Meta-population model about immigrants and natives with heterogeneity mixing and vaccine strategy of tuberculosis in China

China is one of the countries in the world carrying a heavy burden of tuberculosis. Due to the unbalanced economic development, the number of people working in other parts of country is huge, and the mobility of personnel has exacerbated the increase in tuberculosis cases. Most patients affected by this are in their middle and young ages. It is having a great impact among the family and society. Therefore, research on how to control this disease is absolutely necessary. The population is divided into two categories such as local population and the immigrant population. A pulmonary tuberculosis dynamic model with population heterogeneity is established. We calculate the basic reproductive number and the controlled reproductive number, and discuss the two types of population under the constraints given by the amount of vaccine and the optimal immunization ratio obtained is (0.118, 0.107), which can reduce the effective reproduction number from 5.85 to 0.227. It is understood that immunizing the local population will control the spread of the epidemic to a large extent, and we simulate the final scale of infection after immunization under the optimal immunization ratio. It can take a minimum of at least 10 years to reduce the spread of this disease, but to eliminate it forever, it needs at least a minimum of 100 years.