A user’s guide to PDE models for chemotaxis

Keywords

Replicate, Property (philosophy), Chemotaxis, Simplicity, Basis (linear algebra)

References

• Stripe formation in juvenile Pomacanthus explained by a generalized turing mechanism with chemotaxis.F Haghighati, Mahvash Mousavi, Neda Moslemi — 1999
• Biological inferences from a mathematical model for malignant invasion.Abbey J. Perumpanani, Jonathan A. Sherratt, John W. Norbury — 1996
• Free Energy and Self-Interacting ParticlesTakashi Suzuki — 2005
• Mathematical Modelling of AngiogenesisMark A. J. Chaplain — 2000
• Transport Equations in BiologyBenoı̂t Perthame — 2006
• Volume-filling and quorum-sensing in models for chemosensitive movementKevin J. Painter, Thomas Hillen — 2002
• Chemotactic Cellular Migration: Smooth and Discontinuous Travelling Wave SolutionsDonald F. Newgreen, Graeme J. Pettet, Kerry A. Landman — 2003
• Signal transduction in bacterial chemotaxisJeffry B. Stock, Michael G. Surette, William R. McCleary — 1992
• Singular limit of a degenerate chemotaxis-Fisher equationFathi Dkhil — 2004
• A Non-linear Parabolic System Modeling Chemotaxis with Sensitivity FunctionsKatharina Post — 1999
• Convergence to a viscosity solution for an advection-reaction-diffusion equation arising from a chemotaxis-growth modelMarie Henry, Dorothea Hilhorst, Reiner Schätzle — 1999
• Sperm Chemotaxis: A PrimerEilo Hildebrand, U. Benjamin Kaupp — 2005
• Model Analysis of Spatial Patterns in Mountain Pine Beetle Outbreaks.Jesse A. Logan, Peter White, Barbara Bentz — 1998
• Global Behaviour of a Reaction‐Diffusion System Modelling ChemotaxisH. Gajewski, K. Zacharias, Konrad Gröger — 1998
• Models of dispersal in biological systemsHans G. Othmer, Steven R. Dunbar, Wolfgang Alt — 1988
• Chemical control of eukaryotic cell movement: a new model.Jonathan A. Sherratt, E. Helene Sage, J. D. Murray — 1993
• Biased random walk models for chemotaxis and related diffusion approximationsWolgang Alt — 1980
• A new interpretation of the Keller-Segel model based on multiphase modellingHelen M. Byrne, Markus R. Owen — 2004
• The Diffusion Limit of Transport Equations Derived from Velocity-Jump ProcessesHans G. Othmer, Thomas Hillen — 2000
• Spatio-temporal patterns generated by Salmonella typhimurium.Diana E. Woodward, Rebecca C. Tyson, Mary R. Myerscough — 1995

Cited by

• Numerical computation of an Evans function for travelling waves.Bariot Hafif — 2013
• The Impact of Social Behavior on the Attenuation and Delay of Bacterial NanonetworksCarlos Marañón — 2016
• Study of Virus Dynamics by Mathematical ModelsXiulan Lai — 2014
• Pattern formation in a generalized Keller-Segel modelPatrick De Leenheer, Jay Gopalakrishnan, Erica Zuhr — 2011
• Mathematics toward systems biology and complexity: reply to comments on "On the interplay between mathematics and biology - hallmarks toward a new systems biology".Nicola Bellomo, A. M. Ełaiw, Abdullah M. Althiabi — 2015
• Développement et analyse de schémas volumes finis motivés par la présentation de comportements asymptotiques. Application à des modèles issus de la physique et de la biologieMarianne Bessemoulin‐Chatard — 2012
• Non-local models of cell-cell interactions in developmentJ. M. Bloomfield — 2011
• Assessing hematopoietic (stem-) cell behavior during regenerative pressure.Thomas Stiehl, Anthony D. Ho, Anna Marciniak‐Czochra — 2014
• Mathematical modelling of pattern formation in developmental biologyG. S. Hunt — 2013
• Analysis of a chemotaxis system modeling ant foragingRicardo Alonso, Paulo Amorim, Thierry Goudon — 2015
• A Preconditioned Minimal Residual Solver for a Class of Linear Operator EquationsO. Awono, Jacques Tagoudjeu — 2010
• Stabilization in a two-dimensional chemotaxis-Navier–Stokes systemMichael Winkler — 2013
• Systèmes d'équations aux dérivées partielles pour la biologie : modèles, analyse numérique et simulationsM. Ribot — 2014
• Large-Data Global Generalized Solutions in a Chemotaxis System with Tensor-Valued SensitivitiesMichael Winkler — 2015
• Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid systemYoushan Tao, Michael Winkler — 2015
• Stabilization in a two-species chemotaxis system with a logistic sourceJosé Ignacio Tello del Castillo, Michael Winkler — 2012
• Mathematical modelling of cancer cell invasion of tissue : discrete and continuum approaches to studying the central role of adhesionVivi Andasari — 2011
• Local and non-local mathematical modelling of signalling during embryonic developmentGeorgios Vasilopoulos — 2012
• Comparison and numerical treatment of generalised Nernst-Planck modelsJürgen Fuhrmann — 2015
• Global solution for a kinetic chemotaxis model with internal dynamics and its fast adaptation limitJie Liao — 2015

Related papers

• On the Simplicity of a Scientific TheoryLI Xing-mi — 2008
• Simplicity in the Best Systems Account of Laws of NatureJames Woodward — 2014
• Naïve Simplicity: The Overlooked Piece of the Complexity‐Simplicity ParadigmFranklin W. Schwartz, Ganming Liu, Pradeep Aggarwal — 2017
• Correcting replicate variation in spectroscopic data by machine learning and model-based pre-processingValeria Tafintseva, Volha Shapaval, Uladzislau Blazhko — 2021
• Simplicity"Design of Indoor Surroundings ArtLi Bo — 2002
• SimplicityZi‐Ru Chen — 2009
• The Voluntary Simplicity Consumer: A Comparative StudyAvraham Shama — 1988