论文标题
在“流动后”环境中传播过程
Spreading processes in "post-epidemic" environments
论文作者
论文摘要
我们分析在一个系统中只有一小部分$ p $可以受到疾病影响的系统中的感染传播过程，而让$ 1-p $个体的个人是免疫的。这样的图片可以作为先前终止的流行过程的自然结果或以前接种疫苗的人群出现的自然结果。为此，我们将研究固定状态和空间图案的同步细胞自动机算法应用于SI，SIS和SIR模型中的空间图案，并在带有主动位点的分数$ p $的方晶格上。拟议系统中自然出现了被免疫个体包围的易感药物的“安全模式”的概念，该系统在正在考虑的流行过程中起着重要作用。给出了此类模式分布的详细分析，这又决定了固定状态$ i^*（p）$的感染药物的比例。还获得了基本复制号$ r_0^c $的阈值估计值作为活动代理分数$ p $的函数。特别是，我们的结果允许预测个体的最佳比例，需要预先接种疫苗，以便在具有给定的固化率的流行过程中获得最大的未影响药物的值。
We analyze infection spreading processes in a system where only a fraction $p$ of individuals can be affected by disease, while remaining $1-p$ individuals are immune. Such a picture can emerge as a natural consequence of previously terminated epidemic process or arise in formerly vaccinated population. To this end, we apply the synchronous cellular automata algorithm studying stationary states and spatial patterning in SI, SIS and SIR models on a square lattice with the fraction $p$ of active sites. A concept of "safety patterns" of susceptible agents surrounded by immune individuals naturally arises in a proposed system, which plays an important role in the course of epidemic processes under consideration. Detailed analysis of distribution of such patterns is given, which in turn determine the fraction of infected agents in a stationary state $I^*(p)$. Estimates for the threshold values of the basic reproduction number $R_0^c$ as a function of active agents fraction $p$ are obtained as well. In particular, our results allow to predict the optimal fraction of individuals, needed to be vaccinated in advance in order to get the maximal values of unaffected agents in a course of epidemic process with a given curing rate.
