Effective degree network disease models
Effective degree network disease models
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DOI：
10.1007/s00285-010-0331-2
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发表时间：
2011-02-01
影响因子：
1.9
通讯作者：
Willeboordse, Frederick H.
中科院分区：
文献类型：
--
作者：
Lindquist, Jennifer;Ma, Junling;Willeboordse, Frederick H.
引入了一种对网络上传染病传播进行建模的有效程度方法，并将其应用于不赋予免疫力的疾病（易感-感染-易感模型，缩写为 SIS）和赋予永久免疫力的疾病（易感-感染-恢复模型，缩写为 SIR）。每个模型都被表述为一个大型常微分方程组，用于跟踪个体易感和传染性邻居的数量。通过数值模拟，发现这些有效度模型与随机图上网络的相应随机过程非常一致，因为它们捕获了初始指数增长率、SIS 模型的入侵疾病的地方性平衡以及 SIR 模型的流行高峰。对于每个有效程度模型，都会导出疾病阈值条件的公式。对于具有相同疾病和网络参数的模型，SIS 模型的阈值参数大于从渗滤理论推导的阈值参数，因此疾病可能以低于渗滤理论预测的传播率入侵。对于SIR模型，阈值条件等于渗流理论预测的阈值条件。因此，与经典的均质混合疾病模型不同，SIS和SIR有效度模型具有不同的疾病阈值条件。
An effective degree approach to modeling the spread of infectious diseases on a network is introduced and applied to a disease that confers no immunity (a Susceptible-Infectious-Susceptible model, abbreviated as SIS) and to a disease that confers permanent immunity (a Susceptible-Infectious-Recovered model, abbreviated as SIR). Each model is formulated as a large system of ordinary differential equations that keeps track of the number of susceptible and infectious neighbors of an individual. From numerical simulations, these effective degree models are found to be in excellent agreement with the corresponding stochastic processes of the network on a random graph, in that they capture the initial exponential growth rates, the endemic equilibrium of an invading disease for the SIS model, and the epidemic peak for the SIR model. For each of these effective degree models, a formula for the disease threshold condition is derived. The threshold parameter for the SIS model is shown to be larger than that derived from percolation theory for a model with the same disease and network parameters, and consequently a disease may be able to invade with lower transmission than predicted by percolation theory. For the SIR model, the threshold condition is equal to that predicted by percolation theory. Thus unlike the classical homogeneous mixing disease models, the SIS and SIR effective degree models have different disease threshold conditions.