Date of Completion
Charles Wolgemuth; Greg Huber
Applied Mathematics | Other Applied Mathematics | Other Biochemistry, Biophysics, and Structural 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
Rutovytskyy, Yevhen, "Modeling Human Immune Response to the Lyme Disease-Causing Bacteria" (2011). Honors Scholar Theses. Paper 212.