Journal of Biological Dynamics (Jan 2019)

Stochastic optimal switching model for migrating population dynamics

  • Hidekazu Yoshioka,
  • Tomomi Tanaka,
  • Futoshi Aranishi,
  • Tomoki Izumi,
  • Masayuki Fujihara

DOI
https://doi.org/10.1080/17513758.2019.1685134
Journal volume & issue
Vol. 13, no. 1
pp. 706 – 732

Abstract

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An optimal switching control formalism combined with the stochastic dynamic programming is, for the first time, applied to modelling life cycle of migrating population dynamics with non-overlapping generations. The migration behaviour between habitats is efficiently described as impulsive switching based on stochastic differential equations, which is a new standpoint for modelling the biological phenomenon. The population dynamics is assumed to occur so that the reproductive success is maximized under an expectation. Finding the optimal migration strategy ultimately reduces to solving an optimality equation of the quasi-variational type. We show an effective linkage between our optimality equation and the basic reproduction number. Our model is applied to numerical computation of optimal migration strategy and basic reproduction number of an amphidromous fish Plecoglossus altivelis altivelis in Japan as a target species.

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