Mathematical Models for Understanding the Effect of Long-Range Interactions and Intervention Measures on the Spread of Epidemics

制定有效和成本效益高的干预和监测战略，以防止感染在植物和人类世界中的传播，需要了解感染在空间和时间上传播的潜在机制，以及不同干预策略的量化影响。在植物病原体的情况下，远距离传播现象和感染传播的空间异质性可能导致基于朴素模型的疾病控制策略的失败。此外，这种薄弱的控制策略往往是不经济的，并在作物上使用大量的杀虫剂。在人类传染性疾病的情况下，如果知道检疫的数量效应，就可以制定更好的干预策略。通过对具有远距离传播和一定干预策略的空间传染病模型的分析，本研究旨在为揭示传播机制对植物流行病特征的影响，以及检疫策略在抑制人类传染病传播中的作用提供新的见解。为了确保结果与流行病学相关，该项目的一部分将与生态学家和流行病学家合作进行。本科生和研究生参与这项研究将增强他们在数学和生物之间工作的能力。该项目解决了在制定更有效和更经济的干预战略以防止感染在植物和人类世界中传播方面的挑战。大多数已经被严格分析以研究空间在感染传播中的作用的流行病模型本质上是最近邻的。然而，在许多植物疾病中，感染是通过远程传播传播的。为了了解远距离传播对感染传播的影响，利用模拟和理论生物学文献中的一些启发式方法分析了几个基于复杂智能体的模型。这些对流行病模型的不严格处理有时会导致错误的结论。这个项目的主要目标之一是严格了解远程相互作用对感染传播和相关特征的影响。在这个项目中，研究人员计划通过在标准的(最近邻)首次通过渗流模型中添加“远程相互作用”特征来研究远程首次通过渗流模型的几个方面。这位研究人员还计划研究SIS模型的干预策略，SIS模型经常被用于在一维和复杂的异质图上模拟复发性疾病在人类之间的传播。对这些模型的严格分析将需要发展新的数学技术。这些技术预计将导致对广泛的空间随机流行病模型的更深层次的理解。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Developing efficient and cost-effective intervention and monitoring strategies for preventing the spread of infection in the plant and human world requires an understanding of the underlying mechanisms by which infection spreads spatially and temporally, and of the quantitative effect of different intervention strategies. In the case of plant pathogens, long-distance dispersal phenomena and spatial heterogeneity of infection spreading can lead to failure of disease-control strategies that are based on naive models. Furthermore, such weak control strategies are often uneconomical and use copious amounts of pesticides on crops. In the case of human-contagious diseases, better intervention strategies can be developed if quantitative effects of quarantine are known. By analyzing spatial epidemic models with long-distance dispersal and certain intervention strategies, this research project aims to provide new insights into the mechanistic underpinning of dispersal on features of plant epidemics, and into the effects of quarantine strategies on restraining the spread of contagious infection among humans. To guarantee that the results are relevant to epidemiology, a part of the project will be carried out in collaboration with ecologists and epidemiologists. The involvement of undergraduate and graduate students in this research will enhance their ability to work at the interface between mathematics and biology. This project addresses challenges in developing more effective and economical intervention strategies for preventing the spread of infection in the plant and human world. Most of the epidemic models that have been analyzed rigorously to investigate the role of space in infection spreading are nearest-neighbor in nature. However, there are many plant diseases where the infection spreads via long-distance dispersals. To understand the effect of long-distance dispersal on infection spreading, several complex agent-based models have been analyzed using simulation and some heuristic methods in the theoretical biology literature. These non-rigorous treatments of the epidemic models sometimes lead to erroneous conclusions. One of the primary goals of this project is to understand rigorously the effect of long-range interactions on the spread of infections and associated features. In this project, the investigator plans to study several aspects of long-range first-passage percolation models by adding "long-range interaction" features to the standard (nearest-neighbor) first-passage percolation models. The investigator also plans to study intervention strategies for SIS models, which are frequently used for modeling spread of recurring disease among humans, in one dimension and on complex heterogeneous graphs. The rigorous analyses of these models will require the development of novel mathematical techniques. These techniques are expected to lead to a deeper understanding of a broad class of spatial stochastic epidemic models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.