标题： 随机单调性和在克伦-莫德-杰格斯分支过程中定义的函数的连续性性质，应用于流行病建模中的疫苗接种 显示英文标题

标题： Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling

摘要： 本文涉及Crump-Mode-Jagers分支过程，描述了疫情传播依赖于接种疫苗人口比例的情况。 分支过程中的出生事件独立地被中止，其中时间依赖的概率由接种疫苗人口的比例给出。 通过耦合论证，证明了此类分支过程中定义的广泛函数类（例如，灭绝时间和所有时间内的总出生数）的随机单调性和连续性结果，从而得出控制相应函数（例如，持续时间和最终规模）的最优接种方案。 该理论通过应用到保加利亚腮腺炎爆发持续时间的控制进行了说明。 显示英文摘要

摘要： This paper is concerned with Crump-Mode-Jagers branching processes, describing spread of an epidemic depending on the proportion of the population that is vaccinated. Births in the branching process are aborted independently with a time-dependent probability given by the fraction of the population vaccinated. Stochastic monotonicity and continuity results for a wide class of functions (e.g., extinction time and total number of births over all time) defined on such a branching process are proved using coupling arguments, leading to optimal vaccination schemes to control corresponding functions (e.g., duration and final size) of epidemic outbreaks. The theory is illustrated by applications to the control of the duration of mumps outbreaks in Bulgaria.