Tuberculosis was ranked No. 3 among 29 types of infectious diseases in January 2022 of Jiangsu Province, in the southeast of China, and it has strong seasonality whose incidence rate has been high in springs and low in winters. This comprehensive study extends the spreading dynamics to the control strategies of TB in Jiangsu Province with time-varying transmission rate, which is the first one in this type. The periodic transmission rate is incorporated to the classic SEIR model with susceptible, latent, infectious, and recovered compartments. The analysis shows that when the basic reproduction number (Formula presented.) is less than one, the epidemic will eventually disappear but, if (Formula presented.) is larger than one, the disease may persist with a periodic solution. The (Formula presented.) value of Jiangsu TB is calculated as 1.297. In addition, the model predicts that the epidemic will not disappear over time and there will be a major outbreak after certain years. To eradicate TB, this work introduces three control strategies on susceptible, latent, and infectious populations. It turns out that the optimal control solutions can reduce the incidence rate in 2035 by 90% from 2015, the goal of World Health Organization. Simultaneously, we find that the optimal controls have the same seasonality as the transmission rate. This indicates that Jiangsu Province needs to invest more control efforts in springs than in winters. In addition, the cost of control strategies is analyzed in terms of the unit cost, total cost, and incremental cost-effectiveness. Summarizing all results, we recommend targeting the latent patients, or both latent and infectious individuals, with the transmission rate-synchronized control strength as the most effective control strategy, to mitigate or even eradicate TB disease in Jiangsu Province.
- optimal control
- time-dependent transmission rate