Mathematical Resources to Help Understand COVID-19

A collection of resources to help facilitate a better understanding of the novel coronavirus outbreak and the research surrounding it.

Uncertainties in Lagrangian prediction

Sanjeeva Balasuriya examines some recent approaches to ascribing uncertainties to Lagrangian-derived information.

A Fast-Slow Switching Model of Banded Vegetation Pattern Formation in Drylands

A new fast-slow switching model is introduced that captures the ecohydrological processes such as infiltration of water into the soil during rainstorms and  seasonal plant growth and death. 

Carbon Cycle Catastrophes: A Dynamical Systems Perspective

Daniel H. Rothman explains how dynamical systems theory helps in the understanding of disruptions of the carbon cycle in the geological record.

Nearly Three Decades at Snowbird: The Iconic Venue and its Influence on Dynamical Systems at SIAM

Hans Kaper and Marty Golubitsky reflect on the history of Dynamical Systems at Snowbird as the conference moves to Portland in 2021.

Mathematical Modeling Gains Days for Brain Cancer Patients

For brain tumors such as glioblastoma it is difficult for physicians to access the outcome of a particular course of therapy. Matthew R. Francis reports on a proliferation-invasion model that was constructed by Kristin Rae Swanson and her colleagues at the Mayo Clinic. The model consists of a reaction-diffusion equation to estimate how cancer cells spread throughout the brain and uses magnetic resonance imaging data for calibration. Swanson hopes that use of this model might help to predict patient response to a given regimen and therefore lead to an individualized treatment.

Engineered for Function: The Power of Biologically-Constrained Neural Networks for Neurosensory Integration

Charles B. Delahunt, Charles Fieseler, and J. Nathan Kutz report on two bio-inspired models for neurosensory integration that are constructed using data-driven modeling methods. One model is for olfactory processing of the Manduca sexta moth. The other model captures functioning of Caenorhabditis elegans. These organisms use different network architectures for functionality: Manduca sexta moth uses a large, randomly-connected network for sensory information  processing and learning; Caenorhabditis elegans, on the other hand, functions on a small, stereotyped connectivity graph.  

A Fast-Slow Dynamical System Model to Study Drug Addiction

Dynamical systems play an important role in modeling of a variety of cyclical processes in natural and manmade systems. In particular, they can be used to help to understand the mechanisms of drug addiction. Karthika Swamy Cohen tells about a recent  paper published in SIAM Journal on Applied Dynamical Systems, where the authors Jacob Duncan, Teresa Aubele-Futch, and Monica McGrath use a fast-slow dynamical system model to analyze the interplay between levels of mood and craving in a patient with an addictive disorder. 

Four Decades of Kink Interactions in Nonlinear Klein-Gordon Models: A Crucial Typo, Recent Developments and the Challenges Ahead

P. G. Kevrekidis (kevrekid (at) math.umass.edu) and R. H. Goodman summarize the history and recent developments in the field of kink interactions in nonlinear Klein-Gordon models in 1+1-dimensions.