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In this paper, the influence of PM 2. 5 on children's respiratory diseases is taken as the main research focus. Based on the real monitoring data of children's respiratory diseases in Anhui province, the traditional model is modified substantially, leading to the establishment of two mathematical models. First of all, considering that the PM 2. 5 changes over time, a nonautonomous air pollution-related disease model is constructed to study its permanence and extinction. Furthermore, regarding lag days of PM 2. 5 exposure, an air pollution-related disease model with the lag effect is installed and its local and global stabilities and Hopf bifurcation are investigated. Meanwhile, the above two models are numerically simulated, respectively. Our study demonstrates that the threshold conditions of permanence and extinction are obtained by the nonautonomous air pollution-related disease model, and the optimal parameters are obtained through the annual revision of the data by integrating the mathematical model, such that the number of children with respiratory diseases in the future can be checked and predicted. Also our study finds that the lag days of PM 2. 5 exposure have little effect on children with respiratory diseases in the air pollution-related disease model with a lag effect, but the PM 2. 5 has a tremendous influence on the number of patients. Once the lag days are combined with the effect of the PM 2. 5 , it can have a significant impact on the patients' number, e.g. an emergence of periodic oscillations, with an approximate period of 11 days in Anhui Province, due to the Hopf bifurcation. [ABSTRACT FROM AUTHOR]