Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations

Jacek Banasiak; Amartya Goswami; Sergey Shindin

doi:10.1007/s00009-013-0319-4

Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations

Jacek Banasiak
, Amartya Goswami
, Sergey Shindin

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The paper is concerned with asymptotic analysis of a singularly perturbed system of McKendrick equations of population with age and geographical structure. It is assumed that the migration between geographical patches occurs on a much faster time scale than the demographic processes and is described by a reducible Kolmogorov matrix. We apply a novel regularizing technique which makes the error estimates easier than that in previous papers and provide a numerical illustration of theoretical results.

Original language	English
Pages (from-to)	533-559
Number of pages	27
Journal	Mediterranean Journal of Mathematics
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s00009-013-0319-4
Publication status	Published - May 2014
Externally published	Yes

Keywords

aggregation
asymptotic analysis
Chapman-Enskog asymptotic expansion
initial layer
multiple time scales
Reducible matrices
semigroups
singular perturbation
Structured population models

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00009-013-0319-4

Cite this

@article{ab73c9d6747d45689b44a4113182a0b2,

title = "Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations",

abstract = "The paper is concerned with asymptotic analysis of a singularly perturbed system of McKendrick equations of population with age and geographical structure. It is assumed that the migration between geographical patches occurs on a much faster time scale than the demographic processes and is described by a reducible Kolmogorov matrix. We apply a novel regularizing technique which makes the error estimates easier than that in previous papers and provide a numerical illustration of theoretical results.",

keywords = "aggregation, asymptotic analysis, Chapman-Enskog asymptotic expansion, initial layer, multiple time scales, Reducible matrices, semigroups, singular perturbation, Structured population models",

author = "Jacek Banasiak and Amartya Goswami and Sergey Shindin",

year = "2014",

month = may,

doi = "10.1007/s00009-013-0319-4",

language = "English",

volume = "11",

pages = "533--559",

journal = "Mediterranean Journal of Mathematics",

issn = "1660-5446",

publisher = "Birkhauser Verlag Basel",

number = "2",

}

TY - JOUR

T1 - Singularly Perturbed Population Models with Reducible Migration Matrix

T2 - 2. Asymptotic Analysis and Numerical Simulations

AU - Banasiak, Jacek

AU - Goswami, Amartya

AU - Shindin, Sergey

PY - 2014/5

Y1 - 2014/5

N2 - The paper is concerned with asymptotic analysis of a singularly perturbed system of McKendrick equations of population with age and geographical structure. It is assumed that the migration between geographical patches occurs on a much faster time scale than the demographic processes and is described by a reducible Kolmogorov matrix. We apply a novel regularizing technique which makes the error estimates easier than that in previous papers and provide a numerical illustration of theoretical results.

AB - The paper is concerned with asymptotic analysis of a singularly perturbed system of McKendrick equations of population with age and geographical structure. It is assumed that the migration between geographical patches occurs on a much faster time scale than the demographic processes and is described by a reducible Kolmogorov matrix. We apply a novel regularizing technique which makes the error estimates easier than that in previous papers and provide a numerical illustration of theoretical results.

KW - aggregation

KW - asymptotic analysis

KW - Chapman-Enskog asymptotic expansion

KW - initial layer

KW - multiple time scales

KW - Reducible matrices

KW - semigroups

KW - singular perturbation

KW - Structured population models

UR - https://www.scopus.com/pages/publications/84899936704

U2 - 10.1007/s00009-013-0319-4

DO - 10.1007/s00009-013-0319-4

M3 - Article

AN - SCOPUS:84899936704

SN - 1660-5446

VL - 11

SP - 533

EP - 559

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 2

ER -

Singularly Perturbed Population Models with Reducible Migration Matrix: 2. Asymptotic Analysis and Numerical Simulations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this