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AIMS Mathematics, 2018, 3(4): 584-599. doi: 10.3934/Math.2018.4.584. Research article Topical Section

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Smoking dynamics with health education effect

¹ Department of Mathematics, University of Evansville, Evansville, IN 47722, USA
² Department of Computer Science and Engineering, The University of Texas at Arlington, Arlington, TX 76019, USA
³ Department of Applied Mathematics, Western University, London, Ontario, N6A 5B7, Canada
⁴ Department of Information and Statistics, Guangxi University of Finance and Economics, Nanning,Guangxi, 750003, China

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Topical Section: Mathematical modeling

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This paper provides a mathematical study for analyzing the dynamics of smoking with health education campaigns involved. The method of next generation matrix is used to derive the basic reproduction number $R_0$. We prove that the smoking-free equilibrium is both locally and globally asymptotically stable if $R_0 < 1$; and the smoking-present equilibrium is globally asymptotically stable if $R_0 > 1$. By comparing with smoking dynamics without health education involved, we conclude that health education can decrease smoking population. Numerical simulations are used to support our conclusions.

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Keywords: smoking dynamics; mathematical modeling; health education; equilibrium; stability; Lyapunov function

Citation: Pengcheng Xiao, Zeyu Zhang, Xianbo Sun. Smoking dynamics with health education effect. AIMS Mathematics, 2018, 3(4): 584-599. doi: 10.3934/Math.2018.4.584

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