An HIV-TB co-infection model: analysis and data-driven insights for China.

In this work, we propose an HIV-TB coinfection model that incorporates time since recovery from TB. We derive the basic reproduction numbers and the invasion reproduction numbers associated with the two infections, and investigate the existence as well as the local and global stability of the disease-free, HIV-only, and TB-only equilibria. Using data on new HIV and TB cases in China from 2005 to 2019, we estimate the optimal model parameters, and perform a sensitivity analysis of the invasion reproduction numbers. Theoretical analysis and numerical simulations reveal that coexistent equilibria arise in multiple regions of the parameter space. Moreover, bistability and limit cycles may arise under specific conditions. Our study finds that focusing TB control alone is insufficient to continuously reduce the disease burden; without concurrently suppressing HIV transmission, HIV invasibility may increase, reducing the effectiveness of TB control. Therefore, we emphasize that HIV prevention and TB treatment should be carried out simultaneously, and co-infected individuals should be isolated to effectively control the spread. These results support the implementation of integrated HIV-TB control strategies and provide scientific evidence to inform medium and long term planning, monitoring, and evaluation.