Simulation of density-dependence subdiffusion in chemotaxis

This paper presents a nonlinear, non-Markovian model of subdiffusive transport influenced by a chemotactic gradient affecting cellular mobility. In the model, both the stochastic waiting time and the escape rate are modulated by the chemotactic gradient. We derive the subdiffusive fractional master equation, examine its diffusive limit, and implement Monte Carlo simulations to analyse particle transport under varying chemotactic conditions. Simulation results show that, in the absence of chemotaxis, particles exhibit symmetric subdiffusion consistent with the standard continuous time random walk behaviour. A constant chemotactic gradient has little effect on particle distribution, whereas spatially varying gradients-linear or quadratic-produce pronounced effects. Specifically, particles drift away from regions with high chemotactic intensity and tend to aggregate in areas of minimal chemotactic influence, with the strongest aggregation observed under quadratic gradients. These findings highlight the significant role of spatially dependent chemotaxis in shaping anomalous subdiffusive transport dynamics.