"Over in the measles world it's the same way. Once you catch the measles you're done. Through that parallel we started looking at computer viruses in a different way."

-Lora Billings

Attack on the body vs. attack on a network. Can the way a human virus, such as measles, spreads through a community tell us anything about the way a computer virus spreads through a network?

Through a multidisciplinary project sponsored by the Naval Research Laboratory in Maryland, Lora Billings is examining how computer viruses spread by taking a deeper look into human epidemics. When she left the Naval Research Laboratory to accept a teaching position at Montclair State in September, Billings brought with her the $50,000 grant to continue her research on the spread of viruses. The mathematician's research involves deterministic and stochastic dynamical systems, theory and applications of chaos, ordinary differential equations and mathematical biology.

Billings, who earned a Ph.D. in applied math at the University of Colorado, talked about her research and how she applies it in the classroom.

Q. Tell us about your research.
A. We're conducting studies of the identification, causes, spread and control of diseases in living populations. By looking at pre-vaccination data of a measles virus we could properly mimic or model how measles spread through a population of children. Then we needed to test the model to predict how a certain vaccination strategy would affect that number over time. The problem was that the original model looked at for the appropriate parameters for measles did not match the real-world data. By oversimplifying or making assumptions and generalizations about the system, we ended up missing some of the behavior. So we added noise or used small changes to the initial conditions due to things like emigration in and out of cities.

Q. What has your research revealed up to now?
A. By adding noise to the system we could actually get the data to match the model. That was our first result. Since then we've made the analogy that a computer virus spreading through a network is similar to measles spreading through a population of children. Neither measles nor a digital disease is deadly, and once you get a computer virus and recover from it you don't catch that same virus again. Over in the measles world it's the same way. Once you catch the measles you're done. Through that parallel we started looking at computer viruses in a different way.

I'm participating in a work group at Rutgers in June with biologists, mathematicians, computer scientists and physicists. We're pooling our knowledge to examine epidemics of some sort of virus. We want to look at the different techniques and figure out how to approach this computer virus model to not only get a better model, but to get some generalizations as to how it should be handled and if there's any way of controlling it.

Q. What is your particular area of expertise?
A. My specialty is chaotic systems. I draw on that knowledge to pick out patterns in chaotic behavior. It was thought that measles was chaotic, but that hasn't been proven because there isn't enough pre-vaccination data to form a conclusive analysis. But it could possibly be chaotic, and that's what interests me. If the computer virus works like the measles virus, there's a chance the computer virus is chaotic as well.

Q. How do you bring your research into the classroom?
A. I'm visual, so most of my papers have a lot of pictures in them. I go back and forth between doing mathematical simulation with pictures and the theory to explain what I'm seeing. This semester I'm teaching differential equations, which is the basis for the models I use. If you can understand the basics of differential equations you can understand the models. So I bring my visualization aspect of my research to my class.

Q. Are your students involved in your research?
A. Last semester, Carmen Piccolo, a junior biology major on the pre-med. track, said he was interested in how I use calculus to predict epidemic spread. We're utilizing his medical bent to study the spread of rubella and the flu. I know things from the mathematician's world, and he brings to my research what biologists know. I'm also working with Karin Weule, a graduate math student, on chaos. She wants to eventually work on computer virus models with me, hoping to develop that research into a thesis. There's always a mutual exchange when faculty and students work together.

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