Mathematical Models and Methods in Applied Sciences · 2005 · 100 citations · 10 references
Natural SciencesBiologyCell BiologyBiological Systems ModelingDynamical SystemsTheoretical BiophysicsDynamic Systems ModelingEvolutionary DynamicsKinetic ModelingMathematical BiologyReaction DynamicsStatistical MechanicsKinetic TheoryKinetic Theory Of Biomolecular InteractionsNon-equilibrium Statistical MechanicsPopulation Kinetics
This paper develops a variety of mathematical tools to model the dynamics of large systems of interacting cells. Interactions are ruled not only by laws of classical mechanics, but also by some biological functions. The mathematical approach is the one of kinetic theory and non-equilibrium statistical mechanics. The paper deals both with the derivation of evolution equations and with the design of specific models consistent with the above-mentioned mathematical framework. Various hints for research perspectives are proposed in the last part of the paper.
10
From molecular to modular cell biology
Leland H. Hartwell, J. J. Hopfield, Stanislas Leibler et al. · Nature · 1999 · 3.7K citations
Theory and Application of the Boltzmann Equation
C. Cercignani, A. S. Berman · Journal of Applied Mechanics · 1976 · 662 citations · Full text
Dynamics of tumor interaction with the host immune system
Nicola Bellomo, G Forni · Mathematical and Computer Modelling · 1994 · 117 citations
Medicine, Immunology, Oncology +14