Topics: Biology, Chemistry, COVID-19, Mathematics, Physics

*The year 2020 has been defined by the COVID-19 pandemic: The novel coronavirus responsible for it has infected millions of people and caused more than a million deaths. Like HIV, Zika, Ebola, and many influenza strains, the coronavirus made the evolutionary jump from animals to humans before wreaking widespread havoc. The battle to control it continues.When a disease outbreak is identified—usually through an anomalous spike in cases with similar symptoms—scientists rush to understand the new illness. What type of microbe causes the infection? Where did it come from? How does the infection spread? What are its symptoms? What drugs could treat it? In the current epidemic, science has proceeded at a frenetic pace. Virus genomes are quickly sequenced and analyzed, case and death numbers are visualized daily, and hundreds of preprints are shared every day.*

*Some scientists rush for their microscopes and lab coats to study a new infection; others leap for their calculators and code. A handful of metrics can characterize a new outbreak, guide public health responses, and inform complex models that can forecast the epidemic’s trajectory. Infectious disease epidemiologists, mathematical biologists, biostatisticians, and others with similar expertise try to answer several questions: How quickly is the infection spreading? What fraction of transmission must be blocked to control the spread? How long is someone infectious? How likely are infected people to be hospitalized or die?*

*Physics is often considered the most mathematical science, but theory and rigorous mathematical analysis also underlie ecology, evolutionary biology, and epidemiology. ^{1} Ideas and people constantly flow between physics and those fields. In fact, the idea of using mathematics to understand infectious disease spread is older than germ theory itself. Daniel Bernoulli of fluid-mechanics fame devised a model to predict the benefit of smallpox inoculations^{2} in 1760, and Nobel Prize–winning physician Ronald Ross created mathematical models to encourage the use of mosquito control to reduce malaria transmission.^{3} Some of today’s most prolific infectious disease modelers originally trained as physicists, including Neil Ferguson of Imperial College London, an adviser to the UK government on its COVID-19 response, and Vittoria Colizza of Sorbonne University in Paris, a leader in network modeling of disease spread.*

*This article introduces the essential mathematical quantities that characterize an outbreak, summarizes how scientists calculate those numbers, and clarifies the nuances in interpreting them. For COVID-19, estimates of those quantities are being shared, debated, and updated daily. Physicists are used to distilling real-world complexity into meaningful, parsimonious models, and they can serve as allies in communicating those ideas to the public.*

The math behind epidemics, Alison Hill, Physics Today

**Alison Hill** is an assistant professor in the Institute for Computational Medicine and the infectious disease dynamics group at Johns Hopkins University in Baltimore, Maryland. She is also a visiting scholar at Harvard University in Cambridge, Massachusetts.