Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom.
School of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom.
Phys Rev E. 2016 Dec;94(6-1):062408. doi: 10.1103/PhysRevE.94.062408. Epub 2016 Dec 19.
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many contacts. We derive a two-dimensional diffusion model for the full temporal behavior of the stochastic susceptible-infectious-recovered (SIR) model on such a network, by making use of a time-scale separation in the deterministic limit of the dynamics. This low-dimensional process is an accurate approximation to the full model in the limit of large populations, even for cases when the time-scale separation is not too pronounced, provided the maximum degree is not of the order of the population size.
能够传播传染病的接触网络通常表现出高度的异质性，大多数个体的接触人数少于平均值，而少数个体的接触人数相对非常多。我们利用动力学的确定性极限中的时间尺度分离，推导出了这种网络上随机易感-感染-恢复（SIR）模型的完整时间行为的二维扩散模型。这个低维过程在大种群的极限下是对全模型的一个精确逼近，即使在时间尺度分离不明显的情况下，只要最大度数不是种群大小的量级。
