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Title: Dynamics of a Two Subpopulations System Including Immigration
Authors: Zincenko, A.
Petrovskii, Sergei
First Published: 21-Apr-2017
Publisher: EDP Sciences
Citation: Mathematical Modelling of Natural Phenomena, 2017, 12 (2), pp. 46-57
Abstract: The phenomenon of replacement migration into declining population prompts development of multicomponent models in population dynamics. We propose a simple model of population including resident and migrant components with migration flow as an external input. The main assumption is that offspring that are born to migrants will have the same vital rates as the resident population. The proposed model is based on partial differential equation to take into account the age structure of the population. The formulae for exact solutions are derived. We focus on the case when native population declines in the absence of migration. Assuming a sufficiently large constant growth rate of migration we obtain asymptotic solutions as t → â. Using the asymptotic solutions, we have calculated "critical" value of growth rate of migrant inflow that is the value that provides, as time tends to infinity, the equal number of residents and migrants in the population. We provide numerical illustrations using demographic data for Germany in 2010.
DOI Link: 10.1051/mmnp/201712204
ISSN: 0973-5348
eISSN: 1760-6101
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2017, EDP Sciences. Deposited with reference to the publisher’s open access archiving policy.
Appears in Collections:Published Articles, Dept. of Mathematics

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