考虑自愈的SARS的传播模型

Modeling the SARS Epidemic Considering Self-cure

本文根据对SARS传播的分析,把人群分为5类:易感类、潜伏期类、患病未被发现类、患病已被发现类和治愈及死亡组成的免疫类,并考虑自愈因素,提出了两个模型:微分方程模型和基于Small-World Network的模拟模型。对微分方程模型,以香港为例讨论了自愈的影响,在一定意义下说明白愈现象在SARS传播中是普遍存在的。模拟模型利用Small-World Network模拟现实中人们之间的接触;借鉴Sznajd模型观念传播的基本思想"考察区域内每个成员如何影响与其有联系的其他成员",用影响类比传染,从患病者去传染与其有接触的健康人的角度,模拟SARS的传播过程;然后吸收元胞自动机模型同步更新的思想,最终建立了一个患病者传染邻居,且一个成员同时受所有邻居影响的基于Small-WorldNetwork的模拟模型。对此模型,我们讨论了一些主要参数及接种疫苗的影响,最后拟合北京数据,讨论了提前或推迟5天采取措施的影响。

In this paper, a SEIuIiR (susceptible, exposed, unisolated infectious, isolated infectious, recovered) model with self-cure is built to model the SARS epidemic. The problem is solved with two methods: one is ordinary differential equation which we then come to a conclusion that self-cure indeed exists in the SARS transmission; the other is computer simulation based on the small-work network which we also absorb the basic ideas of the Sznajd and the cellular automation model, and then we discuss some parameters and the effects of vaccination. At last we analyze the epidemic situation in Beijing and estimate the results if control measures are taken 5 days later or earlier.