论文标题
流行病的随机方法
Stochastic approach to epidemic spreading
论文作者
论文摘要
我们使用随机方法分析了四个模型的流行病模型，其中主要随机变量是每个班级中的个体数量。主方程描述了随机方法，并使用质量行动定律来建立每个过程（例如感染或恢复）的过渡速率。我们对每类个体平均数量的演化方程进行数值模拟以及数值集成。流行病扩散的发作是通过对无疾病状态的线性分析获得的，从中遵循感染的初始指数增加和新病例的频率。还获得了表征流行病扩散为临界相变的阶段参数和个体数量的差异。
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition rate for each process such as infection or recovery are set up by using the law of mass action. We perform numerical simulations as well as numerical integration of the evolution equations for the average number of each class of individuals. The onset of the epidemic spreading is obtained by a linear analysis of the disease free state, from which follows the initial exponential increase of the infected and the frequency of new cases. The order parameter and the variance in the number of individuals are also obtained characterizing the onset of epidemic spreading as a critical phase transition.
