Modeling Disease

From SARS, flu, Kawasaki disease and now rotavirus, a Yale School of Public Health researcher uses mathematical models to understand the transmission dynamics of infectious diseases.

Virginia Pitzer uses mathematical modeling to study the transmission dynamics of infectious diseases.  Such diseases pose unique challenges to epidemiologists because the risk of becoming infected depends not only on one’s own risk factors, but also on how many other people in the population are infected. Drawing on concepts from fields such as ecology and the physical sciences, Pitzer uses mathematical modeling to understand how interventions such as vaccination, which is targeted at individuals, can sometimes lead to surprising effects at the population level. Much of her current research is focused on enteric diseases such as rotavirus and typhoid fever.  Pitzer, Sc.D, joined the School of Public Health faculty as an assistant professor in the Department of Epidemiology of Microbial Diseases in 2012 after completing her postdoctoral research in the Department of Ecology and Evolutionary Biology at Princeton University and Fogarty International Center at the National Institutes of Health.

Describe the challenges involved in developing an accurate mathematical model that can be used to understand disease transmission and dynamics.

VP: Like any good research, the process starts with having a good question and the data to answer it. The question determines what kind of model you need to develop, and the data often determines how detailed the model needs to be. From there, I typically do a lot of background research and talk to experts in the field to make sure I understand the underlying biology of the disease that I am trying to model. This allows me to establish the model’s framework. After that, there is typically a little bit of math and a lot of computer programming involved. 

Does the process require a lot of fine-tuning?

VP: I would say about 90 percent of it is fine-tuning.

What kinds of information do you need in order to develop such a model?

VP: First you need to understand the natural history of the disease and the nature of immunity.  For example, when you get infected, how long are you capable of spreading it to others, and how does it spread? Once you have been infected and recovered, can you get it again? How are cases of clinical disease (which is typically what gets observed) representative of underlying infections?  Such data typically comes from studies that other people have done and published in the literature. This data is used to define some of the parameters that are needed to describe the model, while other parameters, such as the transmission rate, are estimated by fitting the model to the time series data. Most models require data on the number of cases of the disease over a reasonably long time period as a starting point. Getting such data usually requires establishing collaborations with individuals and institutions (such as the CDC) that are involved in collecting and maintaining the data sets, which is part of the fun.

How long does this process take?

VP: Coming up with the initial model framework and parameters from the literature usually only takes a matter of weeks. But fitting the model to the data, fine-tuning it, then using the model to explore “what if” scenarios, such as what if we introduced a vaccine? or what if we improved treatment strategies? —that part usually takes at least a few months.

What are some of the diseases that you have done this with?

VP: In the past, I’ve worked on SARS, flu and Kawasaki disease, among others. But a big focus of my research now is rotavirus.

What diseases might you work on in the future?

VP: I have recently gotten involved in some work on typhoid fever, which is really interesting because it combines analysis of historical data from the United States with data from present day developing countries where the modeling has important implications for global health. There is also a lot of interesting research on vector-borne and zoonotic diseases going on here at Yale, so I wouldn’t mind getting involved in some of those projects. And who knows what the next emerging disease is going to be!

Your models also involve the elements of space and time. Have you applied these elements to particular diseases?

VP: I have always been very intrigued by questions about seasonality of infectious diseases—for example, why do we get flu in winter but not summer? Flu, rotavirus, and RSV (an important cause of respiratory disease, especially in infants) all exhibit winter outbreaks in the United States, but have very different spatial patterns of spread.  Flu tends to jump from city to city, then spread out from there into the more rural areas. Prior to introduction of vaccines, rotavirus epidemics began in the southwestern part of the United States and gradually spread to the northeast. RSV epidemics tend to begin in Florida then spread north and west from there. My collaborators and I have been using mathematical models to try to understand some of the potential drivers behind these different patterns.

What did you find?

VP: To some extent, the different patterns can be explained by how sensitive the bug is to climatic conditions and which age groups are most important to transmission. For flu, school kids and working adults tend to play a big role in transmission, whereas for rotavirus, it seems like infants are responsible for driving the epidemics—which helps to explain some of the differences in the patterns.  But there is still a lot that remains to be understood.

You’ve done a lot of work with rotavirus. Describe this disease and its public health implications. 

VP: Rotavirus is one of the leading causes of diarrhea in young children worldwide. You can get infected with rotavirus throughout your life, but it is usually only infants who don’t have any immunity to the disease who have severe infections, which can result in hospitalization or even death. Rotavirus used to cause around 60,000 hospitalizations per year in the United States; but now there are vaccines against it, and the number of hospitalizations for rotavirus has gone way down.  However, these vaccines have yet to be introduced in most developing countries, where rotavirus accounts for nearly half a million deaths each year.

What has modeling revealed about the disease?

VP: The rotavirus model that we came up with was able to explain the southwest-to-northeast pattern of pre-vaccination epidemics in the United States based on variations in birth rates across states.  Birth rates tend to be higher in the southwestern states and lower in the northeast. Susceptible infants provide the “fuel for the fire” of rotavirus epidemics, so to speak, and you build up a sufficient population of infants to set off an epidemic more quickly in high birth rate places than in the lower birth rate places. When you start to vaccinate infants against rotavirus, it acts like a reduction in the birth rate, because you reduce the number of fully susceptible infants entering the population. This helped explain why the rotavirus epidemic that occurred in 2007-08 (which was the first season with decent vaccination coverage) was much later than normal. Modeling also helps to explain why vaccination not only protects the infants receiving the vaccines, but also provides protection for unvaccinated age groups, at least temporarily, by reducing the amount of transmission in the population. 

What has been your most surprising research finding to date? 

VP: One of the things that our rotavirus model predicted back in 2009 was that when vaccination coverage among infants reached around 90 percent (which it is now), you would start to see rotavirus outbreaks only every two years instead of the annual winter outbreaks that occurred prior to vaccination. So far, that prediction seems to have been borne out, which is pretty cool! It is really difficult to make accurate long-term predictions with models—it’s like trying to predict the weather next month.

You joined the School of Public Health faculty in 2012. What do you want to accomplish in the long term?

VP: Ultimately, my goal is to collaborate with researchers around the world to better link up models for the transmission dynamics of infection with data from settings in which the diseases cause the greatest burden of morbidity and mortality. This will not only lead to a better understanding of the factors that drive differences in disease patterns across countries, but will also hopefully lead to better ways to evaluate and promote interventions to reduce the burden of these diseases.

This article was submitted by Denise L Meyer on January 18, 2013.