Modeling Bacterial Clearance Using Stochastic-Differential Equations

A. Jeremic, and A. Atalla
McMaster University, Hamilton, ON, Canada

In this paper, we develop a mathematical model to simulate the movement of bacteria into and within a capillary segment. Also, we model the transportation through capillary walls by means of anisotropic diffusivity that depends on the pressure difference across the capillary walls. By solving the model using COMSOL, it was possible to predict the concentration of bacteria at points within the capillary. These results are consequently integrated in order over the domain of interest to evaluate probabilities of transmission and absorption in the capillary network. In order to reduce the computational complexity we also propose segmented model in which the integration is performed on a smaller domain and the corresponding probabilities are then adequately combined in order to evaluate the overall probabilities of transmission and absorption.