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Dynamics of a Two Subpopulations System Including Immigration

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posted on 2017-06-22, 14:22 authored by A. Zincenko, Sergei Petrovskii
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.

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Citation

Mathematical Modelling of Natural Phenomena, 2017, 12 (2), pp. 46-57

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • VoR (Version of Record)

Published in

Mathematical Modelling of Natural Phenomena

Publisher

EDP Sciences

issn

0973-5348

eissn

1760-6101

Acceptance date

2017-01-01

Copyright date

2017

Available date

2017-06-22

Publisher version

https://www.mmnp-journal.org/articles/mmnp/abs/2017/02/mmnp2017122p46/mmnp2017122p46.html

Language

en

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