Keeling M J, Rand D A, Morris A J
Department of Zoology, University of Cambridge, UK.
Proc Biol Sci. 1997 Aug 22;264(1385):1149-56. doi: 10.1098/rspb.1997.0159.
One of the simplest set of equations for the description of epidemics (the SEIR equations) has been much studied, and produces reasonable approximations to the dynamics of communicable disease. However, it has long been recognized that spatial and social structure are important if we are to understand the long-term persistence and detailed behaviour of disease. We will introduce three pair models which attempt to capture the underlying heterogeneous structure by studying the connections and correlations between individuals. Although modelling the correlations necessarily leads to more complex equations, this pair formulation naturally incorporates the local dynamical behaviour generating more realistic persistence. In common with other studies on childhood diseases we will focus our attention on measles, for which the case returns are particularly well documented and long running.
用于描述流行病的最简单方程组之一（SEIR方程组）已得到广泛研究，并能对传染病动态做出合理近似。然而，长期以来人们认识到，如果要理解疾病的长期持续存在和详细行为，空间和社会结构很重要。我们将介绍三种配对模型，它们试图通过研究个体之间的联系和相关性来捕捉潜在的异质结构。尽管对相关性进行建模必然会导致更复杂的方程，但这种配对形式自然地纳入了局部动态行为，从而产生更现实的持续性。与其他关于儿童疾病的研究一样，我们将把注意力集中在麻疹上，其病例报告记录特别完善且持续时间长。
