论文标题
流行病
Epidemic spreading
论文作者
论文摘要
我们对流行病扩散的六个确定性模型进行了分析。每个班级个体数量的演变由第一阶的普通微分方程给出，这些方程是通过使用规定定义每个模型的几个过程的速率的质量行动定律来设置的。流行病的特征是新病例的频率，即每单位时间被感染的个体数量。它的特征在于基本的繁殖数，我们表明这与与进化方程的无疾病溶液相关的稳定矩阵的最大特征值有关。我们还强调了流行病的爆发与关键相变的爆发之间的类比。当人口的密度达到扩散集的临界价值时，这是Kermack和McKendrick在研究模型中提出的结果，在该模型中，回收的个体获得了永久性免疫，这是这里分析的模型之一。
We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws of mass action providing the rates of the several processes that define each model. The epidemic spreading is characterized by the frequency of new cases, which is the number of individuals that are becoming infected per unit time. It is also characterized by the basic reproduction number, which we show to be related to the largest eigenvalue of the stability matrix associated with the disease-free solution of the evolution equations. We also emphasize the analogy between the outbreak of an epidemic with a critical phase transition. When the density of the population reaches a critical value the spreading sets in, a result that was advanced by Kermack and McKendrick in their study of a model in which the recovered individuals acquire permanent immunization, which is one of the models analyzed here.
