The spread and impact of infectious diseases, such as polio in the past and COVID-19 today, are long-standing challenges for humanity. While at first glance this may appear as a problem for medical researchers and practitioners alone, mathematical scientists can contribute a great deal to analysis of emerging outbreaks. Mathematical and statistical modeling allow us to better understand how an outbreak has spread, and how it is likely to progress in the future. This information is crucial in helping doctors, policy makers, and everyone else decide how to adjust behavior and combat the disease.
Mathematical sciences modeling of the coronavirus pandemic is already beginning to appear. Some of this work is detailed below.
From The Lancet:
This article shows how researchers used stochastic transmission models to predict how previous cases and travel would lead to new outbreaks worldwide. Read the report here (equations and graphs can be found using the link at the end of the report, or in the supplementary materials page here). Courtesy of the Centre for Mathematical Modelling of Infectious Diseases COVID-19 working group, London School of Hygiene & Tropical Medicine, London, UK.
An interactive dashboard allows us to see data on the disease in real-time here, as well as the full report by Dong, Du and Gardner detailing the model.
The University of Washington:
The COVID-19 health service utilization forecasting team, Institute for Health Metrics and Evaluation, at the University of Washington has been working with predictive algorithms to estimate when the number of patients and deaths will exceed hospital capabilities on a state-by-state basis.
The full report can be found here, with the math in the appendix, and state-by-state visualizations found here.
This article published by the Imperial College COVID-19 Response Team details how different non-pharmaceutical implementations effect the spread and mortality of the virus.
Professor David I. Ketcheson:
Professor Ketcheson, an associate professor of applied mathematics at King Abdullah University of Science and Technology (KAUST), has a webpage which features several pieces that break down the mathematical COVID-19 model, as well as offers an interactive version of the model for users to manipulate.
American Mathematical Society:
AMS has provided a downloadable project on the transmissiblity of COVID-19 which features exercises and a starter Mathematica file.
The SIAM Epidemiology Collection, focused on disease modeling, pandemics, and vaccines, is freely available to all for one year.
SIAM also offers more resources and further reading on mathematics and COVID-19 which can be found here.
This is a constantly evolving situation. Check in for updates as more information becomes available.