Bacteria--phagocyte dynamics,axiomatic modelling and mass-action kinetics

Roy Malka; Vered Rom-Kedar

doi:10.3934/mbe.2011.8.475

Article Contents

2011, Volume 8, Issue 2: 475-502. Doi: 10.3934/mbe.2011.8.475

This issue Previous Article Preliminary analysis of an agent-based model for a tick-borne disease Next Article Physiologically structured populations with diffusion and dynamic boundary conditions

Bacteria--phagocyte dynamics, axiomatic modelling and mass-action kinetics

Roy Malka^1, and
Vered Rom-Kedar^2,

1.
Department of Computer Science and Applied Mathematics, The Weizmann Institute, Rehovot, 76100
2.
The Estrin Family Chair of Computer Science and Applied Mathematics, Department of Computer Science and Applied Mathematics, The Weizmann Institute, Rehovot, 76100

Received: February 28, 2010

Revised: September 30, 2010

Published: March 2011

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Abstract

Axiomatic modeling is ensued to provide a family of models that describe bacterial growth in the presence of phagocytes, or, more generally, prey dynamics in a large spatially homogenous eco-system. A classification of the possible bifurcation diagrams that arise in such models is presented. It is shown that other commonly used models that do not belong to this class may miss important features that are associated with the limited growth curve of the bacteria (prey) and the saturation associated with the phagocytosis (predator kill) term. Notably, these features appear at relatively low concentrations, much below the saturation range. Finally, combining this model with a model of neutrophil dynamics in the blood after chemotherapy treatments we obtain new insights regarding the development of infections under neutropenic conditions.

Keywords:

Axiomatic modelling,
bacteria-phagocyte dynamics.

Mathematics Subject Classification: Primary: 92-06, 92B99; Secondary: 92D25.

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