Persistence and extinction of diffusing populations with two sexes and short reproductive season

Wen Jin; Horst Thieme

doi:10.3934/dcdsb.2014.19.3209

Persistence and extinction of diffusing populations with two sexes and short reproductive season

Wen Jin, Horst Thieme

Mathematical and Statistical Sciences, School of (SoMSS)

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

11 Scopus citations

Abstract

A model is considered for a spatially distributed population of male and female individuals that mate and reproduce only once in their life during a very short reproductive season. Between birth and mating, females and males move by diffusion on a bounded domain Ω. Mating and reproduction is described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number R₀ that acts as a threshold between extinction and persistence. If R₀ < 1, the population dies out while it persists (uniformly weakly) if R₀ > 1. R0 is the cone spectral radius of a bounded homogeneous map.

Original language	English (US)
Pages (from-to)	3209-3218
Number of pages	10
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	19
Issue number	10
DOIs	https://doi.org/10.3934/dcdsb.2014.19.3209
State	Published - Dec 1 2014

Keywords

Basic reproduction number
Cone spectral radius
Difference equation
Discrete dynamical system
Discrete semi-flow
Eigenvector
Homogeneous map
Impulsive reaction diffusion system
Ordered Banach space
Stability.
Two-sex population

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcdsb.2014.19.3209

Cite this

@article{3ef585944037406db748b0eb20633889,

title = "Persistence and extinction of diffusing populations with two sexes and short reproductive season",

abstract = "A model is considered for a spatially distributed population of male and female individuals that mate and reproduce only once in their life during a very short reproductive season. Between birth and mating, females and males move by diffusion on a bounded domain Ω. Mating and reproduction is described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number R0 that acts as a threshold between extinction and persistence. If R0 < 1, the population dies out while it persists (uniformly weakly) if R0 > 1. R0 is the cone spectral radius of a bounded homogeneous map.",

keywords = "Basic reproduction number, Cone spectral radius, Difference equation, Discrete dynamical system, Discrete semi-flow, Eigenvector, Homogeneous map, Impulsive reaction diffusion system, Ordered Banach space, Stability., Two-sex population",

author = "Wen Jin and Horst Thieme",

year = "2014",

month = dec,

day = "1",

doi = "10.3934/dcdsb.2014.19.3209",

language = "English (US)",

volume = "19",

pages = "3209--3218",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "Southwest Missouri State University",

number = "10",

}

TY - JOUR

T1 - Persistence and extinction of diffusing populations with two sexes and short reproductive season

AU - Jin, Wen

AU - Thieme, Horst

PY - 2014/12/1

Y1 - 2014/12/1

N2 - A model is considered for a spatially distributed population of male and female individuals that mate and reproduce only once in their life during a very short reproductive season. Between birth and mating, females and males move by diffusion on a bounded domain Ω. Mating and reproduction is described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number R0 that acts as a threshold between extinction and persistence. If R0 < 1, the population dies out while it persists (uniformly weakly) if R0 > 1. R0 is the cone spectral radius of a bounded homogeneous map.

AB - A model is considered for a spatially distributed population of male and female individuals that mate and reproduce only once in their life during a very short reproductive season. Between birth and mating, females and males move by diffusion on a bounded domain Ω. Mating and reproduction is described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number R0 that acts as a threshold between extinction and persistence. If R0 < 1, the population dies out while it persists (uniformly weakly) if R0 > 1. R0 is the cone spectral radius of a bounded homogeneous map.

KW - Basic reproduction number

KW - Cone spectral radius

KW - Difference equation

KW - Discrete dynamical system

KW - Discrete semi-flow

KW - Eigenvector

KW - Homogeneous map

KW - Impulsive reaction diffusion system

KW - Ordered Banach space

KW - Stability.

KW - Two-sex population

UR - http://www.scopus.com/inward/record.url?scp=84907552974&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907552974&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2014.19.3209

DO - 10.3934/dcdsb.2014.19.3209

M3 - Article

AN - SCOPUS:84907552974

SN - 1531-3492

VL - 19

SP - 3209

EP - 3218

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 10

ER -

Persistence and extinction of diffusing populations with two sexes and short reproductive season

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this