Using Math to Understand COVID-19 Outbreak Dynamics

By Amanda Chase, PhD

April 30, 2020

The World Health Organization has declared that coronavirus disease 2019, COVID-19, is a global pandemic. Infection with the virus causing this disease, a novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), can result in mild symptoms, such as fever or cough. However, severe complications can arise when the disease progresses to viral pneumonia and multi-organ failure. SARS-CoV-2 is able to spread quickly during close contact or via small droplets, such as those from coughing or sneezing. The increasing knowledge of SARS-CoV-2 is allowing us to understand more about COVID-19, but we still lack a precise timeline of the disease, infectivity, and the effect of the strategies put in place to stop spread. This is critical information for easing restrictions in the safest way possible.

A group of researchers at Stanford, led by first author Mathias Peirlinck and senior author Ellen Kuhl, PhD, used mathematical modeling to help estimate outbreak dynamics and provide guidelines for outbreak control. The researchers, who are known for their simulations of the human heart, have just published their first COVID-19 study in Biomechanics and Modeling in Mechanobiology. Mathematical models have been used for infectious disease outbreaks as far back as the smallpox outbreak in 1760. These models can account for many variables, including transitioning from exposed to infectious to recovered, as well as restrictive measures put in place to reduce spread including shelter-in-place and travel restrictions.  The team utilized COVID-19 outbreak data from the United States as well as from China. Importantly, they used machine learning to infer, from the outbreak in China, how the outbreak dynamics in the United States would evolve.

With the rich data sets, Dr. Kuhl and her team were able to establish a simulation tool to estimate the dynamics of the COVID-19 pandemic, both at a local level for individual states and globally for the entire United States. Their results reinforce the benefit of the steps currently underway, including isolating infectious people, contact tracing, travel restrictions, and physical distancing. Critically, the simulation tool has the potential to predict the timeline of the outbreak in individual states to help optimize planning and essential distribution of medical resources. It can quantify the impact of different restriction measures, and predict the risk of relaxing those restrictions both for low- and high-risk subgroups of the population and for the population as a whole.

As we collectively work to limit the spread of COVID-19 and consider how to move into the next phase of re-opening businesses, schools, parks, and our own campus, the simulation tool developed by Dr. Peirlinck and Dr. Kuhl will be important in helping to guide decision-making.

This study was motivated and inspired by a Bio-X IIP seed grant.