Air pollution increases the risk of getting respiratory diseases. Both the removal of air pollutants and the transmission of diseases can be influenced by random perturbations. In this work, we develop a stochastic differential equation (SDE) model, coupled with seasonal air pollution, to study the dynamics of infectious respiratory disease spread. The periodicity of disease outbreaks is assumed to be caused by seasonal air pollution. The SDE of the air quality index (AQI) is proved to be ultimately bounded. The complexity of the SDE of infected individuals lies in the transmission rate that depends on air pollution. We prove that the system driven by the periodic clearance rate has at least one stochastic periodic solution under certain conditions. By computing the closed form of the Hermite expansion of transformation density, we construct an approximate likelihood function to fit the data of AQI and influenza-like illness cases, as a case study. Data fitting shows that the stochastic periodic model can well capture the dynamical behavior of air pollution and outbreaks of the infectious respiratory disease. We also study the impact of parameters on the reduction of air pollution and disease spread. This work shows the correlation between air pollution and infectious respiratory disease outbreaks and illustrates that the intensity of the environmental disturbance is a factor that cannot be ignored.

空气污染会增加患上呼吸道疾病的风险。除去空气污染物和疾病传播都可能受到随机扰动的影响。在这项工作中，我们开发了一个随机微分方程（SDE）模型，并结合季节性空气污染，以研究传染性呼吸道疾病传播的动态。疾病暴发的周期性被认为是由季节性空气污染引起的。事实证明，空气质量指数（AQI）的SDE最终是有界的。受感染个体的SDE的复杂性在于其传播速率取决于空气污染。我们证明，在一定条件下，由周期清除率驱动的系统具有至少一个随机周期解。通过计算转换密度的Hermite展开的闭合形式，作为案例研究，我们构建了一个近似似然函数来拟合AQI和流感样疾病病例的数据。数据拟合表明，随机周期模型可以很好地捕获空气污染和传染性呼吸道疾病暴发的动力学行为。我们还研究了参数对减少空气污染和疾病传播的影响。这项工作表明了空气污染与传染性呼吸道疾病暴发之间的相关性，并说明了环境干扰的强度是一个不可忽视的因素。我们还研究了参数对减少空气污染和疾病传播的影响。这项工作表明了空气污染与传染性呼吸道疾病暴发之间的相关性，并说明了环境干扰的强度是一个不可忽视的因素。我们还研究了参数对减少空气污染和疾病传播的影响。这项工作表明了空气污染与传染性呼吸道疾病暴发之间的相关性，并表明环境干扰的强度是一个不可忽视的因素。