Collaborative Research: MODULUS: Stochastic reaction-diffusion equations on metric graphs and spatially-resolved dynamics of virus infection spread

该奖项支持开发新的数学工具和生物实验，这些工具和生物实验对于理解病毒传播和灭绝的机制至关重要。为了能够进行综合的实验-数学研究，将开发一个新的框架，以控制宿主细胞群体的空间分布，并量化这种空间结构如何影响病毒的进化和衰退。该项目具有基础研究、医学和公共卫生影响，因为分析和实验方法可以扩展到阐明具有公共卫生重要性的病毒传播的机制，包括甲型流感病毒、寨卡病毒和冠状病毒。作为一项跨学科研究，这项研究将交叉培训数学家、生物学家和工程师，为劳动力发展做出重大贡献。更广泛的目标包括增加科学、技术和经济管理领域的参与度和多样性，同时通过广泛传播促进公众对科学和技术的更广泛了解。该项目的目标是根据宿主细胞种群的空间结构来确定感染传播期间病毒灭绝的可能性和传播速度。一个新的数学框架，度量图上的随机反应-扩散方程，将被开发来研究任何网络结构上的病毒感染的动力学。生物学实验是尖端的：病毒感染将在微图案宿主细胞上进行，这使得能够量化在任何网络结构中传播的感染的种群水平特征，这是相对于传统的培养皿研究的关键优势。对经验随机方程的分析有可能推动关于空间和随机性在种群动力学中的作用的现有知识的前沿。这一新的框架激发了一些跨越几个数学学科(概率、偏微分方程式和数学生物学)的问题，这些问题是一大群应用数学家和应用科学家感兴趣的。这些问题包括：(I)病毒灭绝的概率和传播速度与度量图的几何性质有关，如图的分枝结构和边长？(Ii)在共感染传播过程中，病毒和缺陷干扰粒子共存的概率是多少，以及底层空间结构对这一概率的影响？该项目带来了新的概率工具和视角来解决这些问题，并产生关于病毒感染传播的机械性见解。该奖项由MPS数学科学部(DMS)通过数学生物学计划和分子和细胞生物科学部(MCB)通过系统和合成生物学以及细胞动力学和功能集群共同资助。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。

This award supports the development of new mathematical tools and biological experiments that are essential to understanding the mechanisms of virus spread and extinction. A new framework, to enable an integrated experimental-mathematical study, will be developed to control the spatial distribution of the host cell population and to quantify how such spatial structure affects viral evolution and decay. The project has basic research, medical, and public health impact, since the analytical and experimental methods can be extended to elucidate mechanisms of infection spread by viruses of public health importance, including influenza A virus, Zika virus, and coronaviruses. As an interdisciplinary study, the research will cross-train mathematicians, biologists, and engineers, contributing significantly to workforce development. Broader objectives include increased participation and diversity in STEM fields while promoting a broader understanding of science and technology by the public through wide dissemination. The project goal is to determine both the probability of virus extinction during infection spread and the spreading speed in terms of the spatial structure of host cell populations. A new mathematical framework, stochastic reaction-diffusion equations on metric graphs, will be developed to study the dynamics of virus infections over any network structure. The biological experiments are cutting edge: virus infections will be performed on micro-patterned host cells that enable quantification of population level features of infection spread in any network structure, a key advantage over traditional Petri-dish studies. Analysis of the experimentally informed stochastic equations has the potential to push the frontier of current knowledge about the role of space and stochasticity in population dynamics. This new framework motivates problems that cut across several mathematical disciplines (probability, partial differential equations and mathematical biology) and that are of interest to a large group of applied mathematicians and applied scientists. These problems include (i) What is the probability of extinction of virus and the propagation speed in terms of geometric properties of the metric graph, such as the branching structure and the edge lengths of the graph? (ii) What is the probability of coexistence of virus and defective interfering particles during co-infection spread, and the effect of the underlying spatial structure on this probability? The project brings new probabilistic tools and perspectives to solve these problems and to generate mechanistic insights about virus infection spread. This award is being co-funded by the MPS Division of Mathematical Sciences (DMS) through the Mathematical Biology Program and by the Division of Molecular and Cellular Biosciences (MCB) through the Systems and Synthetic Biology and the Cellular Dynamics and Function Cluster.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.