Date of Completion

Spring 5-8-2011

Thesis Advisor(s)

Greg Huber; Charles Wolgemuth

Honors Major

Cell Biology


Cell Biology | Molecular Biology


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.