AIDS sub-models is undertaken. The basic reproduction numbersR0 P for Pneumonia sub-model, R0 H for HIV/AIDS sub-model and R0 for Pneumonia and HIV/AIDS co-infection model are computed, the results are then fielded to establish the local and global asymptotic stabilities of the corresponding models' equilibrium points. Sensitivity analysis is done and results reveal that Pneumonia spreading rate, HIV spreading rate and treatment rates of the infected sub-populations are the most sensitive parameters. The model is further modified to incorporate intervention schemes, namely Pneumonia prevention, screening and treatment efforts, HIV/AIDS prevention, screening and treatment efforts in the form of time-dependent controls. Numerical simulations portray that prevention and treatment of both diseases averts the biggest numbers of co-infected individuals. However, in a situation when there are scarce resources to deploy all intervention schemes, a combination of treatment for both diseases become a scheme of choice in reducing the co-infection burden.