From enzyme kinetics to epidemiological models with Michaelis-Menten contact rate: design of nonstandard finite difference schemes

DOI10.1016/j.camwa.2011.12.058zbMath1252.65131OpenAlexW2015233093MaRDI QIDQ692237

Ronald E. Mickens, Jean M.-S. Lubuma, Michael Chapwanya

Publication date: 4 December 2012

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.12.058

zbMATH Keywords

SIR modelexact schemenonstandard finite difference methodMichaelis-Menten equationLambert W functionadvection-reaction equations

Mathematics Subject Classification ID

Epidemiology (92D30) Finite difference and finite volume methods for ordinary differential equations (65L12) Computational methods for problems pertaining to biology (92-08)

Related Items (9)

An explicit nonstandard finite difference scheme for the FitzHugh–Nagumo equations ⋮ Numerical solution for fuzzy enzyme kinetic equations by the Runge-Kutta method ⋮ Numerical dynamics of nonstandard finite difference schemes for a logistics model with feedback control ⋮ Traveling waves of nonlocal delayed disease models: critical wave speed and propagation speed ⋮ Traveling waves in epidemic models: non-monotone diffusive systems with non-monotone incidence rates ⋮ A second-order modified nonstandard theta method for one-dimensional autonomous differential equations ⋮ Nonstandard finite difference schemes for Michaelis–Menten type reaction‐diffusion equations ⋮ Nonstandard finite difference methods: recent trends and further developments ⋮ Global dynamics of target-mediated drug disposition models and their solutions by nonstandard finite difference method

Cites Work

• Positive and elementary stable nonstandard numerical methods with applications to predator-prey models
• Enzyme kinetics at high enzyme concentration
• Mathematical epidemiology.
• Singular perturbation methods for ordinary differential equations
• Mathematical biology. Vol. 1: An introduction.
• On the Lambert \(w\) function
• The Mathematics of Infectious Diseases
• Contributions to the mathematics of the nonstandard finite difference method and applications
• An exact discretization of Michaelis–Menten type population equations
• Topological dynamic consistency of non-standard finite difference schemes for dynamical systems
• Construction of a Finite-Difference Scheme that Exactly Conserves Energy for a Mixed Parity Oscillator
• The Quasi-Steady-State Assumption: A Case Study in Perturbation
• Nonstandard finite difference schemes for Michaelis–Menten type reaction‐diffusion equations
• Advances in the Applications of Nonstandard Finite Difference Schemes
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