Modeling and dynamic analysis of tuberculosis in mainland China from 1998 to 2017: the effect of DOTS strategy and further control

Abstract

Abstract Background Tuberculosis (TB) is one of the most important health topics in the world. Directly observed treatment and short course chemotherapy (DOTS) strategy combines medicine care and modern health system firmly, and it has been carried out by World Health Organization (WHO) since 1997. In the struggle with TB, China has promoted the process of controlling the disease actively, and the full coverage of DOTS strategy has been reached around 2004. Mathematical modeling is a very useful tool to study the transmission of diseases. Understanding the impact of DOTS strategy on the control of TB is important for designing further prevention strategy. Methods We investigate the impact of control strategy on the transmission of TB in China by dynamic model. Then we discuss further control for TB aiming at developing new vaccine and improving treatment. The optimal control problem, minimizing the total number of infectious individuals with the lowest cost, is proposed and analyzed by Pontryagin’s maximum principle. Numerical simulations are provided to illustrate the theoretical results. Results Theoretical analysis for the epidemic model is given. Based on the data reported by National Bureau of Statistics of China (NBSC), the basic reproduction number of each stage is estimated and compared, and they are $\mathcal {R}_{0}^{1}=1.7885$R01=1.7885 and $\mathcal {R}_{0}^{2}=1.0741$R02=1.0741, respectively. Optimal control strategy for further control is designed and proved well. An intuitionistic comparison between the optimal control strategy and the current control strategy is given. Conclusions The diagnosis and treatment of TB in China have been promoted a lot and the $\mathcal {R}_{0}$R0 is reduced by the full coverage of DOTS strategy. However, the $\mathcal {R}_{0}$R0 in China is still greater than 1 now. The relationship between $\mathcal {R}_{0}$R0 and vaccination strategy is shown. Optimal strategy aiming at exposed and infected population is suggested for further control.