Understanding the Dynamics of Stochastic Disease Spread in Metapopulations

确定传染病爆发、传播和灭绝的条件是一个重要的公共卫生问题。全球根除一种传染病的目标很少实现，但它仍然是许多疾病的公共卫生目标。更常见的是，人们可以观察到当地疾病的消失或淡出，然后通过迁徙效应从其他地区重新引入疾病。一般而言，灭绝发生在由于随机转变而受到随机影响的种群中。随机性的起源可能是系统内部的，也可能是外部环境的。种群规模小，频率相关传播的接触频率低，对资源的竞争和进化压力，以及种群和传播的异质性，都可能是导致灭绝的决定因素。灭绝事件的可能性受随机噪声的性质和强度以及其他因素的影响，包括爆发的幅度和季节性发生。对于较大的种群，内部种群噪声的强度一般较小。然而，罕见的大波动可能以非零概率发生，系统可能会达到灭绝态。研究目标是使用由耦合区域或斑块组成的随机集合种群模型来研究疾病传播和灭绝的动力学。主方程形式主义将被用来理解疾病动力学，并找到使疾病消失的可能性最大化的路径。这一结果将使人们能够通过使用包括疫苗接种和检疫计划在内的控制方法来加快疾病的灭绝。该建议是高度多学科的，涉及动力系统、随机过程、统计力学和控制理论。即将开发的数学工具将提供分析和确认数值结果的新方法。此外，分析将导致对新的信息和系统行为的预测，并将提供对传染病爆发、传播和灭绝过程的更好理解。特别是，这种对疾病动态的新理解将使开发最佳控制方法来减少疾病的爆发和传播成为可能。该提案包括精心规划的项目，这些项目将涉及并支持本科生和研究生进行前沿研究。值得注意的是，蒙特克莱尔州立大学，尤其是数学科学系的学生中，有相当一部分是在STEM学科中代表性不足的群体(包括女性和少数族裔)，研究计划将利用针对这些学生的现有计划。研究成果将通过研讨会、在会议上的陈述以及在同行评议期刊上发表的文章来传播。

Determining the conditions for the outbreak, spread, and extinction of an infectious disease is an important public health problem. Global eradication of an infectious disease has rarely been achieved, but it continues to be a public health goal for many diseases. More commonly, one can observe local disease extinction, or fade out, followed by a reintroduction of the disease from other regions through a migratory effect. In general, extinction occurs in populations undergoing stochastic effects owing to random transitions. The origins of stochasticity may be internal to the system or may arise from the external environment. Small population size, low contact frequency for frequency-dependent transmission, competition for resources and evolutionary pressure, as well as heterogeneity in populations and transmission, may all be determining factors for extinction to occur. The possibility of an extinction event is affected by the nature and strength of the stochastic noise, as well as other factors, including outbreak amplitude and seasonal phase occurrence. For large populations, the intensity of internal population noise is generally small. However, a rare, large fluctuation can occur with non-zero probability and the system may be able to reach the extinct state. The research objective is to study the dynamics of disease spread and extinction using stochastic metapopulation models that consist of coupled regions or patches. A master equation formalism will be used to understand the disease dynamics and to find the path that maximizes the probability of disease extinction. The results will enable one to speed up disease extinction through the use of control methods including vaccination and quarantine programs. The proposal is highly multidisciplinary, and involves dynamical systems, stochastic processes, statistical mechanics, and control theory. The mathematical tools that will be developed will provide new ways of analyzing and confirming numerical results. In addition, the analysis will lead to the prediction of novel information and system behavior, and will provide for improved understanding of infectious disease outbreak, spread, and extinction processes. In particular, this new understanding of disease dynamics will enable the development of optimal control methods to lessen disease outbreak and spread. The proposal includes carefully planned projects that will involve and support undergraduate and graduate students in leading-edge research. Significantly, the student population at Montclair State University, and in particular, the Department of Mathematical Sciences, includes a substantial proportion who are members of groups underrepresented in STEM disciplines (including women and minorities) and the research program will leverage existing programs directed to these students. The outcome of the research will be disseminated through seminars, presentations at meetings, and publications in peer-reviewed journals.