大规模人群中流行病的随机绝灭和疫苗接种的作用
Stochastic extinction of epidemics in large populations and role of vaccinations
摘要：
我们研究了流行病模型中的随机灭绝现象以及在最优逃逸路径下的大种群中随机接种疫苗的影响，发现在相同的疫苗接种量下，不同的随机接种策略在减少灭绝时间上会有很大的不同.根据两个参数考虑疫苗接种策略：由$γ$给出的疫苗接种的平均频率，以及疫苗接种的幅度$ε$，其中$ε\ll 1$是指在某个特定时刻接种疫苗的人口比例。研究发现，当单位时间内接种疫苗的平均个体数$γε$保持恒定时，$γ$和$ε$的特定值可以在增加流行病灭绝的机会方面发挥非常显著的作用。研究结果表明，如果在较大的群体中发生较低频率的疫苗接种，对应于低$γ$，高$ε$策略，则预期的灭绝时间可以显著缩短。
英文摘要：
We investigate stochastic extinction in an epidemic model and the impact of random vaccinations in large populations formulated in terms of an optimal escape path. We find that different random vaccination strategies can have widely different results in decreasing expected time till extinction, for the same total amount of vaccines used. Vaccination strategies are considered in terms of two parameters: average frequency of vaccinations, given by $γ$, and the amplitude of the vaccinations, $ε$, where $ε\ll 1$ refers to the proportion of the population being vaccinated at some particular instant. It is found that while the average number of individuals vaccinated per unit time, $γε$, is kept constant, the particular values of $γ$ and $ε$ can play a highly significant role in increasing the chance of epidemic extinction. The findings suggest that expected time till extinction can be significantly shortened if less frequent vaccinations occur in larger groups, corresponding to low $γ$, high $ε$ strategy.
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