The deterministic limit of infectious disease models with dynamic partners
The deterministic limit of infectious disease models with dynamic partners
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DOI：
10.1016/s0025-5564(98)00012-1
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发表时间：
1998-06-15
影响因子：
4.3
通讯作者：
Altmann, M
中科院分区：
文献类型：
--
作者：
Altmann, M
本文分析了在伙伴关系期间发生接触的传染病模型的大种群动态。该模式允许并行的伙伴关系，遵循非常广泛的动态法律。以前的工作，与随机版本的模型，计算繁殖数，初始增长率，和最终的大小。在本文中，确定性系统，这是大人口的限制。该构造不寻常地需要两个不同的缩放因子。接下来，近似使用的瓦特和可能的相关模型进行比较的精确解。这种近似值在疫情开始和伙伴关系时间较短时最为准确。最后，该模型被推广到允许伙伴关系之间的依赖关系。这一概括允许按比例混合与任意分布的合作伙伴的数量。(C)1998年爱思唯尔科学公司保留所有权利。
This paper analyzes the large population dynamics of an infectious disease model with contacts that occur during partnerships. The model allows for concurrent partnerships following a very broad class of dynamic laws. Previous work, with a stochastic version of the model, computed the reproductive number, the initial growth rate, and the final size. In the present paper, the deterministic system that is the limit for large populations is constructed. The construction is unusual in requiring two different scaling factors. Next, the approximation used by Watts and May for a related model is compared with the exact solution. This approximation is most accurate at the beginning of the epidemic and when partnerships are short. Lastly, the model is generalized to allow dependencies among partnerships. This generalization permits proportional mixing with an arbitrary distribution on the number of partners. (C) 1998 Elsevier Science Inc. Ail rights reserved.