Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2017; 54(6): 1893-1912

Online first article November 6, 2017      Printed November 30, 2017

https://doi.org/10.4134/BKMS.b160240

Copyright © The Korean Mathematical Society.

A nonstandard finite difference method applied to a mathematical cholera model

Shu Liao, Weiming Yang

Chongqing Technology and Business University, Chongqing Technology and Business University

Abstract

In this paper, we aim to construct a nonstandard finite difference (NSFD) scheme to solve numerically a mathematical model for cholera epidemic dynamics. We first show that if the basic reproduction number is less than unity, the disease-free equilibrium (DFE) is locally asymptotically stable. Moreover, we mainly establish the global stability analysis of the DFE and endemic equilibrium by using suitable Lyapunov functionals regardless of the time step size. Finally, numerical simulations with different time step sizes and initial conditions are carried out and comparisons are made with other well-known methods to illustrate the main theoretical results.

Keywords: cholera, nonstandard finite difference scheme, dynamical systems, global stability

MSC numbers: Primary 34D20, 92D30