Bacteria--phagocyte dynamics,
axiomatic modelling and mass-action kinetics
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Department of Computer Science and Applied Mathematics, The Weizmann Institute, Rehovot, 76100
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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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Received:
01 March 2010
Accepted:
29 June 2018
Published:
01 April 2011
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MSC :
Primary: 92-06, 92B99; Secondary: 92D25.
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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.
Citation: Roy Malka, Vered Rom-Kedar. Bacteria--phagocyte dynamics,axiomatic modelling and mass-action kinetics[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 475-502. doi: 10.3934/mbe.2011.8.475
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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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