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How behaviors complicate epidemic outcomes

Picture of a grocery store checkout with people wearing masks

A new mathematical model describes how people’s changing behaviors can influence – and be influenced by – the course of an epidemic or pandemic.

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Feb 15 2021

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Research, Faculty

A new epidemiological model, detailed in a paper published Feb. 10 in PLOS Computational Biology, has revealed a complex interplay between health and economic motivations and social contact.

Unlike standard epidemic models, this model assumes that people face a behavioral trade-off and describes this as a mathematical function known as a utility function. In the model, people are motivated to improve their utility and do so by interacting with other people – perhaps by working, attending school, or socializing. Under normal circumstances, they would arrive at an ideal level of social contact to maximize their utility, but in an epidemic, interacting becomes risky. So, rationally, they will cut back their contacts to a level that balances their interactions with their risk of catching the disease.

According to the model, there is a theoretical endemic equilibrium to such a system, which means that absent successful eradication, such a disease may not go away. In fact, according to the model, it is possible there will be waves of infection surges and reactionary social change – in an ordered or chaotic way – in perpetuity.

This fluctuation around an equilibrium results from a negative feedback loop between behavior and health risk. As a population attempts to attain the best possible utility, a higher risk of disease leads to less social contact, which then leads to lower risk and greater social contact, which increases risk once again in a repeating cycle.

When there are delays in the spread of information about disease risks, these fluctuations become even more chaotic. “There is some inherent uncertainty in modeling that really is brought out in our work, because you have feedback mechanisms that can toss entire conclusions out the window,” said Arthur.

When the social system is reacting to an epidemiological reality that is no longer accurate, people’s behavioral responses become derailed from the actual, current circumstances. These complexities make for interesting math where small changes in the parameters, even the number of initial infected, can have outsized and qualitative effects on the epidemic outcomes.

“The problem is that you usually get information about the infection with a delay and, in epidemics, those delays can cause all sorts of weirdness to happen in your prediction,” said Marcus Feldman, the Burnet C. and Mildred Finley Wohlford Professor in the School of Humanities and Sciences and senior author of the paper. “In our model, we see that the delay of information turns out to be critical.”