How Does Disease Modeling Work?

Mathematical models of outbreaks such as COVID-19 provide important information about the progression of disease through a population and the impact of intervention measures. For COVID-19, models have informed government policies, including calls for social or physical distancing.

S-I-R models

At a basic level, standard models divide populations into three groups: people who are susceptible to the disease (S), people who are infected by the disease and can spread it to others (I), and people who have recovered or died from the disease (R). S-I-R models look at changes in group size as people move from one group to another. These models can help to predict the number of people who will be affected by the end of an outbreak. More advanced models may include other groups, such as asymptomatic people who are still capable of spreading the disease.

Basic reproduction number

A key parameter of mathematical models is the basic reproduction number, often denoted by R₀. This is the number of previously unexposed individuals who get infected by a single new disease carrier. A basic reproduction number of two means that each person who has the disease spreads it to two others on average. Those others then each go on to spread it to two more people, and so on. If R₀ is less than one, the infection will eventually die out. If R₀ is greater than one, the outbreak will grow. R₀ can vary among different populations, and it will change over the course of a disease outbreak. Its value also influences how many people need to be immune to keep the disease from spreading, a phenomenon known as herd immunity.

Case fatality rate

Another important parameter is the case fatality rate for an outbreak. This is the proportion of infected people who die from the disease. The case fatality rate for different demographics can vary. For example, in the case of COVID-19, the case fatality rate for the elderly is higher than the rate for younger people.

Assumptions

Models require researchers to make assumptions about the conditions of the outbreak based on the current data available, such as:

• the time that passes between when a person is infected and when they can pass it to others
• how many people an infected person interacts with
• the rates at which people of different ages transmit the virus
• the number of people who are immune to the disease

Because of these assumptions, different early models can produce very different outcomes. Models will improve as new data becomes available, especially from well-documented cases.

Try it out: Adjust assumptions to see how the model changes with an interactive COVID-19 Scenarios model from the University of Basel in Switzerland.

Read more about testing, another important tool for addressing the coronavirus epidemic, on the Caltech Science Exchange >