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Individual and patch behaviour in structured metapopulation models.

  • Barbour AD Institut für Mathematik, Universität Zürich, Winterthurertrasse 190, 8057, Zürich, Switzerland, a.d.barbour@math.uzh.ch.
  • Luczak MJ
  • 2014-10-01
Published in:
  • Journal of mathematical biology. - 2015
Animals
Computer Simulation
Host-Pathogen Interactions
Humans
Markov Chains
Mathematical Concepts
Models, Biological
Population Density
Population Dynamics
Stochastic Processes
English Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total population size is large. They also exhibit diffusive stochastic fluctuations on a smaller scale about this deterministic path. Here, it is shown that the individuals in such processes experience an almost deterministic environment. Small groups of individuals behave almost independently of one another, evolving as Markov jump processes, whose transition rates are prescribed functions of time. In the context of metapopulation models, we show that 'individuals' can represent either patches or the individuals that migrate among the patches; in host-parasite systems, they can represent both hosts and parasites.
Language
  • English
Open access status
green
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Persistent URL
https://sonar.ch/global/documents/298390
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