2010/03/08 by T. A. M. Langlands, B. I. Henry · 3 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Fractional Differential Equations Solutions #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #cond-mat.stat-mech #math.DS #msc:35K57 #msc:35R11 #msc:60G22 #q-bio.OT
paper · pdf · doi:10.1103/physreve.81.051102
published as Phys. Rev. E 81, 051102 (2010) · 25pages
arxiv created 2010/03/08 · openalex publication_date 2010/05/04 · arxiv updated 2012/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.