Leung Ka Yin, Diekmann Odo
Mathematical Institute, Utrecht University, Utrecht, The Netherlands.
Julius Center for Primary Care and Health Sciences, University Medical Center Utrecht, Utrecht, The Netherlands.
J Math Biol. 2017 Feb;74(3):619-671. doi: 10.1007/s00285-016-1037-x. Epub 2016 Jun 20.
We formulate models for the spread of infection on networks that are amenable to analysis in the large population limit. We distinguish three different levels: (1) binding sites, (2) individuals, and (3) the population. In the tradition of physiologically structured population models, the formulation starts on the individual level. Influences from the 'outside world' on an individual are captured by environmental variables. These environmental variables are population level quantities. A key characteristic of the network models is that individuals can be decomposed into a number of conditionally independent components: each individual has a fixed number of 'binding sites' for partners. The Markov chain dynamics of binding sites are described by only a few equations. In particular, individual-level probabilities are obtained from binding-site-level probabilities by combinatorics while population-level quantities are obtained by averaging over individuals in the population. Thus we are able to characterize population-level epidemiological quantities, such as [Formula: see text], r, the final size, and the endemic equilibrium, in terms of the corresponding variables.
我们构建了网络上感染传播的模型，这些模型在大群体极限情况下便于进行分析。我们区分三个不同层次：（1）结合位点，（2）个体，以及（3）群体。按照生理结构群体模型的传统，模型构建从个体层面开始。个体受到的“外部世界”的影响由环境变量来描述。这些环境变量是群体层面的量。网络模型的一个关键特征是个体可以分解为若干条件独立的成分：每个个体有固定数量的与伙伴的“结合位点”。结合位点的马尔可夫链动力学仅由少数方程描述。特别地，个体层面的概率通过组合数学从结合位点层面的概率得到，而群体层面的量通过对群体中的个体求平均得到。因此，我们能够根据相应变量来刻画群体层面的流行病学量，比如[公式：见原文]、r、最终规模以及地方病平衡点。
