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In 1766, a young Dutch mathematician named Daniel Bernoulli developed an epidemiological model during a smallpox epidemic that raged across North America. A process called variolation, the technique of deliberate exposure to the disease by blowing dried smallpox scabs into the nose of healthy individuals, was being questioned. This process would spark an immune response in most but a fraction of those exposed would develop full-blown small pox and die while some would spread the mild form they contracted. Hence, doctors were hesitant to perform the procedure and parents even more so to let their children be test subjects, despite the procedure’s amazing success rate. Bernoulli formed a model that showed the public benefit of large-scale variolation – the significant decrease in the mortality rate, which far outweighed the fraction of cases where people died. His is perhaps the earliest example of using a mathematical model to evaluate a disease and possible intervention strategies. This is what Dr. Lauren Ancel Meyers, assistant professor of integrative biology, studies today at UT. “I am interested in understanding how disease spreads through animal and human populations,” she said. Using mathematical methods, she is able to forecast the spread of infectious diseases and to evaluate different control strategies. Using network theory, Meyers creates contact patterns using statistical information about a certain area – a household, a school, a city – to describe patterns of interaction that lead to disease transmission. For instance, Meyers is currently working with a graduate student from the University of Minnesota who spends much of her time following the prides of lions in the Serengeti. They are interested in understanding canine distemper virus (CDV) that infects various carnivore populations. “Researchers with the Serengeti Lion Project tracked lionesses continuously for four days and nights. We are using their data to build a model of the contact patterns within lion populations and between lions and other carnivores that may lead to the spread of this disease,” she said. “We believe that the disease is occasionally transmitted to lions from other species, perhaps when they feed on the same carcasses.” Building these models for animal diseases is similar to building models for human diseases, said Meyers. “The common thread is that all of the diseases we study spread via physical interactions between organisms.” During the SARS outbreak, the University of British Columbia Centre for Disease Control (UBC CDC) asked Meyers to help them understand the spread of SARS in Canada and worldwide. She helped them build a network model that can predict the transmission patterns of a respiratory disease through an urban area like Vancouver. In this network, individuals are represented as nodes and contacts between individuals are represented as lines (or edges) connecting appropriate nodes. They used this model to evaluate different control strategies, such as vaccination, anti-viral medication or just simple social measures like closing down certain public spaces or maintaining personal hygiene. “To model the vaccination of certain individuals, for example, you can simply remove the corresponding nodes in the network.” Meyers explains, “The advantage of mathematical modeling is that it allows us to conduct virtual experiments that would be impractical or unethical in the real world. For example, we cannot withhold potentially life-saving interventions for the sake of evaluating the effectiveness of a particular control strategy.” Meyers’ lab group includes three PHD students, two postdoctoral students and four undergraduate students. In addition to mathematical epidemiology, they also study the evolution of communities made up of multiple species of bacteria. By allowing them to grow together for thousands of generations in test tubes, “we can study their ecological interactions and the evolution of these interactions through time. They can compete for resources, consume metabolic byproducts of another species, or produce toxins that inhibit another species growth.” Not much is known about how in this complex community called the Earth, these organisms live together and possibly influence each other’s evolution. “Although these experiments take place in microbial communities, they may provide general insight into the evolution of complex biological communities. We would like to know, for example, how biodiversity influences a community’s ability to withstand perturbation, like the introduction of an invasive species or unexpected environmental change.” Meyers also enjoys outreach to younger students. This summer, she is advising a research project at the Mathworks Honors Summer Math Camp at Texas State University. Three high school students are developing mathematical models to study the dynamics of a disease that occurs seasonally and hence is regularly reintroduced into a population. "It's a vital time for training students in mathematical biology. This interdisciplinary field has exploded in recent years thanks to the deluge of data-rich information sets that require sophisticated analyses and an increasing appreciation for the utility of models. There are many more important problems at the interface of math and biology than there are scientists with the expertise to address them." |
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