Journal
APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES
Volume 1487, Issue -, Pages 212-223Publisher
AMER INST PHYSICS
DOI: 10.1063/1.4758961
Keywords
Epidemiological models; asymptotic global stability; nonstandard finite difference scheme; advection reaction / diffusion equation
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Funding
- National Research Foundation of South Africa
- French Ministry of Health and the European Union
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We design, analyze and implement nonstandard finite difference (NSFD) schemes for some differential models in biosciences. The NSFD schemes are reliable in three directions. They are topologically dynamically consistent for one-dimensional models. They can replicate the global asymptotic stability of the disease-free equilibrium of the MSEIR model in epidemiology whenever the basic reproduction number is less than 1. They preserve the positivity and boundedness property of solutions of advection-reaction and reaction-diffusion equations.
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