Mathematical Formulae Help Predict Disease Eradication in Outbreak Scenario

We’ve all heard that washing your hands more frequently during an influenza outbreak or staying home from work when you’re sick with the flu can help reduce the risk of disease spread. But which practices are most effective, which ones help protect the largest number of people, and which are more likely to lead to disease eradication?

Investigators at the Georgia Institute of Technology in Atlanta and The King Abdullah University of Science and Technology in Thuwal, Saudi Arabia have developed a group of mathematical formulae to help answer those questions. Their research was published recently in Nature.

According to the formulae, disease transmission during an outbreak is dictated partially by the inherent infectivity of the organism, but this infectivity is reduced when sick people and healthy people both take steps to reduce transmission, such as self-isolation (eg, staying home when you are ill). The formulae also show that contagion can only occur when sick and healthy people both fail to self-isolate.

Not surprisingly, the calculations show that the risk of disease transmission to any one healthy person increases as the number of his or her healthy neighbors that don’t take protective measures increases. According to this model, one’s neighbors play an important role in whether an individual will contract an infection or remain healthy. Additionally, a healthy person who is surrounded by sick neighbors that are all taking precautions to minimize disease spread has a very low likelihood of becoming ill, even if that individual doesn’t take any precautionary actions him- or herself.

Using this logic, the investigators reported that people consider a group of variables before deciding how (or whether) to protect themselves from contagious disease—including what their neighbors are doing. For example, people who know that all of their sick neighbors are staying home may not take precautions of their own because the neighbors are already taking steps to reduce their exposure risk.

According to the authors, the actions of sick individuals are mathematically more important than the behaviors of healthy people who are trying to avoid becoming ill. “Risk averse behavior by the healthy individuals cannot eradicate the disease without the preemptive measures of the sick individuals,” they noted. So, although hand-washing is helpful and may reduce disease spread, the likelihood of disease eradication is lower if people who are already sick don’t also take precautions to reduce their chances or infecting others.

The authors also noted that “self-isolation decisions of sick individuals guarantee the prevention of disease spread to all their neighbors, whereas self-isolation of a healthy individual averts only a single potential infection.” Similarly, covering your mouth for a cough or sneeze protects a large number of potentially susceptible people, but washing your hands if you are not already infected primarily protects you. Therefore, the authors suggest that public health campaigns should focus more on things like staying home from work when ill and covering one’s mouth for a cough.

In contrast, precautions taken by healthy individuals alone do reduce the average number of infected people when the disease becomes endemic, although this is a long-term development for an infectious disease. The authors recommend that future research should investigate the effects of these risk-aversion practices on endemic disease versus an outbreak scenario.

The authors stress the point that social behaviors change during disease outbreaks. Predicting what these changes might entail and calculating how they can alter the course of a disease outbreak can improve society’s ability to manage epidemics and institute policies that help facilitate disease eradication.