论文标题
SIS流行病的通用性从小初始条件开始
Universality of SIS epidemics starting from small initial conditions
论文作者
论文摘要
我们正在研究大型网络上的确定性SIS动力学，仅从少数受感染的个体开始。在温和的假设下，我们表明，在同一网络和具有相同参数的任何两种流行曲线 - 当初始条件足够小时，无论是在开始时如何分布的，直到时间翻译都几乎相同。极限物体（从无限的过去的无限流行率开始）被确定为将无疾病状态与地方性平衡相关联的非平凡的永恒解决方案。我们的框架涵盖了几个基准模型，包括N互换平均场近似（NIMFA）和不均匀平均场近似（IMFA）。
We are investigating deterministic SIS dynamics on large networks starting from only a few infected individuals. Under mild assumptions we show that any two epidemic curves - on the same network and with the same parameters - are almost identical up to time translation when initial conditions are small enough regardless of how infections are distributed at the beginning. The limit object - an epidemic starting from the infinite past with infinitesimal prevalence - is identified as the nontrivial eternal solution connecting the disease free state with the endemic equilibrium. Our framework covers several benchmark models including the N-Intertwined Mean Field Approximation (NIMFA) and the Inhomogeneous Mean Field Approximation (IMFA).
