Hybrid Kinetic Monte Carlo Methods with Applications in Biofabrication and Epidemics

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.