RAPID: Data-Based Spatiotemporal Models of Ebola Epidemics and Control

DMS-1518529匡 西非的埃博拉疫情继续造成严重的发病率和死亡率。 2014年8月8日，世界卫生组织宣布西非埃博拉疫情为国际关注的突发公共卫生事件。 随着疫情继续以惊人的速度在西非一些地区蔓延，迫切需要开发、测试和校准埃博拉传播和控制的新型数学模型，目标是对西非疫情进行实时、基于科学的预测，以量化实现控制所需的干预措施的时间、地点、类型和强度。 为此，调查人员及其同事制定并验证了可用于预测新病例数量和地点的模型，以便利就资源分配作出决策，从而能够及时对病人进行医疗和隔离，并实施有效和合理的旅行控制。 该项目为本科生和研究生提供跨学科交流和探索的第一手教育经验以及前沿研究机会。 它还为研究生提供专业发展。 研究人员将他们的发现传播给各种各样的数学家，建模者，公共卫生和生物医学研究人员。 研究人员将项目工作分为三个建模任务。 首先，他们制定了不断变化的感染复制数量的动态模型，比较了简单的SI模型和逻辑模型与过去和当前真实的埃博拉疫情数据的拟合程度。 在这个初始任务中，他们不将整个人群视为易感人群，而是将易感人群规模和最终流行规模视为参数，并允许报告的数据为这些参数值提供信息。 随后，他们提出了一种新的基于延迟微分方程的建模框架，该框架允许模型将易感人群规模视为与当前感染人群规模高度相关的动态变量。 更具体地说，他们将易感群体规模初始化为零，而不是目前认为易感群体规模等于最初的总人口规模。 这仅仅是因为，只有在与感染性埃博拉患者有直接和密切接触的情况下，个人才容易感染埃博拉病毒。 在该项目的后半部分，他们制定并验证了基于偏微分方程的模型，以估计埃博拉病毒的传播速度，并预测受各种治疗方案和旅行控制政策影响的新埃博拉病例的位置和数量。 该项目得到数学科学部和环境生物学部的支持。

DMS-1518529Kuang The Ebola epidemic in West Africa continues to cause significant morbidity and mortality. The World Health Organization declared the Ebola epidemic in West Africa a Public Health Emergency of International Concern on 8 August 2014. As the epidemic continues to spread at an alarming rate in some areas of West Africa, there is an urgent need to develop, test, and calibrate novel mathematical models of Ebola transmission and control with the goal of generating real-time, science-based forecasts of the epidemic in West Africa in order to quantify the times, locations, type and intensity of interventions that would be required to achieve control. To this end, the investigators and their colleagues formulate and validate models that can be used to predict the number and location of new cases, in order to facilitate decision-making on the allocation of resources that will allow timely medical treatment and isolation of the sick and to implement effective and sensible travel controls. This project provides first-hand educational experience in cross-disciplinary communication and exploration and cutting-edge research opportunities for undergraduates and graduate students. It also provides professional development for graduate students. The investigators disseminate their findings to a diverse range of mathematicians, modelers, and public health and biomedical researchers. The investigators divide the project efforts into three modeling tasks. At first, they formulate dynamical models of the evolving infection reproduction number, comparing how well a simple SI model and the logistic model fit past and current real Ebola epidemics data. In this initial task, instead of treating the whole population as susceptible, they treat the susceptible population size and the final epidemics size as parameters and allow the reported data to inform these parameter values. Subsequently, they present a novel delay differential equation based modeling framework that allows models to treat susceptible population size as a dynamical variable, which is highly correlated to current infectious population size. More specifically, they initialize the susceptible population size as zero instead of the current thinking that susceptible population size equals the total population size initially. This is simply due to the fact that individuals become susceptible to Ebola only if they had a direct and close contact with infectious Ebola patients. In the second half of this project, they formulate and validate partial differential equation-based models in order to estimate the Ebola spread speed and to predict the locations and numbers of new Ebola cases subject to various treatment options and travel control policies. The project is supported by the Division of Mathematical Sciences and the Division of Environmemtal Biology.