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.

最优的切换控制形式主义与随机动态规划相结合，首次被用于建模具有非重叠世代的人口动态种群迁移的生命周期。生境之间的迁移行为被有效地描述为基于随机微分方程的脉冲切换，这是对生物现象进行建模的新观点。假定发生种群动态，以便在预期的情况下使繁殖成功最大化。找到最佳迁移策略最终将减少为求解准变量类型的最优方程。我们展示了我们的最优方程与基本繁殖数之间的有效联系。在日本将Plecoglossus altivelis altivelis作为目标物种。