A Positivity-preserving Mickens-type Discretization of an Epidemic Model

S. M. Moghadas; M. E. Alexander; B. D. Corbett; A. B. Gumel

doi:10.1080/1023619031000146913

A Positivity-preserving Mickens-type Discretization of an Epidemic Model

S. M. Moghadas, M. E. Alexander, B. D. Corbett, A. B. Gumel

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

47 Scopus citations

Abstract

A deterministic model for the transmission dynamics of two strains of an epidemic in the presence of a preventive vaccine is considered. Theoretical results on the existence and stability of the associated equilibria of the model are given. A robust, positivity-preserving, non-standard finite-difference scheme, having the same qualitative features as the continuous model, is constructed. The theoretical and numerical analyses of the model enable the determination of a threshold level of vaccination coverage needed for community-wide eradication of the epidemic.

Original language	English (US)
Pages (from-to)	1037-1051
Number of pages	15
Journal	Journal of Difference Equations and Applications
Volume	9
Issue number	11
DOIs	https://doi.org/10.1080/1023619031000146913
State	Published - Nov 1 2003
Externally published	Yes

Keywords

Basic reproductive number
Epidemic model
Mickens-type discretization
Preventive vaccine

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1080/1023619031000146913

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title = "A Positivity-preserving Mickens-type Discretization of an Epidemic Model",

abstract = "A deterministic model for the transmission dynamics of two strains of an epidemic in the presence of a preventive vaccine is considered. Theoretical results on the existence and stability of the associated equilibria of the model are given. A robust, positivity-preserving, non-standard finite-difference scheme, having the same qualitative features as the continuous model, is constructed. The theoretical and numerical analyses of the model enable the determination of a threshold level of vaccination coverage needed for community-wide eradication of the epidemic.",

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note = "Funding Information: This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors are grateful to the referees for their comments which have improved the paper.",

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AU - Alexander, M. E.

AU - Corbett, B. D.

AU - Gumel, A. B.

N1 - Funding Information: This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors are grateful to the referees for their comments which have improved the paper.

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N2 - A deterministic model for the transmission dynamics of two strains of an epidemic in the presence of a preventive vaccine is considered. Theoretical results on the existence and stability of the associated equilibria of the model are given. A robust, positivity-preserving, non-standard finite-difference scheme, having the same qualitative features as the continuous model, is constructed. The theoretical and numerical analyses of the model enable the determination of a threshold level of vaccination coverage needed for community-wide eradication of the epidemic.

AB - A deterministic model for the transmission dynamics of two strains of an epidemic in the presence of a preventive vaccine is considered. Theoretical results on the existence and stability of the associated equilibria of the model are given. A robust, positivity-preserving, non-standard finite-difference scheme, having the same qualitative features as the continuous model, is constructed. The theoretical and numerical analyses of the model enable the determination of a threshold level of vaccination coverage needed for community-wide eradication of the epidemic.

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KW - Mickens-type discretization

KW - Preventive vaccine

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A Positivity-preserving Mickens-type Discretization of an Epidemic Model

Abstract

Keywords

ASJC Scopus subject areas

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