Sharkey Kieran J
Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, UK.
J Math Biol. 2008 Sep;57(3):311-31. doi: 10.1007/s00285-008-0161-7. Epub 2008 Feb 14.
In many fields of science including population dynamics, the vast state spaces inhabited by all but the very simplest of systems can preclude a deterministic analysis. Here, a class of approximate deterministic models is introduced into the field of epidemiology that reduces this state space to one that is numerically feasible. However, these reduced state space master equations do not in general form a closed set. To resolve this, the equations are approximated using closure approximations. This process results in a method for constructing deterministic differential equation models with a potentially large scope of application including dynamic directed contact networks and heterogeneous systems using time dependent parameters. The method is exemplified in the case of an SIR (susceptible-infectious-removed) epidemiological model and is numerically evaluated on a range of networks from spatially local to random. In the context of epidemics propagated on contact networks, this work assists in clarifying the link between stochastic simulation and traditional population level deterministic models.
在包括种群动态学在内的许多科学领域中，除了非常简单的系统外，所有系统所占据的巨大状态空间可能会排除确定性分析。在此，一类近似确定性模型被引入流行病学领域，该模型将这种状态空间简化为在数值上可行的状态空间。然而，这些简化的状态空间主方程通常并不构成一个封闭集。为了解决这个问题，使用封闭近似对这些方程进行近似。这个过程产生了一种构建确定性微分方程模型的方法，该模型具有潜在的广泛应用范围，包括使用时间相关参数的动态定向接触网络和异构系统。该方法在SIR（易感 - 感染 - 康复）流行病学模型的案例中得到了例证，并在从空间局部到随机的一系列网络上进行了数值评估。在接触网络上传播的流行病背景下，这项工作有助于阐明随机模拟与传统种群水平确定性模型之间的联系。
