论文标题
具有不同感染性的流行模型的功能性中心极限定理
Functional central limit theorems for epidemic models with varying infectivity
论文作者
论文摘要
在本文中，我们证明了在Forien，Pang和Pardoux（2020年）最近引入的随机流行病模型的功能性中心定理（FCLT）（FCLTS）。感染过程（每次感染的总体感染力）是独立的感染性随机感染性的感染性。这些感染性随机功能会引起传染性时期（以及完全普遍的暴露，恢复或免疫时期），其概率分布可能是非常一般的。流行病模型包括具有感染年龄依赖性感染性的广义非马克维亚SIR，SEIR，SIS，SIS，SIRS模型。在广义的SIR和SEIR模型的FCLT中，感染性和易感过程的扩散范围波动的局限性是对二维高斯驱动的随机燃烧器积分方程的独特解决方案，然后给出了这些求解的（这些溶液）的限制（这些求解）的限制，并予以验证的范围（均可恢复的过程），这些过程是逐渐恢复的，是在渗透的过程中的范围（均可恢复的过程）。 Volterra积分方程。我们还为广义SIS和SIRS模型提供了FCLT。
In this paper, we prove functional central limit theorems (FCLTs) for a stochastic epidemic model with varying infectivity and general infectious periods recently introduced in Forien, Pang and Pardoux (2020).The infectivity process (total force of infection at each time) is composed of the independent infectivity random functions of each infectious individual, which starts at the time of infection. These infectivity random functions induce the infectious periods (as well as exposed, recovered or immune periods in full generality), whose probability distributions can be very general. The epidemic model includes the generalized non-Markovian SIR, SEIR, SIS, SIRS models with infection-age dependent infectivity. In the FCLTs for the generalized SIR and SEIR models, the limits of the diffusion-scaled fluctuations of the infectivity and susceptible processes are a unique solution to a two-dimensional Gaussian-driven stochastic Volterra integral equations, and then given these solutions, the limits for the infected (exposed/infectious) and recovered processes are Gaussian processes expressed in terms of the solutions to those stochastic Volterra integral equations. We also present the FCLTs for the generalized SIS and SIRS models.
