Proof of conjecture in: The basic reproduction number obtained from Jacobian and next generation matrices—A case study of dengue transmission modelling

Hyun Mo Yang; David Greenhalgh

doi:10.1016/j.amc.2015.04.112

Proof of conjecture in: The basic reproduction number obtained from Jacobian and next generation matrices—A case study of dengue transmission modelling

Hyun Mo Yang
, David Greenhalgh

Mathematics And Statistics

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Abstract

The spectral radius of the next generation matrix provides an expression for the basic reproduction number. Instead of calculating the dominant eigenvalue of the characteristic equation corresponding to the next generation matrix, a threshold parameter can be obtained by handling the coefficients of this equation. Here we prove two conjectures presented in [9].

Original language	English
Pages (from-to)	103-107
Number of pages	5
Journal	Applied Mathematics and Computation
Volume	265
Early online date	22 May 2015
DOIs	https://doi.org/10.1016/j.amc.2015.04.112
Publication status	Published - 15 Aug 2015

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

compartmental modelling
Routh–Hurwitz criteria
spectral radius
threshold
single infection
coinfection

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10.1016/j.amc.2015.04.112

Yang-Greenhalgh-AMC-2015-Proof-of-conjecture-in-the-basic-reproduction-number-obtained-from-JacobianAccepted author manuscript, 88.1 KBLicence: CC BY-NC-ND 4.0

Cite this

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title = "Proof of conjecture in: The basic reproduction number obtained from Jacobian and next generation matrices—A case study of dengue transmission modelling",

abstract = "The spectral radius of the next generation matrix provides an expression for the basic reproduction number. Instead of calculating the dominant eigenvalue of the characteristic equation corresponding to the next generation matrix, a threshold parameter can be obtained by handling the coefficients of this equation. Here we prove two conjectures presented in [9].",

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AU - Greenhalgh, David

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Y1 - 2015/8/15

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AB - The spectral radius of the next generation matrix provides an expression for the basic reproduction number. Instead of calculating the dominant eigenvalue of the characteristic equation corresponding to the next generation matrix, a threshold parameter can be obtained by handling the coefficients of this equation. Here we prove two conjectures presented in [9].

KW - compartmental modelling

KW - Routh–Hurwitz criteria

KW - spectral radius

KW - threshold

KW - single infection

KW - coinfection

UR - http://www.sciencedirect.com/science/article/pii/S0096300315005743

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DO - 10.1016/j.amc.2015.04.112

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JO - Applied Mathematics and Computation

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ER -

Proof of conjecture in: The basic reproduction number obtained from Jacobian and next generation matrices—A case study of dengue transmission modelling

Abstract

UN SDGs

Keywords

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