Keywords

markov process, cell motion, interevent time

Abstract

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.

Original Publication Citation

Journal of Mathematical Biology 74:727-753 (2017) doi:10.1007/s00285-016-1040-2

Document Type

Peer-Reviewed Article

Publication Date

2017

Publisher

Springer

Language

English

College

Physical and Mathematical Sciences

Department

Mathematics

University Standing at Time of Publication

Full Professor

Included in

Mathematics Commons

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