论文标题
非马克维亚流行模型的功能极限定理
Functional Limit Theorems for Non-Markovian Epidemic Models
论文作者
论文摘要
我们研究非马克维亚随机流行模型（SIS，爵士，爵士和SEIR），其中感染性（和潜在/暴露，免疫）时期具有一般分布。我们使用感染的时间时期（以及潜伏/暴露，免疫力）来表示演变动力学。随着人口规模倾向于无穷大的限制，我们证明了这些模型感兴趣的过程的大量功能定律（FLLN）和功能性中心极限定理（FCLT）。在FLLN中，极限是确定性Volterra积分方程系统的独特解决方案，而在FCLT中，极限过程是线性Volterra随机积分方程的多维高斯解决方案。在FCLT的证明中，我们提供了一个重要的泊松随机度量的表示，将扩散尺度的过程融合到驱动极限过程的高斯组件。
We study non-Markovian stochastic epidemic models (SIS, SIR, SIRS, and SEIR), in which the infectious (and latent/exposing, immune) periods have a general distribution. We provide a representation of the evolution dynamics using the time epochs of infection (and latency/exposure, immunity). Taking the limit as the size of the population tends to infinity, we prove both a functional law of large number (FLLN) and a functional central limit theorem (FCLT) for the processes of interest in these models. In the FLLN, the limits are a unique solution to a system of deterministic Volterra integral equations, while in the FCLT, the limit processes are multidimensional Gaussian solutions of linear Volterra stochastic integral equations. In the proof of the FCLT, we provide an important Poisson random measures representation of the diffusion-scaled processes converging to Gaussian components driving the limit process.
