急性传染病对人民生命健康所造成的威胁不容小觑，利用数学模型和统计方 法能够对传染病疫情动态进行刻画，从而为疫情预防和控制工作的决策提供参考。 然而，现有的疫情动态传播模型大多集中在单一种群的简单假设之下，从而欠缺 对疫情在我国全国范围内空间传播描述的适用性;部分集合种群假设下的模型或 是适用于城镇、社区等小范围内的疫情动态，或是依赖于真实的交通数据。因此， 本文以我国 2009 年甲型 H1N1 流感疫情病例数据为例，基于集合种群理论建立 了一个我国全国范围内的疫情时空动态传播模型。
考虑将疫情传播分为两个部分，一是子种群内部的病例变化，二是子种群之 间的人口流动。针对子种群内部的病例变化，采用单一种群的思路进行建模。首 先，基于有效再生数在整个疫情期间的阶段性波动，利用调整后的 PLR (Piecewise Linear Represent)方法对时间序列数据进行划分，得到了与节假日具有明显对应 关系的疫情分段结果。其次，在 SEIR 模型的基础上对仓室流动规则进行设置， 重点体现了假期、疫苗接种、媒体报道三者对疫情传播的影响。最终，在单一种 群假设下，全国数据所得拟合结果的可决系数约为 99.26%。针对子种群之间的 人口流动，采用交通规划的经典方法进行建模。首先，以区域社会经济指标为特 征，采用 Poission 回归对各子种群的出行生成量和吸引量进行拟合;其次，采用 重力模型与辐射模型分别对出行分布进行建模，从而得到子种群间的人口流动模 型。最后，综合这两个部分得到集合种群思想下的疫情时空动态传播模型。
针对 2009 年甲流疫情数据的应用结果表明，模型拟合所得的累积病例数与 真实数据间的可决系数平均约为 98.77%，Pearson 相关系数平均约为 95.05%;模 型拟合所得的各子种群累计病例数达到指定规模的先后顺序与真实情况贴合良 好，在指定 100 人、200 人及 500 人规模下的拟合准确性分别约为 85.23%、89.47% 及 90.05%。此外，模型拟合结果也为疫情防控决策提供了参考，如假期对疫情 传播的明显抑制作用，尤其在天津、山西、广东等地;又如东部及南部沿海地区， 媒体报告疫情数据对疫情传播的抑制作用更为显著等。

The threat posed by acute infectious diseases to people's health cannot be underestimated. The use of mathematical models and statistical methods can depict the dynamics of infectious disease outbreaks, and then provide reference for decision- making in epidemic prevention and control efforts. However, most existing models of epidemic dynamics focus on simplistic assumptions of single populations, lacking applicability in describing the spatial spread of the epidemic across the entire country. Some models based on the assumption of aggregated populations are either suitable for small-scale dynamics within cities or communities or rely on actual traffic data. Therefore, using the 2009 A(H1N1) influenza case data in China as an example, this paper establishes a spatiotemporal dynamic transmission model for the nationwide spread of the epidemic based on the theory of aggregated populations.
The spread of the epidemic is considered in two parts: one is the change in cases within subpopulations, and the other is the movement of people between subpopulations. For the change in cases within subpopulations, a single-population approach is used for modeling. First, based on the phased fluctuations of the effective reproductive number throughout the epidemic period, the adjusted PLR (Piecewise Linear Represent) method is used to divide the time series data, yielding segmented epidemic results that have a clear corresponding relationship with holidays. Next, the SEIR model is used as a basis for setting compartment flow rules, with a focus on the impact of holidays, vaccinations, and media reporting on the spread of the epidemic. Ultimately, under the single-population assumption, the coefficient of determination for the fitting results from national data is approximately 99.26%. For the movement of people between subpopulations, a classic method of traffic planning is used for modeling. First, using regional socio-economic indicators as characteristics, Poisson regression is employed to fit the travel generation and attraction volumes of each subpopulation; second, the gravity model and radiation model are used to model travel distribution, thereby obtaining a population flow model between subpopulations.
Finally, integrating these two parts results in a spatiotemporal dynamic transmission model of the epidemic under the concept of metapopulation model.
The application of the model to the 2009 influenza A data shows that the coefficient of determination between the cumulative number of cases fitted by the model and the real data is approximately 98.77% on average, and the Pearson correlation coefficient is about 95.05% on average; the order in which the cumulative number of cases in each subpopulation reaches a specified size fits well with the real situation, with fitting accuracies of about 85.23%, 89.47%, and 90.05% at the specified sizes of 100, 200, and 500 people, respectively. Additionally, the results of the model fitting also provide a reference for epidemic prevention and control decisions. For instance, holidays have a significant inhibitory effect on the spread of the epidemic, especially in regions such as Tianjin, Shanxi, and Guangdong. Moreover, in the eastern and southern coastal areas, the inhibitory effect of media-reported epidemic data on the spread of the disease is even more pronounced.