HIV/AIDS and HBV co-infection with optimal control strategies and cost-effectiveness analyses using integer order model.

Hepatitis B virus (HBV) and HIV/AIDS co-infection is a common infectious disease that has been spreading through different nations in the world. The main objective of the study is to minimize the number of HBV and HIV co-infected individuals in the community and the cost incurred to the effort applied towards protection and treatment control strategies. In this study, a novel HBV and HIV/AIDS co-infection model has been formulated and analyzed to investigate the effects of protection and treatment control strategies on the spreading dynamics of the HBV and HIV/AIDS co-infection in the community. In the qualitative analyses we have computed all the models disease-free equilibrium points, all the models effective reproduction numbers and unique endemic equilibrium points, we have proved the two sub-models disease-free equilibrium points are locally as well as globally asymptotically stable whenever their associated effective reproduction numbers are less than one. In our understanding no one is formulated and analyzed the HBV and HIV/AIDS co-infection model with optimal control and cost-effective analyses so that we have formulated the associated optimal control problem and carried out the optimal control analysis on the HBV and HIV/AIDS co-infection model by implementing the Pontryagin's minimum principle. Numerical simulations with various combinations of the control efforts implemented are then carried out to investigate the impacts of protection and treatments to tackle the HBV and HIV/AIDS co-infection diseases spreading in the community. Finally, we also carried out cost-effectiveness analysis for the implemented control strategies. From the findings of the numerical simulations we observed that implementing all the proposed controlling strategies simultaneously has fundamental impact to minimize and control the HBV and HIV/AIDS co-infection spreading in the community but cost-effectiveness analysis proved that implemented strategy 4 (implemented the HIV protection and HBV treatment controls simultaneously) is the most cost-effective strategy as compared with all other implemented strategies and we recommend for the health stake holders and policy makers to implement this strategy to tackle the HBV and HIV/AIDS co-infection spreading problem in the community.