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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
computer science
From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate: Design of nonstandard finite difference schemes
Computers and Mathematics with Applications, Volume 64, No. 3, Year 2012
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Description
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. © 2011 Elsevier Ltd. All rights reserved.
Authors & Co-Authors
Chapwanya, Michael
South Africa, Pretoria
University of Pretoria
Lubuma, Jean M.S.
South Africa, Pretoria
University of Pretoria
Mickens, Ronald Elbert
United States, Atlanta
Clark Atlanta University
Statistics
Citations: 13
Authors: 3
Affiliations: 2
Identifiers
Doi:
10.1016/j.camwa.2011.12.058
ISSN:
08981221