@article{54e0c0c0d51949baa0db33acc494d1fc,
title = "Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates",
abstract = "In this paper, by applying a variation of the backward Euler method, we propose a discrete-time SIR epidemic model whose discretization scheme preserves the global asymptotic stability of equilibria for a class of corresponding continuous-time SIR epidemic models. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria is fully determined by the basic reproduction number, when the infection incidence rate has a suitable monotone property.",
keywords = "SIR epidemic model, backward Euler method, basic reproduction number, difference equation, global asymptotic stability",
author = "Yoichi Enatsu and Yukihiko Nakata and Yoshiaki Muroya and Giuseppe Izzo and Antonia Vecchio",
note = "Funding Information: The authors wish to express their gratitude to the editor and anonymous referees for helpful comments and suggestion, which improved the quality of this paper. The work of this paper was partially prepared during the first three authors{\textquoteright} two months stay at Technische Universit{\"a}t Darmstadt from the beginning of January to the end of February 2010 as members of International Research Training Group 1529 and the third author{\textquoteright}s two weeks stay at Universit{\`a} degli Studi di Napoli {\textquoteleft}Federico II{\textquoteright} on March 2010. The second author is partially supported by Spanish Ministry of Science and Innovation (MICINN), MTM2010–18318. Research is partially supported by Scientific Research (c), No. 21540230 of Japan Society for the Promotion of Science.",
year = "2012",
month = jul,
doi = "10.1080/10236198.2011.555405",
language = "English",
volume = "18",
pages = "1163--1181",
journal = "Journal of Difference Equations and Applications",
issn = "1023-6198",
publisher = "Taylor and Francis Ltd.",
number = "7",
}