Truscott J E, Gilligan C A, Webb C R
Department of Plant Sciences, University of Cambridge, U.K.
Bull Math Biol. 2000 Mar;62(2):377-93. doi: 10.1006/bulm.1999.0158.
Models of particular epidemiological systems can rapidly become complicated by biological detail which can obscure their essential features and behaviour. In general, we wish to retain only those components and processes that contribute to the dynamics of the system. In this paper, we apply asymptotic techniques to an SEI-type model with primary and secondary infection in order to reduce it to a much simpler form. This allows the identification of parameter groupings discriminating between regions of contrasting dynamics and leads to simple approximations for the model's transient behaviour. These can be used to follow the evolution of the developing infection process. The techniques examined in this paper will be applicable to a large number of similar models.
特定流行病学系统的模型可能会因生物学细节而迅速变得复杂，这些细节可能会掩盖其基本特征和行为。一般来说，我们希望只保留那些对系统动态有贡献的组成部分和过程。在本文中，我们将渐近技术应用于一个具有初次和二次感染的SEI型模型，以便将其简化为一个简单得多的形式。这使得能够识别区分不同动态区域的参数分组，并得出模型瞬态行为的简单近似值。这些可用于跟踪感染发展过程的演变。本文所研究的技术将适用于大量类似模型。
