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

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.