dc.contributor.author |
Chapwanya, Michael
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dc.contributor.author |
Lubuma, Jean M.-S.
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|
dc.contributor.author |
Mickens, Ronald E.
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|
dc.date.accessioned |
2012-09-11T07:11:42Z |
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dc.date.available |
2012-09-11T07:11:42Z |
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dc.date.issued |
2012-08 |
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dc.description.abstract |
We consider the basic SIR epidemiological model with the Michaelis-Menten formulation of the contact rate. From the study of the Michaelis-Menten basic enzymatic reaction, we design two types of Nonstandard Finite Difference (NSFD) schemes for the SIR model: Exact-related schemes based on the Lambert W function and schemes obtained by using Mickens’s rules of more complex denominator functions for discrete derivatives and nonlocal approximations of nonlinear terms. We compare and investigate the performance of the two types of schemes by showing that they are dynamically consistent with the continuous model. Numerical simulations that support the theory and demonstrate computationally the power of NSFD schemes are presented. |
en_US |
dc.description.sponsorship |
The South African National Research Foundation |
en_US |
dc.description.uri |
http://www.elsevier.com/locate/camwa |
en_US |
dc.identifier.citation |
Michael Chapwanya, Jean M.-S. Lubuma, Ronald E. Mickens, From enzyme kinetics to epidermiological models with Michealis-Menten contact rate : Design of nonstandard finite difference schemes, Computers and Mathermatics with Applications, vol. 64, no. 3, pp. 201-213 (2012), doi: 10.1016/j.camwa.2011.12.058. |
en_US |
dc.identifier.issn |
0898-1221 (print) |
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dc.identifier.issn |
1873-7668 (online) |
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dc.identifier.other |
10.1016/j.camwa.2011.12.058 |
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dc.identifier.uri |
http://hdl.handle.net/2263/19733 |
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dc.language.iso |
en |
en_US |
dc.publisher |
Elsevier |
en_US |
dc.rights |
© 2011 Elsevier. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Computers and Mathematics with Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers and Mathematics with Applications, vol 64, issue 3, August 2012, doi: 10.1016/j.camwa.2011.12.058. |
en_US |
dc.subject |
Nonstandard finite difference method |
en_US |
dc.subject |
Exact scheme |
en_US |
dc.subject |
Lambert W function |
en_US |
dc.subject |
Michaelis-Menten equation |
en_US |
dc.subject |
SIR model |
en_US |
dc.subject |
Advection-reaction equations |
en_US |
dc.title |
From enzyme kinetics to epidermiological models with Michealis-Menten contact rate : design of nonstandard finite difference schemes |
en_US |
dc.type |
Postprint Article |
en_US |