Analytical solutions of a minimal model of species migration in a bounded domain

Feltham, D.L. ORCID: https://orcid.org/0000-0003-2289-014X and Chaplain, M. A. J. (2000) Analytical solutions of a minimal model of species migration in a bounded domain. Journal of Mathematical Biology, 40 (4). pp. 321-342. ISSN 0303-6812 doi: 10.1007/s002850050183

Abstract/Summary

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally.