Miller Joel C
Mathematical Modeling & Analysis Group and Center for Nonlinear Studies, MS B284, Los Alamos National Laboratory, Los Alamos, New Mexico, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 1):010101. doi: 10.1103/PhysRevE.76.010101. Epub 2007 Jul 10.
We analytically address disease outbreaks in large, random networks with heterogeneous infectivity and susceptibility. The transmissibility T_{uv} (the probability that infection of u causes infection of v ) depends on the infectivity of u and the susceptibility of v . Initially, a single node is infected, following which a large-scale epidemic may or may not occur. We use a generating function approach to study how heterogeneity affects the probability that an epidemic occurs and, if one occurs, its attack rate (the fraction infected). For fixed average transmissibility, we find upper and lower bounds on these. An epidemic is most likely if infectivity is homogeneous and least likely if the variance of infectivity is maximized. Similarly, the attack rate is largest if susceptibility is homogeneous and smallest if the variance is maximized. We further show that heterogeneity in the infectious period is important, contrary to assumptions of previous studies. We confirm our theoretical predictions by simulation. Our results have implications for control strategy design and identification of populations at higher risk from an epidemic.
我们通过分析研究具有异质传染性和易感性的大型随机网络中的疾病爆发。传播率(T_{uv})（即(u)感染导致(v)感染的概率）取决于(u)的传染性和(v)的易感性。最初，单个节点被感染，随后可能会或可能不会发生大规模疫情。我们使用生成函数方法来研究异质性如何影响疫情发生的概率，以及如果发生疫情，其攻击率（感染的比例）。对于固定的平均传播率，我们找到了这些概率的上下界。如果传染性是均匀的，疫情最有可能发生；如果传染性的方差最大化，则疫情最不可能发生。同样，如果易感性是均匀的，攻击率最大；如果方差最大化，则攻击率最小。我们进一步表明，与先前研究的假设相反，传染期的异质性很重要。我们通过模拟证实了我们的理论预测。我们的结果对控制策略设计和识别疫情中高风险人群具有启示意义。
