On the spread of epidemics in a closed heterogeneous population.
On the spread of epidemics in a closed heterogeneous population.
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DOI：
10.1016/j.mbs.2008.07.010
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发表时间：
2008-10
影响因子：
4.3
通讯作者：
Novozhilov, Artem S.
中科院分区：
文献类型：
--
作者：
Novozhilov, Artem S.
异质性是任何经历疾病的群体的重要特性。在这里，我们将异质群体理论的一般方法应用于流行病学中最简单的数学模型。特别是，SIR（易感染-感染-去除）模型制定和分析时，对特定疾病的易感性或传染性分布。研究表明，非均质模型可以化为具有非线性传递函数的齐次模型，并给出了显式的传递函数。在疾病参数初始分布为伽玛分布的情况下，从具有分布易感性和传染性的模型推导出了广泛使用的功率传递函数。因此，提供了被认为是以高精度模仿现实的现象学模型的机械推导。对于任意初始易感性分布，得到了流行病最终规模的方程，讨论了种群异质性的含义，特别指出了通常的矩封闭方法在研究模型的长期行为时可能导致错误的结论。
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from the model with distributed susceptibility and infectivity with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which is believed to mimic reality with high accuracy, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution of susceptibility is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the models.
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影响因子：
4.3
作者：
DUSHOFF, J;LEVIN, S
通讯作者：
LEVIN, S
DOI：
10.1142/s0218202599000610
发表时间：
1999-12-01
影响因子：
3.5
作者：
Ackleh, AS;Marshall, DF;Fitzpatrick, BG
通讯作者：
Fitzpatrick, BG
影响因子：
1.4
作者：
Dushoff, J
通讯作者：
Dushoff, J
影响因子：
2.9
作者：
Dwyer, G;Elkinton, JS;Buonaccorsi, JP
通讯作者：
Buonaccorsi, JP
影响因子：
1.9
作者：
Hyman, JM;Li, J
通讯作者：
Li, J