SIR dynamics in random networks with heterogeneous connectivity.
SIR dynamics in random networks with heterogeneous connectivity.
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DOI：
10.1007/s00285-007-0116-4
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发表时间：
2008-03
影响因子：
1.9
通讯作者：
Volz E
中科院分区：
文献类型：
--
作者：
Volz E
具有指定度分布的随机网络已被提出作为人口结构的现实模型，但在随机网络中动态建模 SIR 型流行病的问题仍然很复杂。我通过展示如何使用三个非线性 ODE 系统对 SIR 动力学进行建模来解决这个难题。该方法利用概率生成函数（PGF）形式来表示随机网络的度分布，并利用以网络为中心的量（例如明确定义的类别中的边数），而不是以节点为中心的量（例如感染者或易感者的数量）。 PGF 提供了一种在网络和以节点为中心的变量之间进行转换并随时确定流行病发生率的简单方法。该理论还提供了一种简单的方法来跟踪易感者或感染者之间程度分布的演变。这些方程用于证明程度分布对流行病最终规模及其在人群中传播速度的巨大影响。据观察，幂律度分布几乎立即产生扩展相，但与泊松等均匀度分布相比，最终尺寸较小。将方程与随机模拟进行比较，结果与理论吻合良好。最后，动态方程提供了另一种方法来确定预计会发生大规模流行病的流行病阈值，低于该阈值时流行病行为仅限于有限规模的爆发。
Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by showing how the SIR dynamics can be modeled with a system of three nonlinear ODE’s. The method makes use of the probability generating function (PGF) formalism for representing the degree distribution of a random network and makes use of network-centric quantities such as the number of edges in a well-defined category rather than node-centric quantities such as the number of infecteds or susceptibles. The PGF provides a simple means of translating between network and node-centric variables and determining the epidemic incidence at any time. The theory also provides a simple means of tracking the evolution of the degree distribution among susceptibles or infecteds. The equations are used to demonstrate the dramatic effects that the degree distribution plays on the final size of an epidemic as well as the speed with which it spreads through the population. Power law degree distributions are observed to generate an almost immediate expansion phase yet have a smaller final size compared to homogeneous degree distributions such as the Poisson. The equations are compared to stochastic simulations, which show good agreement with the theory. Finally, the dynamic equations provide an alternative way of determining the epidemic threshold where large-scale epidemics are expected to occur, and below which epidemic behavior is limited to finite-sized outbreaks.
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