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http://dx.doi.org/10.4134/BKMS.b160240

A NONSTANDARD FINITE DIFFERENCE METHOD APPLIED TO A MATHEMATICAL CHOLERA MODEL  

Liao, Shu (School of Mathematics and Statistics Chongqing Technology and Business University)
Yang, Weiming (School of Mathematics and Statistics Chongqing Technology and Business University)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.6, 2017 , pp. 1893-1912 More about this Journal
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;
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