Linear character-dependent models with constant time delay in population dynamics

C. Castillo-Chavez

doi:10.1016/0270-0255(87)90502-1

Linear character-dependent models with constant time delay in population dynamics

C. Castillo-Chavez

Mathematical Computational Modeling Sciences Center, Simon A. Levin (MCMSC)

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

1 Scopus citations

Abstract

We reduce the extended MacKendrick-Von Foerster formalism of Gurney and Nisbet-an initial boundary value problem-to the solution of a single Volterra integral equation with a constant time lag. We then establish the existence, uniqueness and continuation of solutions for all t > 0, and reduce a simplified version of this model to a time-delay version of the classical MacKendrick model, for which the standard stability results for persistent distributions are available.

Original language	English (US)
Pages (from-to)	821-836
Number of pages	16
Journal	Mathematical Modelling
Volume	9
Issue number	11
DOIs	https://doi.org/10.1016/0270-0255(87)90502-1
State	Published - 1987

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Engineering(all)

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10.1016/0270-0255(87)90502-1

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title = "Linear character-dependent models with constant time delay in population dynamics",

abstract = "We reduce the extended MacKendrick-Von Foerster formalism of Gurney and Nisbet-an initial boundary value problem-to the solution of a single Volterra integral equation with a constant time lag. We then establish the existence, uniqueness and continuation of solutions for all t > 0, and reduce a simplified version of this model to a time-delay version of the classical MacKendrick model, for which the standard stability results for persistent distributions are available.",

author = "C. Castillo-Chavez",

note = "Funding Information: Acknowledgements-The main ideas of this paper are part of my Ph.D. Dissertation at the University of Wisconsin-Madison under the supervision of Fred G. Brauer. I take this opportunity to thank him for his continued support and encouragement. I am also pleased to acknowledge the partial support of Simon A. Levin and his National Science Foundation Grant No. DMS-8406472 in completing this research.",

year = "1987",

doi = "10.1016/0270-0255(87)90502-1",

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T1 - Linear character-dependent models with constant time delay in population dynamics

AU - Castillo-Chavez, C.

N1 - Funding Information: Acknowledgements-The main ideas of this paper are part of my Ph.D. Dissertation at the University of Wisconsin-Madison under the supervision of Fred G. Brauer. I take this opportunity to thank him for his continued support and encouragement. I am also pleased to acknowledge the partial support of Simon A. Levin and his National Science Foundation Grant No. DMS-8406472 in completing this research.

PY - 1987

Y1 - 1987

N2 - We reduce the extended MacKendrick-Von Foerster formalism of Gurney and Nisbet-an initial boundary value problem-to the solution of a single Volterra integral equation with a constant time lag. We then establish the existence, uniqueness and continuation of solutions for all t > 0, and reduce a simplified version of this model to a time-delay version of the classical MacKendrick model, for which the standard stability results for persistent distributions are available.

AB - We reduce the extended MacKendrick-Von Foerster formalism of Gurney and Nisbet-an initial boundary value problem-to the solution of a single Volterra integral equation with a constant time lag. We then establish the existence, uniqueness and continuation of solutions for all t > 0, and reduce a simplified version of this model to a time-delay version of the classical MacKendrick model, for which the standard stability results for persistent distributions are available.

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SP - 821

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JO - Mathematical Modelling

JF - Mathematical Modelling

IS - 11

ER -

Linear character-dependent models with constant time delay in population dynamics

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