标题： 流行病模型中的极端爆发动力学 显示英文标题

标题： Extreme outbreak dynamics in epidemic models

摘要： 受最近的疫情爆发，包括新冠状病毒病（COVID-19）的启发，我们解决了在包含人口噪声的大类随机疫情模型中计算大规模疫情动态和可能性的经典问题，包括易感-感染-恢复（SIR）模型及其一般扩展。 在大人群的极限情况下，我们计算了所有大规模疫情的概率分布，包括那些涉及异常大或小（极端）比例人口感染的情况。 我们的方法揭示了，与离散状态随机系统中发生的其他著名罕见事件不同，极端疫情的统计特性来源于一个完整的哈密顿路径连续体，每个路径都满足独特的边界条件，并具有守恒的概率通量。 显示英文摘要

摘要： Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with demographic noise, including the Susceptible-Infected-Recovered (SIR) model and its general extensions. In the limit of large populations, we compute the probability distribution for all extensive outbreaks, including those that entail unusually large or small (extreme) proportions of the population infected. Our approach reveals that, unlike other well-known examples of rare events occurring in discrete-state stochastic systems, the statistics of extreme outbreaks emanate from a full continuum of Hamiltonian paths, each satisfying unique boundary conditions with a conserved probability flux.