U.S. Naval Research Laboratory, Washington, D.C. 20375, USA.
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Phys Rev Lett. 2022 Feb 18;128(7):078301. doi: 10.1103/PhysRevLett.128.078301.
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.
受最近的疫情爆发的启发，包括 COVID-19，我们解决了在具有人口统计学噪声的大型随机传染病模型中计算人群中广泛爆发的动力学和可能性的典型问题，包括易感-感染-恢复（SIR）模型及其一般扩展。在大群体的极限下，我们计算了所有广泛爆发的概率分布，包括那些涉及异常大或小（极端）比例的人口感染的爆发。我们的方法表明，与离散状态随机系统中发生的其他罕见事件的例子不同，极端爆发的统计数据源于完整的哈密顿路径连续统，每个路径都满足独特的边界条件和守恒的概率通量。
