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

doi:10.3934/mbe.2011.8.475

Mathematical Biosciences and Engineering, 2011, 8(2): 475-502. doi: 10.3934/mbe.2011.8.475. Primary: 92-06, 92B99; Secondary: 92D25.

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

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

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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.

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Keywords: bacteria-phagocyte dynamics.; Axiomatic modelling

Citation: Roy Malka, Vered Rom-Kedar. Bacteria--phagocyte dynamics, axiomatic modelling and mass-action kinetics. Mathematical Biosciences and Engineering, 2011, 8(2): 475-502. doi: 10.3934/mbe.2011.8.475

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This article has been cited by:

1. Roy Malka, Baruch Wolach, Ronit Gavrieli, Eliezer Shochat, Vered Rom-Kedar, Evidence for bistable bacteria-neutrophil interaction and its clinical implications, Journal of Clinical Investigation, 2012, 122, 8, 3002, 10.1172/JCI59832
2. Junyan Xu, Tonghua Zhang, Keying Song, A stochastic model of bacterial infection associated with neutrophils, Applied Mathematics and Computation, 2020, 373, 125025, 10.1016/j.amc.2019.125025

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