论文标题
是否有可能暂停流行病感染的传播？动态的蒙特卡洛方法
Is it possible to suspend the spread of an epidemic infection? The dynamic Monte Carlo approach
论文作者
论文摘要
我们研究了使用动态蒙特卡洛方法（DMC）的风险因素$β$（控制参数）的流行病学感染扩散的动力学。在我们的玩具模型中，由于随机移动个体的接触而引起的感染传播。我们表明，恢复的行为严重取决于$β$的值。对于亚临界值$β<β_{c} \ sim 0.6 $，被感染病例的数量渐近地收敛到零，因此对于中等风险因素，感染可能会随着时间而消失。我们的模拟表明，随着时间的流逝，这种系统的属性渐近地接近2D渗透系统中的临界过渡。我们还分析了一个扩展系统，其中包括两个附加参数：隔离隔离状态的限制。发现早期的隔离度确实会导致感染的不规则（带有阳性的Lyapunov指数）振荡动力学。如果隔离区的下限足够小，则恢复动力学将获得具有几个阻尼峰的特征性非单调形状。在有免疫力的个体中，感染传播的动力学也得到了研究。
We study a dynamics of the epidemiological infection spreading at different values of the risk factor $β$ (a control parameter) with the using of dynamic Monte Carlo approach (DMC). In our toy model, the infection transmits due to contacts of randomly moving individuals. We show that the behavior of recovereds critically depends on the $β$ value. For sub-critical values $β<β_{c}\sim 0.6$, the number of infected cases asymptotically converges to zero, such that for a moderate risk factor the infection may disappear with time. Our simulations shown that over time, the properties of such a system asymptotically become close to the critical transition in 2D percolation system. We also analyzed an extended system, which includes two additional parameters: the limits of taking on/off quarantine state. It is found that the early quarantine off does result in the irregular (with positive Lyapunov exponent) oscillatory dynamics of infection. If the lower limit of the quarantine off is small enough, the recovery dynamics acquirers a characteristic nonmonotonic shape with several damped peaks. The dynamics of infection spreading in case of the individuals with immunity is studied too.
