Public Health Interventions in the COVID-19 Endgame: Insights from Percolation Theory

新冠肺炎大流行呼唤广泛的科学方法创新，包括数学模型。到目前为止，在大流行期间开发的大多数数学模型都研究了单一、混合良好的人群中的流行病。然而，在平坦的流行曲线的另一边，疾病传播的特点将是零星的、地理上分散的疫情。随着我们开始重新开放经济，有必要了解疫情曲线的这一阶段将如何变化，这取决于我们应用的传染病干预措施。渗流理论是一种基于物理的理论，与许多传统的数学建模方法相比，它更适合于研究大流行后期的流行病动力学。我们建议开发一种基于渗流的方法来理解新冠肺炎的后期动态，以及它如何响应不同的测试、隔离、疫苗接种和接触者跟踪方法。然后，我们将把这个渗流模型的结果整合到一个基于代理的网络模拟中，模拟新冠肺炎在加拿大各省人口中心之间的传播，包括物理距离和学校/工作场所关闭对感染传播的影响。我们将使用现实的人口统计和新冠肺炎疾病数据作为模型输入。该模型将预测不同方法下的病例、住院和死亡情况，以重新开放经济，例如根据当地病例数量的规定“触发”条件逐个县进行预测。这将使我们能够评估测试、物理距离和学校/工作场所关闭的组合策略。最关键的是，它将提供一种工具，供省级决策者用来决定如何在不冒重启新冠肺炎案例的风险的情况下，重启省级经济。

The COVID-19 pandemic calls for innovation in a broad range of scientific methods, including mathematical models. Thus far, most mathematical models developed during the pandemic have studied epidemics in a single, well-mixed population. However, on the far side of a flattened epidemic curve, disease spread will be characterized by sporadic, geographically dispersed outbreaks. It will be necessary to understand how this phase of the epidemic curve will change depending on what infectious disease interventions we apply, as we begin to re-open our economies. Percolation theory-the study of how fluids move through a material-is a physics-based theory that is much better suited to study epidemic dynamics in the later stages of the pandemic than many conventional mathematical modelling approaches. We propose to develop a percolation-based approach to understanding late-stage COVID-19 dynamics and how it responds to different testing, isolation, vaccination, and contact tracing approaches. Then, we will integrate the results of this percolation model into an agent-based network simulation of COVID-19 spread between population centres across Canadian provinces, including the impacts of physical distancing and school/workplace closure on infection spread. We will use realistic demographic and COVID-19 disease data as model inputs. The model will project cases, hospitalizations, and deaths under different approaches to re-opening the economy, such as on a county-by-county basis according to stipulated "trigger" conditions on the number of local cases. This will enable us to assess combined strategies of testing, physical distancing, and school/workplace closure. Most crucially, it will provide a tool that provincial decision-makers can use to determine how to re-open provincial economics without risking a resurgence of COVID-19 cases.