论文标题
具有一般暴露和传染性时期的多局部流行模型
Multi-patch epidemic models with general exposed and infectious periods
论文作者
论文摘要
我们研究了多方面的流行模型，在任何一个易感性，暴露/潜伏，传染性和恢复状态中，个体可以从一个斑块迁移到另一个斑块。我们假设感染都在局部发生，其速率取决于贴片，以及从所有其他斑块的“距离”。暴露和传染性时期具有一般分布，不受个人可能迁移的影响。假定这三个州中的任何一个中的迁移过程是马尔可夫人，并且独立于暴露和传染性时期。我们为易感性，暴露/潜在，传染性和恢复过程建立了大数字（FLLN）和函数中心限制定理（FCLT）的功能定律。在FLLN中，限制由一组伏特拉积分方程确定。在确定性暴露和传染性时期的特殊情况下，极限变成了延迟的ods系统。在FCLT中，限制由一组由独立的布朗运动和具有显式协方差结构的连续高斯过程驱动的随机伏都积分方程。
We study multi-patch epidemic models where individuals may migrate from one patch to another in either of the susceptible, exposed/latent, infectious and recovered states. We assume that infections occur both locally with a rate that depends on the patch as well as "from distance" from all the other patches. The exposed and infectious periods have general distributions, and are not affected by the possible migrations of the individuals. The migration processes in either of the three states are assumed to be Markovian, and independent of the exposed and infectious periods. We establish a functional law of large number (FLLN) and a function central limit theorem (FCLT) for the susceptible, exposed/latent, infectious and recovered processes. In the FLLN, the limit is determined by a set of Volterra integral equations. In the special case of deterministic exposed and infectious periods, the limit becomes a system of ODEs with delays. In the FCLT, the limit is given by a set of stochastic Volterra integral equations driven by a sum of independent Brownian motions and continuous Gaussian processes with an explicit covariance structure.
