Haas V J, Caliri A, da Silva M A
Departamento de Física e Matemática, Universidade de São Paulo, FFCLRP - 14040-900 Ribeirão Preto, SP - Brasil.
J Biol Phys. 1999 Dec;25(4):309-24. doi: 10.1023/A:1005115117228.
The epidemic event, seen as a nonequilibrium dynamic process, is studied through a simple stochastic system reminiscent of the classical SIR model. The system is described in terms of global and local variables and was mainly treated by means of Monte Carlo simulation; square lattices N×N, with N=23, 51, 100, 151, and 211 were used. Distinct extensive runs were performed and then classified as corresponding to epidemic or non-epidemic phase. They were examined with detail through the analysis of the event duration and event size; illustrations, such as density-like plots in the space of the model's parameters, are provided. The epidemic/non-epidemic phase presents smaller/larger relative fluctuations, whereas closer to the threshold the uncertainty reaches its highest values. Far enough from the threshold, the distribution φ(t) of the events time duration t shows a step-like appearance. However at the threshold line it shows an exponential behavior of the form φ (t) ∼ exp (-ωt); the same behavior is observed for the event size distribution. These results help to explain why the approach to epidemic threshold would be hard to anticipate with standard census data.
该疫情事件被视为一个非平衡动态过程，通过一个类似于经典SIR模型的简单随机系统进行研究。该系统用全局变量和局部变量来描述，主要通过蒙特卡罗模拟进行处理；使用了N = 23、51、100、151和211的方形晶格N×N。进行了不同的大量运行，然后分类为对应于流行或非流行阶段。通过对事件持续时间和事件规模的分析进行详细检查；提供了诸如模型参数空间中的密度样图等图示。流行/非流行阶段呈现出较小/较大的相对波动，而越接近阈值，不确定性达到其最高值。远离阈值时，事件持续时间t的分布φ(t)呈现出阶梯状外观。然而，在阈值线上，它呈现出φ(t) ∼ exp(-ωt)形式的指数行为；事件规模分布也观察到相同的行为。这些结果有助于解释为什么用标准普查数据很难预测接近疫情阈值的情况。
