A continuous-time model of centrally coordinated motion with random switching

• DOI: 10.1007/s00285-016-1040-2
• Publication Date: 2016-07-09T01:55:47Z
• Authors: J. C. Dallon; Lynnae C. Despain; Emily J. Evans; Christopher P. Grant; W. V. Smith
• Keywords: Jump process; Stochastic modelling

This paper considers differential problems with random switching, with specific applications to the motion of cells and centrally coordinated motion. Starting with a differential-equation model of cell motion that was proposed previously, we set the relaxation time to zero and consider the simpler model that results. We prove that this model is well-posed, in the sense that it corresponds to a pure jump-type continuous-time Markov process (without explosion).We then describe the model's long-time behavior, first by specifying an attracting steady-state distribution for a projection of the model, then by examining the expected location of the cell center when the initial data is compatible with that steady-state. Under such conditions, we present a formula for the expected velocity and give a rigorous proof of that formula's validity. We conclude the paper with a comparison between these theoretical results and the results of numerical simulations.