A tuberculosis model with early and late latency, imperfect vaccination, and relapse: An application to China

Screening those individuals who are latent but at higher risk of rapidly developing active tuberculosis (TB) is one of the intervention measures to control the spread of TB. This work proposes a TB SVELIT (S‐Susceptible, V‐Vaccinated, E‐Early latent, L‐Late latent, I‐Infected, T‐Treated) transmission model with relapse. In particular, a complete threshold dynamical analysis for the model is performed and the existence of optimal control is obtained. Meanwhile, the validity of the model is shown by comparing the real data with the fitted curve and the future trend in the incidence of TB in China is predicted. More importantly, the effects of four strategies, including vaccination, media propaganda, screening latent individuals, and receiving treatment, are evaluated numerically. The results suggest that the above four strategies can effectively control TB and shorten the duration of the epidemic. Interestingly, treatment is more effective than vaccination in controlling TB, but media propaganda and latent screening are cheaper and easier to implement.