Bauch C T
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada.
J Math Biol. 2002 Nov;45(5):375-95. doi: 10.1007/s002850200153.
We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been attempted. Our goals are 1). to investigate issues relating to the application of moment closure approximations to dynamic and irregular networks, and 2). to understand the impact of concurrent casual partnerships on STD transmission through a population of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations. We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic. Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure approximation is very flexible in the kinds of network models it can approximate.
我们针对通过稳定/偶然伴侣网络传播的性传播疾病（STD）网络模型开发了一种矩闭合近似（MCA）方法。MCA先前已被用于近似静态规则晶格，而将其应用于动态不规则网络是一项新的尝试，并且尚未尝试将其应用于具有社会学动机的网络模型。我们的目标是：1）研究与矩闭合近似应用于动态和不规则网络相关的问题；2）了解在以稳定的一夫一妻制伴侣为主的人群中，同时存在的偶然伴侣关系对性传播疾病传播的影响。我们能够为表示性伴侣动态的动态不规则网络推导矩闭合近似，然而，由于标准对近似的误差较大，我们被迫使用三重近似。这个例子强调了对矩闭合近似进行误差分析的重要性。我们还发现，少量的偶然伴侣关系会大幅增加流行病的患病率和传播速度。最后，尽管该近似是针对特定网络模型推导出来的，但我们只需通过改变控制动态网络结构的模型参数，就能恢复对广泛网络模型的近似。因此，我们的矩闭合近似在其能够近似的网络模型类型方面非常灵活。
