López-Pintado Dunia, López-Pintado Sara, García-Milán Iván, Yao Zonghui
Economics Department, Universidad Pablo de Olavide, 41013, Seville, Spain.
Department of Health Sciences, Northeastern University, Boston, 02115-5005, USA.
Sci Rep. 2023 Sep 19;13(1):15522. doi: 10.1038/s41598-023-42041-0.
The spread of a disease, product or idea in a population is often hard to predict. We tend to observe one or few realizations of the contagion process and therefore limited information can be obtained for anticipating future similar events. The stochastic nature of contagion generates unpredictable outcomes throughout the whole course of the dynamics. This might lead to important inaccuracies in the predictions and to the over or under-reaction of policymakers, who tend to anticipate the average behavior. Through an extensive simulation study, we analyze properties of the contagion process, focusing on its unpredictability or uncertainty, and exploiting the functional nature of the data. In particular, we define a novel non-parametric measure of variance based on weighted depth-based central regions. We apply this methodology to the susceptible-infected-susceptible epidemiological model and small-world networks. We find that maximum uncertainty is attained at the epidemic threshold. The density of the network and the contagiousness of the process have a strong and complementary effect on the uncertainty of contagion, whereas only a mild effect of the network's randomness structure is observed.
疾病、产品或思想在人群中的传播通常很难预测。我们往往只能观察到传染过程的一个或少数几个实例，因此对于预测未来类似事件所能获得的信息有限。传染的随机性在整个动态过程中会产生不可预测的结果。这可能导致预测出现重大偏差，并使政策制定者反应过度或不足，因为他们往往预期的是平均行为。通过广泛的模拟研究，我们分析了传染过程的特性，重点关注其不可预测性或不确定性，并利用数据的函数性质。特别是，我们基于加权深度中心区域定义了一种新的非参数方差度量。我们将这种方法应用于易感-感染-易感流行病学模型和小世界网络。我们发现，在流行阈值处达到最大不确定性。网络的密度和过程的传染性对传染的不确定性有强烈且互补的影响，而观察到网络随机结构的影响较小。
