时域统计分析在疾病传播动力学中的应用

Application of time-domain statistical analysis in the dynamics of epidemic outbreaks

文章介绍了运用时域统计分析进行疾病传播动力学研究所得到的新结果.在给定某一类疾病的潜伏期和活动期的时域统计分布参数后,该疾病在具有一定感染几率的封闭系统中的传播动力学过程即可通过求解概率微分积分方程来决定.计算结果表明,在经过长时间传播后,该系统的最终被感染率由指数τ2=cNt2决定,这里c是系统内个体的接触感染几率,Ⅳ是系统所包含的个体数量,t2是疾病活动期的平均时间长度.如果τ2>3,则该系统的最终被感染率可达到100％,因此τ2又称为疾病传播的危险指数.而在疾病传播的初期,新发病例所出现的振荡和间歇行为则由另一个指数τ1=cNt1决定,这里t1是平均潜伏期的长度.这一理论较好地弥补了以往常用的SIR模型对时域统计考虑不足的缺陷,从而对疾病在封闭系统中的传播动力学过程给出理论预测.

New results in the dynamics of epidemic outbreaks obtained by time-domain statistical analysis are presented. Once the parameters of the time-domain statistical distributions for the incubation period and active period of an epidemic disease are given, the dynamics of the disease outbreak in a closed system with given infection probability can be completely determined by solving stochastic differential-integrative equations. Calculation shows that, after a long enough time, the final infection rate of the system is determined by the index T2 = cNt2 , where is the infection probability of individuals in the system, N the number of individuals, and t2 the average length of the active period of the disease. If τ2 > 3, the final infection rate of the system may reach 100% , so τ2 can also be called the risk index. In the early days of the epidemic, the oscillatory and intermittent behavior of the new-active rate is determined by another index, τ1 =cNt1 where t1 is the average length of the incubation period. This theory overcomes the drawback of the SIR model which does nottake sufficient account of the time-domain statistics, and can provide a better theoretical prediction for the infection dynamics in a closed system.