Hybrid Kinetic Monte Carlo Methods with Applications in Biofabrication and Epidemics

由严重急性呼吸综合征冠状病毒2型（SARS-CoV-2）引起的冠状病毒病2019 （COVID-19）已在全球迅速蔓延。截至2022年7月30日，报告的病例超过5.77亿例，死亡人数超过640万人，使其成为迄今为止最致命的大流行病之一。近几十年来，艾滋病、肝炎、非典、H1N1猪流感、埃博拉、寨卡、麻疹、疟疾和结核病等其他流行病也造成了数千万人死亡。为了应对新发和再发传染病的大流行，数学建模和模拟在预测、评估和控制潜在疫情方面发挥着重要作用。内皮网络的形成是构建功能性血管结构的关键过程，也是目前生物构建技术的瓶颈。该项目的目标是开发新的混合动力学蒙特卡罗（KMC）方法和算法，用于研究复杂的生物系统和流行病和生物制造中出现的问题。该项目将为对计算数学和数学生物学/计算流行病学感兴趣的研究生和本科生提供多学科研究培训。在主旨(1)中，为了研究流行病的时空动态，PI建议开发一种混合KMC方法，将重点放在个人和空间结构的流动性和异质性上，作为确定流行病可能结果的关键方面。该模型描述了个体在离散晶格上的运动，具有相邻位点之间的移动速率，并结合了类似sir的过渡机制来描述个体健康状态之间的转换。在推力(2)中，PI计划开发另一种混合KMC模型，重点关注内皮网络形成中的细胞运动、细胞-基质和细胞-细胞相互作用。该方法将混合力学化学模型与KMC算法相结合，显著提高了计算建模平台研究细胞-细胞和细胞-基质相互作用的能力。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has rapidly spread throughout the world. By July 30, 2022, more than 577 million cases and over 6.4 million fatalities have been reported, making it one of the deadliest pandemics to date. Over recent decades other epidemics such as HIV/AIDS, hepatitis, SARS, H1N1 swine flu, Ebola, Zika, measles, malaria, and tuberculosis have also caused tens of millions of deaths. To combat the pandemics of emergent and re-emergent infectious diseases, mathematical modeling and simulation plays an important role in predicting, assessing, and controlling potential outbreaks. Endothelial network formation is a critical process in fabricating functional vascular constructs, and it is a very crucial impediment in the state-of-the-art biofabrication technology. The goal of this project is to develop new hybrid kinetic Monte Carlo (KMC) methods and algorithms for the study of complex biological systems and problems arising in epidemics and biofabrication. This project will provide multidisciplinary research training to graduate and undergraduate students interested in both computational mathematics and mathematical biology/computational epidemiology.In the thrust (1), to study spatial and temporal dynamics of epidemics, the PI proposes to develop a hybrid KMC method with focuses on the mobility and heterogeneity of individuals and spatial structures as critical aspects in determining possible outcomes for an epidemic. The proposed model describes the motion of individuals on a discrete lattice with moving rates between neighboring sites and couple the SIR-like transition mechanism to describe the conversion between individuals' health states. In the thrust (2), the PI plans to develop another hybrid KMC model with focuses on cell motility, cell-matrix and cell-cell interactions in endothelial network formation. The approach combines a hybrid mechanochemical model with the KMC algorithm to enhance the capability of the computational modeling platform in studying cell-cell and cell-matrix interactions significantly.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.