Mathematicians Quickly Respond to the COVID-19 Pandemic
By Juan C. Meza, Zhilan Feng, Tie Luo, and Junping Wang
The Division of Mathematical Sciences (DMS) at the National Science Foundation (NSF) recently participated in an NSF-wide Dear Colleague Letter, which was published on April 3 and requested proposals that address the COVID-19 pandemic. The mathematical sciences community was quick to respond! Ideas ranged from developing tools to help decision-makers better understand the possible outcomes of proposed nonpharmaceutical intervention policies to combining mathematicians’ expertise with other disciplines—like biology and chemistry, for example—to study new approaches and accelerate the identification of potential therapeutic treatments.
Overall, the DMS issued a set of 15 Rapid Response Research (RAPID) awards over the span of several weeks that could have a significant impact in mitigating the spread of COVID-19. These awards highlight the critically important need for swift and reliable prediction of epidemics’ spatial and temporal risks. Furthermore, many of them use mathematical, statistical, and computational models to evaluate various therapeutic and non-therapeutic mitigation policies, thus allowing policymakers to quickly identify intervention strategies that effectively slow the inevitable. Such strategies can buy additional time to put pandemic plans into effect, reducing peak demand for hospital-based care and ultimately saving lives.
The collection of RAPID awards spans a range of diverse ideas, including novel variations of well-known SIR (susceptible-infected-recovered) models, statistical inference approaches for rapidly changing situations where only partial data is available, and techniques that employ a combination of deep learning and mechanistic methods to quickly improve mathematical models that capture the specific characteristics of COVID-19. Other awards dive deeper into our understanding of how the novel coronavirus infects hosts cells, targeting the identification of critical areas in the viral genome that could be attacked during drug design. Yet another common theme is the use of data and corresponding mathematical procedures to improve existing models, particularly in situations where the data is incomplete and changes rapidly.
In general, the awards fell into one of two major areas: (i) mathematical models for predicting the spread of COVID-19 and the effects of different mitigation strategies, and (ii) study of the novel coronavirus, the viral evolution, and subsequent plans for detecting target areas in the viral genome for drug compounds. We can subdivide the awards in the first major area into three general categories: (i) SIR/SEIR (susceptible-exposed-infected-recovered) types of compartmental models with various levels of extensions and complexities; (ii) stochastic, statistical, or probabilistic models; and (iii) network or graph theory-based models.
The DMS made five awards in the first subgroup that will investigate various aspects of the well-known SIR/SEIR model. Andrea Bertozzi and Mason Porter (DMS – 2027438) plan to integrate a basic SIR framework with high-resolution societal mixing patterns in epidemics and models with self-exciting point processes that are fitted to real-world data. These actions will allow them to study the stochasticity of infection and latency, analyze the uncertainty in disease transmission rates, and evaluate intervention policies. The pair will also examine the outcomes of social distancing using data from a Princess Cruise ship and lecture halls at the University of California, Los Angeles.
Jeffrey Shaman (DMS – 2027369) will utilize SIR-type models with spatial movements and statistical/computational tools to estimate critical epidemiological characteristics that are associated with the transmission of SARS-CoV-2. He will then forecast future COVID-19 incidence, estimate the effectiveness of public health policies (such as school closures and travel restrictions), and project the geographic spread of COVID-19 for given scenarios with various levels of intervention.
Yulia Gel and Georgiy Bobashev (DMS – 2027793/2027802) plan to use a predictive approach based on multiple data sources and dynamical SEIR models to train deep learning networks. If one then views simulation SEIR models as surrogate pre-trainers for deep learning models, Gel and Bobashev’s work could minimize the amount of real data needed to retrain the predictive model and reflect real-world COVID-19 progression. In contrast, Grzegorz Rempala (DMS – 2027001) will employ dynamical survival analysis—which exploits aggregated mean field equations for the underlying large stochastic network approach—to estimate parameters that are similar to those in SIR models. The survival dynamical system may yield new understanding of the pandemic, as it does not require knowledge of the susceptible population’s size or overall disease prevalence.
