Date of Completion

Spring 5-7-2011

Thesis Advisor(s)

Charles Wolgemuth; Greg Huber

Honors Major

Mathematics

Disciplines

Applied Mathematics | Other Applied Mathematics | Other Biochemistry, Biophysics, and Structural Biology

Abstract

The purpose of this project is to develop and analyze a mathematical model

for the pathogen-host interaction that occurs during early Lyme disease.

Based on the known biophysics of motility of Borrelia burgdorferi and a

simple model for the immune response, a PDE model was created which tracks

the time evolution of the concentrations of bacteria and activated immune

cells in the dermis. We assume that a tick bite inoculates a highly

localized population of bacteria into the dermis. These bacteria can

multiply and migrate. The diffusive nature of the migration is assumed and

modeled using the heat equation. Bacteria in the skin locally activate

immune cells, such as macrophages. These cells track down the bacteria

and kill them.

The immune cells' "tracking" of the bacteria is modeled using the

Keller-Segel model for chemotaxis. Assuming the periodic boundary

condition, the model is investigated over a 1D Cartesian domain. Six

different parameters are considered and their effects on the velocity of

propagation of the traveling fronts are investigated. With one exception,

there seemed to be no regiment of parameters under which the bacteria were

totally exterminated.

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