In the early stages of a disease outbreak, health officials have pressing questions. Where will cases emerge next? How many people will become sick? How can the spread be controlled? But data are sparse, especially in the first days and weeks. This is when researchers who use mathematical models to study diseases come in.

Modeling in the midst of a pandemic

In 2009, a novel H1N1 influenza strain emerged, causing a global pandemic. Dr. Hugo Lopez-Gatell, then Mexico's Assistant Director General of Epidemiology and now the Director of National Health Surveys at the National Institute of Public Health, was on the front lines. “We wanted a measure of the speed of transmission and of propagation throughout the country”, Lopez-Gatell recalled. The World Health Organization (WHO) and the U.S. Centers for Disease Control and Prevention (CDC) worked with Mexican officials to review available data. But the analyses lacked predictive power. “We saw modeling as an essential tool for understanding the complexity of the outbreak”, he said.

Lopez-Gatell and colleagues teamed up with researchers from the Medical Research Council Centre for Outbreak Analysis and Modelling at Imperial College London. Using models to fit the outbreak data, they calculated a measure called the basic reproduction number (R0), which approximates how many people one sick individual infects, and can be used to estimate the speed of transmission. They reported R0 to be up to 1.6 – higher transmissibility than seasonal influenza, but lower than some previous pandemic strains. They also estimated the case fatality rate to be 0.4% and later adjusted it to 0.091% – far lower than initially feared – as more data came in. “This was a relief”, Lopez-Gatell said. “It lowered the pressure and increased the credibility of the health authorities”.

In a separate collaborative effort, researchers from Mexico and the United States presented modeling studies forecasting the progression of the epidemic in Mexico and showing that government-implemented social distancing measures were effective in reducing transmission. According to Lopez-Gatell, their work also improved communication with the media and public. “Having the modeler at the press conferences helped the minister of health to be more effective in conveying his message. [The minister] could say, 'Here is the scientist, and here is what he found out'.”

Predicting the next big wave

In 2008, Dr. Sherry Towers, a PhD in physics who returned to graduate school to study statistics at Purdue University, took a course in epidemiology and built a model to fit data from a 1914 polio epidemic. In 2009, she heard news of the H1N1 outbreaks and wondered whether she could use a similar model to fit the case data being published weekly by the WHO and CDC. She teamed up with Purdue mathematics professor, Dr. Zhilan Feng.

Soon, Towers and Feng noticed something alarming. “I was fitting parameters to the data as it was coming in and it was predicting a significant fall wave” of infection would hit the U.S., peaking at the end of October, Towers said. Sure enough, the second wave came and peaked as predicted. “It's amazing to me how useful these simple models are at helping to answer quite complicated questions”, she said. And it's not just about predictions. It's about discovering mechanisms. “The advantage of mathematical models”, Towers explained, “is that they allow us to simulate the underlying dynamics of the disease spread. Once you understand the dynamics, you have a better chance of figuring out how best to control the spread”.

Towers is now a research professor in the Mathematical, Computational, and Modeling Sciences Center at Arizona State University. She is currently modeling the recent H7N9 influenza outbreaks in China and the influence live bird markets may have on disease spread.

How do researchers model epidemics?

Modeling comes in many flavors, but the most basic disease transmission models are comprised of two populations: those susceptible to infection and those infected. Equations govern how people move from one population to another over time. A recovered population of those immune to the disease can also be included. Or, infected people may become susceptible again to study diseases that can be repeatedly contracted, like some STDs. More complicated models have additional populations or geographical locations. Another type of model, known as agent-based, focuses on individuals. As Towers explained, “[agent-based models] simulate the daily activities and social interactions of people, and the random contacts they might make throughout the day”.

Modeling has many advantages. The unknowns in nature are known in the model and can be changed to examine the effects. For example, the likelihood that a susceptible person gets sick given contact with an infected person can be varied. How are the inputs to the model selected? In part, researchers rely on data from past outbreaks. They also examine simulations to see whether the spread matches new data coming in and adjust the model accordingly. Lopez-Gatell said one of the appealing things about modeling is the friendly environment. “We can explore phenomena that can be devastating in real life in a place where nobody gets hurt.” Towers agreed. “Life is a non-repeatable experiment”, she said. But simulations can be repeated to test different scenarios.

Working together

Modeling isn't a substitute for data. In fact, Towers pointed out, having good data is crucial for building good models. But data are not always easy to obtain. “People who have the skills and a strong interest in modeling an outbreak as it's occurring can't do that effectively unless they have access to the data”, she said. Lopez-Gatell admitted there is often a disconnect between modelers and health officials. “Modelers, like many scientists, are within academic settings and their communication element is papers. Decision makers are within government offices. They don't always understand the models and they see the science with some skepticism”, he said. It's important these communities find ways to come together. Bilateral communication will be key to effectively responding to the next disease outbreak.

Acknowledgements: The author thanks Jef Akst and Marco Herrera Valdez for feedback on previous drafts of this article.

Image: Masked subway passengers in Mexico City during the 2009 H1N1 pandemic, by Eneas De Troya via Flickr