Folashade Agusto (DMS – 2028297) and her collaborators intend to develop disease transmission models that incorporate various factors, including public perception of risk, age structure within a hospitalized population, population demographics, socioeconomic conditions, and spatial structure. They will then use the models to inform coordination of disease control policies with different scales, ranging from local communities to entire countries. Finally, Cameron Browne (DMS – 2028728) and his team will create a modeling framework at the interface of mathematics, epidemiology, and genetics. Their approach may help derive the outbreak size’s dependence on contact tracing and broad quarantine intervention parameters, thus quantifying region-specific control characteristics for COVID-19.
Deterministic models are not the only possible tactic. To study systems with high stochasticity, Jason Xu and Allison Aiello (DMS – 2030355/2030242) will generate new stochastic compartmental models that extend classical mechanisms to explicitly account for changes to the social contact network that underlies disease spread. They will combine these developments with likelihood-based methods to infer key epidemic parameters that offer mechanistic interpretations with uncertainty quantification.
Two other interesting techniques involve modeling the COVID-19 pandemic via network and graph theory. In this group, Nicole Eikmeier and Matthew Junge (DMS – 2028880/2028892) plan to study quarantine’s effect on the network connectivity of graphs to better model societal connections. Individual quarantine is akin to removing a vertex from a graph; the systematic removal of vertices is called site percolation. Eikmeier and Junge will explore biased site percolation’s effect on graph structure, particularly the way in which different percolation rules influence the size of a given graph’s largest component. The second part of the project will then focus on how an epidemic’s critical threshold and size change after percolation for an SIR model.
Faryad Darabi Sahneh’s (DMS-2028401) research will take a similar approach but emphasize a data-driven mathematical modeling framework for the forecast of temporal and spatial COVID-19 trends. His team’s modeling framework can handle a constantly evolving environment, including individuals’ behavioral changes in response to mitigation efforts. Interestingly, Darabi Sahneh borrows this idea from economics.
The second major area of network and graph theory addresses the infectivity and virulence of the novel coronavirus itself, such as the viral evolution, virus structure, and effect on host cells. Here the general line of attack involves studying the RNA viral genome for clues on the way in which it infects the host cells, and determining treatments that might disrupt the infective process.
Gregory Forest’s (DMS – 2028758) group has teamed up with two experimental biology laboratories to develop a mathematical modeling platform that will explore the delicate interplay among inhaled loads of SARS-CoV-2 and their diffusion within—and potentially through—the mucus-coated respiratory tract. This will allow the researchers to determine infectivity onset as the virus reaches and invades epithelial cells and propagates the infection. Their ultimate goal is to optimize design of monoclonal antibodies (mAb), characterize efficiency of given mAb affinities to COVID-19 and mucus, and quantify the inhaled mAb dose required to arrest COVID-19 infection at various stages of progression.
Two other awards seek to understand the specific protein that is key to the coronavirus’ invasion of host cells: the so-called spike or S-protein in the RNA viral genome. Tamar Schlick’s (DMS – 2030377) project involves comprehending the COVID-19 RNA viral genome through structural analysis and molecular dynamics studies. The coronavirus is known to mutate over time, but few specifics are currently established. Javier Arsuaga, Raymond Rodriguez, and Mariel Vasquez (DMS – 2030491) intend to employ a combination of Markov processes, graph theory, and topological data analysis to better understand this mutation process and estimate evolutionary parameters and the S-protein’s fitness function.
The DMS is thankful to the mathematical sciences community for its incredible response to our call for proposals regarding the worldwide COVID-19 pandemic.
Juan C. Meza is a professor of applied mathematics at the University of California, Merced and currently serves as the division director for the Division of Mathematical Sciences (DMS) at the National Science Foundation (NSF). He became a SIAM Fellow in 2019. Zhilan Feng is a professor of mathematics at Purdue University and presently serves as a program director in the DMS’s Mathematical Biology Program. She is an editor for the SIAM Journal on Applied Mathematics. Tie Luo joined the NSF as a program director in the Algebra and Number Theory Program before serving as deputy division director of the DMS. He is currently the Acting Deputy Assistant Director for Mathematical and Physical Sciences. Junping Wang joined the NSF in 2003 and is currently serving as a program director in the Mathematical Biology Program, as well as the acting deputy division director for the DMS. He is also a member of the working group for the NSF’s Big Idea on “Understanding the Rules of Life.”