A novel pulmonary tuberculosis infectious disease model with piecewise periodic transmission rate for epidemic analysis in Zhejiang province, China

Pulmonary tuberculosis is a highly infectious disease that causes great harm to human health. This paper establishes a dynamic transmission tuberculosis model with a piecewise periodic transmission rate function, in which this piecewise periodic transmission rate function can depict the impact of prevention and control measures with respect to COVID-19 on in Zhejiang Province, China.The existence of incubation period will cause the delay of the number of patients in the model and present a periodic form, which increases the difficulty of theoretical analysis and numerical experiment. By defining the basic reproduction number operator, the comparison principle, consistent persistence theory, and other methods are used to establish sufficient conditions for disease extinction and persistence in the proposed model. In the numerical application of the model, by setting a suitable piecewise periodic transmission rate function model the COVID-19 outbreak period as a cut-off point, the model is analysed the effect of COVID-19 on pulmonary tuberculosis, which is different from other studies that only used statistical methods to explore the effect of COVID-19 on pulmonary tuberculosis. Then the model is applied to predict the future prevalence of tuberculosis. Finally, the numerical results show that the change of tuberculosis epidemic is highly dependent on the change of COVID-19 prevention and control measures in Zhejiang, China.