Intervention-Based Stochastic Disease Eradication

Disease control is of paramount importance in public health, with infectious disease extinction as the ultimate goal. Although diseases may go extinct due to random loss of effective contacts where the infection is transmitted to new susceptible individuals, the time to extinction in the absence of control may be prohibitively long. Intervention controls are typically defined on a deterministic schedule. In reality, however, such policies are administered as a random process, while still possessing a mean period. Here, we consider the effect of randomly distributed intervention as disease control on large finite populations. We show explicitly how intervention control, based on mean period and treatment fraction, modulates the average extinction times as a function of population size and rate of infection spread. In particular, our results show an exponential improvement in extinction times even though the controls are implemented using a random Poisson distribution. Finally, we discover those parameter regimes where random treatment yields an exponential improvement in extinction times over the application of strictly periodic intervention. The implication of our results is discussed in light of the availability of limited resources for control.

疾病防控在公共卫生领域举足轻重，根除传染病是其终极目标。尽管传染病可能因感染向新易感个体传播所需的有效接触随机中断而自然消亡，但在无任何防控措施的情况下，疾病根除所需的时间往往长得令人望而却步。干预防控措施通常按确定性时间表制定实施，然而在实际场景中，这类政策往往以随机流程执行，不过仍存在平均执行周期。本文针对大型有限种群，探讨以随机分布方式实施的干预防控措施的效果。我们明确阐明了基于平均周期与治疗比例的防控措施，如何根据种群规模与感染传播速率调节疾病的平均根除时间。尤为关键的是，即便防控措施以泊松分布（Poisson distribution）的随机方式实施，我们的研究结果仍表明疾病根除时间可实现指数级优化。最后，我们确定了相较于严格周期性干预，随机实施治疗措施可使疾病根除时间实现指数级优化的参数域，并结合防控资源有限的现实背景，探讨了本研究结果的实际意义。