A nonstandard finite difference method applied to a mathematical cholera model
Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 1893-1912
Published online November 6, 2017
Printed November 30, 2017
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
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