Analysis of the HBV and TB Coinfection Model With Optimal Control Strategies and Cost-Effectiveness

The coinfection of HBV and TB diseases affects millions of individuals throughout the nations in the world. The main objective of this study is to formulate and analyze the HBV and TB coinfection dynamical system, investigate the impact of time-dependent optimal control measures and cost-effectiveness analysis, and tackle the coinfection transmission dynamics in the population. Each of the submodels and the coinfection model's qualitative analyses were carried out independently, whereas the TB-only submodel and the coinfection model reveal the phenomenon of backward bifurcation. The coinfection model's optimal control problem with five time-dependent optimal control measures is formulated and analyzed. Using the parameter values described in the paper, we carried out numerical simulations and verified the models' qualitative analysis results. To minimize invectives and the cost of the implementing effort toward the protection and the treatment, optimal control analysis is performed for the HBV and TB coinfection model using Pontryagin's minimum principle. Numerical simulations with different combinations of efforts are then carried out to explore the effect of protection in the presence of treatment for both diseases. Numerical simulations emphasize the fact that to reduce coinfection from the population, programs to accelerate the protection of both diseases are also required along with the treatment. The results reveal that the implementation of the combination of protective and treatment-optimal control strategies suppresses the occurrence of HBV and TB coinfection, and protective control measures are more effective than treatment control measures for individuals who are coinfected with HBV and TB diseases. Implementing all the proposed protective and treatment control measures significantly minimized the transmission dynamics of HBV and TB confection in the community. From the cost-effectiveness analysis of the proposed time-dependent control strategies, treatment of HBV is the most cost-effective control strategy required to tackle the spread of the HBV and TB coinfection in the community.