Upscaling from discrete to continuous mathematical models of two interacting populations
Authored by Alicia Prieto-Langarica, Hristo V Kojouharov, Benito M Chen-Charpentier
Date Published: 2013
DOI: 10.1016/j.camwa.2013.02.010
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Platforms:
MATLAB
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
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Abstract
Populations interact in a wide variety of ways: through cooperation, competition, or predation. In this work we consider two interacting
populations, individuals and a stimulus. Individuals move in response to
the stimulus population while the stimulus only diffuses. Both
populations grow while the stimulus population is being depleted by the
individuals. In order to account for the random nature of the system, an
individual-based model (IBM) is first developed and then upscaled into a
continuous partial differential equation (PDE) model by considering
transition probabilities of the individuals at each site. Finally, a set
of numerical experiments is presented showing very good agreement
between the IBM and the PDE model. Published by Elsevier Ltd
Tags
movement