Department of Ecology, College of Veterinary Medicine, University of Georgia, Athens, GA, USA
Center for the Ecology of Infectious Diseases, College of Veterinary Medicine, University of Georgia, Athens, GA, USA.
J R Soc Interface. 2018 Jun;15(143). doi: 10.1098/rsif.2018.0034.
The epidemic threshold of the susceptible-infected-recovered model is a boundary separating parameters that permit epidemics from those that do not. This threshold corresponds to parameters where the system's equilibrium becomes unstable. Consequently, we use the average rate at which deviations from the equilibrium shrink to define a distance to this threshold. However, the vital dynamics of the host population may occur slowly even when transmission is far from threshold levels. Here, we show analytically how such slow dynamics can prevent estimation of the distance to the threshold from fluctuations in the susceptible population. Although these results are exact only in the limit of long-term observation of a large system, simulations show that they still provide useful insight into systems with a range of population sizes, environmental noise and observation schemes. Having established some guidelines about when estimates are accurate, we then illustrate how multiple distance estimates can be used to estimate the rate of approach to the threshold. The estimation approach is general and may be applicable to zoonotic pathogens such as Middle East respiratory syndrome-related coronavirus (MERS-CoV) as well as vaccine-preventable diseases like measles.
易感-感染-恢复模型的流行阈值是区分允许流行和不允许流行的参数的界限。该阈值对应于系统平衡变得不稳定的参数。因此，我们使用偏离平衡状态的收缩速度的平均值来定义与该阈值的距离。然而，即使在传播远低于阈值水平的情况下，宿主群体的重要动态也可能缓慢发生。在这里，我们从理论上展示了这种缓慢的动态如何阻止从易感人群的波动中估计到阈值的距离。尽管这些结果在长期观察大系统的极限情况下是精确的，但模拟表明，它们仍然为具有一系列种群大小、环境噪声和观测方案的系统提供了有用的见解。在确定了估计值何时准确的一些准则之后，我们然后说明了如何使用多个距离估计来估计接近阈值的速度。该估计方法是通用的，可能适用于中东呼吸综合征冠状病毒（MERS-CoV）等人畜共患病原体以及麻疹等可通过疫苗预防的疾病。
