HIV/AIDS and TB co-infection deterministic model bifurcation and optimal control analysis

Abstract

HIV/AIDS-TB co-infection is a worldwide common health problem. In this paper a compartmental model with optimal control strategies on the spread of HIV/AIDS-TB co-infection has been developed and analyzed with preventive measure dependent behavioral changes in the population and treatment of infected (and infectious) classes. And the impact of the co-infection and single infection treatment on the spreading dynamics of HIV/AIDS-TB co-infection and single infection were assessed. The two sub-models were analyzed mathematically when each of the two diseases was considered separately and the TB-only system shows backward bifurcation. Optimal control strategy analysis is applied to the full model with the aim to evaluate the impacts of control measures. Various combinations of controls are also analyzed and presented. The numerical simulation section shows that an optimal combination of preventive and therapeutic controls will suppress the occurrence of HIV, TB and HIV/AIDS-TB co-infection. Moreover, the therapeutic controls were found to be more effective than preventive controls for the infected individuals, preventive controls in turn were more effective than therapeutic controls in uninfected individuals.

Keywords

• HIV/AIDS-TB co-infection
• Bifurcation analysis
• Next generation matrix
• Optimal control
• Numerical simulation