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Citation

Hapca S, Crawford JW, MacMillan K, Wilson MJ & Young IM (2007) Modelling nematode movement using time-fractional dynamics. Journal of Theoretical Biology, 248 (1), pp. 212-224. https://doi.org/10.1016/j.jtbi.2007.05.002

Abstract
We use a correlated random walk model in two dimensions to simulate the movement of the slug parasitic nematode Phasmarhabditis hermaphrodita in homogeneous environments. The model incorporates the observed statistical distributions of turning angle and speed derived from time-lapse studies of individual nematode trails. We identify strong temporal correlations between the turning angles and speed that preclude the case of a simple random walk in which successive steps are independent. These correlated random walks are appropriately modelled using an anomalous diffusion model, more precisely using a fractional sub-diffusion model for which the associated stochastic process is characterised by strong memory effects in the probability density function.

Keywords
Correlated random walk; Stochastic process with memory; Conditional probability; Mean square displacement

Journal
Journal of Theoretical Biology: Volume 248, Issue 1