On the Three Properties of Stationary Populations and Knotting with Non-stationary Populations

Arni S.R.Srinivasa Rao; James R. Carey

doi:10.1007/s11538-019-00652-7

On the Three Properties of Stationary Populations and Knotting with Non-stationary Populations

Arni S.R.Srinivasa Rao, James R. Carey

Epidemiology

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

4 Scopus citations

Abstract

A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is nonzero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These properties provide deeper insights into cohort formation in real-world populations and the length of the duration for which stationary and non-stationary conditions hold. The new concepts are based on the time gap between the occurrence of stationary and non-stationary populations within the SPI framework that we refer to as Oscillatory SPI and the Amplitude of SPI.

Original language	English (US)
Pages (from-to)	4233-4250
Number of pages	18
Journal	Bulletin of Mathematical Biology
Volume	81
Issue number	10
DOIs	https://doi.org/10.1007/s11538-019-00652-7
State	Published - Oct 1 2019

Keywords

Functional knots
Oscillatory properties
PDEs
Stationary population identity

ASJC Scopus subject areas

Neuroscience(all)
Immunology
Mathematics(all)
Biochemistry, Genetics and Molecular Biology(all)
Environmental Science(all)
Pharmacology
Agricultural and Biological Sciences(all)
Computational Theory and Mathematics

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10.1007/s11538-019-00652-7

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title = "On the Three Properties of Stationary Populations and Knotting with Non-stationary Populations",

abstract = "A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is nonzero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These properties provide deeper insights into cohort formation in real-world populations and the length of the duration for which stationary and non-stationary conditions hold. The new concepts are based on the time gap between the occurrence of stationary and non-stationary populations within the SPI framework that we refer to as Oscillatory SPI and the Amplitude of SPI.",

keywords = "Functional knots, Oscillatory properties, PDEs, Stationary population identity",

author = "Rao, {Arni S.R.Srinivasa} and Carey, {James R.}",

note = "Funding Information: We thank three referees for their critical review of the concepts introduced and for their several useful structural comments which helped us to thoroughly revise our original submission. Research supported in part through the UC Berkeley CEDA Grant P30AG0128 to JRC. Publisher Copyright: {\textcopyright} 2019, Society for Mathematical Biology.",

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AU - Rao, Arni S.R.Srinivasa

AU - Carey, James R.

N1 - Funding Information: We thank three referees for their critical review of the concepts introduced and for their several useful structural comments which helped us to thoroughly revise our original submission. Research supported in part through the UC Berkeley CEDA Grant P30AG0128 to JRC. Publisher Copyright: © 2019, Society for Mathematical Biology.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is nonzero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These properties provide deeper insights into cohort formation in real-world populations and the length of the duration for which stationary and non-stationary conditions hold. The new concepts are based on the time gap between the occurrence of stationary and non-stationary populations within the SPI framework that we refer to as Oscillatory SPI and the Amplitude of SPI.

AB - A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is nonzero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These properties provide deeper insights into cohort formation in real-world populations and the length of the duration for which stationary and non-stationary conditions hold. The new concepts are based on the time gap between the occurrence of stationary and non-stationary populations within the SPI framework that we refer to as Oscillatory SPI and the Amplitude of SPI.

KW - Functional knots

KW - Oscillatory properties

KW - PDEs

KW - Stationary population identity

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On the Three Properties of Stationary Populations and Knotting with Non-stationary Populations

Abstract

Keywords

ASJC Scopus subject areas

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