Smoking dynamics with health education effect

Pengcheng Xiao; Zeyu Zhang; Xianbo Sun; Pengcheng Xiao; Zeyu Zhang; Xianbo Sun

doi:10.3934/Math.2018.4.584

AIMS Mathematics

2018, Volume 3, Issue 4: 584-599. doi: 10.3934/Math.2018.4.584

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Research article Topical Sections

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

Received: 12 July 2018 Accepted: 21 November 2018 Published: 30 November 2018

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 $R_0 \lt 1$; and the smoking-present equilibrium is globally asymptotically stable if $R_0 \gt 1$. 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.
- smoking dynamics,
- mathematical modeling,
- health education,
- equilibrium,
- stability,
- Lyapunov function
Citation: Pengcheng Xiao, Zeyu Zhang, Xianbo Sun. Smoking dynamics with health education effect[J]. AIMS Mathematics, 2018, 3(4): 584-599. doi: 10.3934/Math.2018.4.584

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Abstract

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 $R_0 \lt 1$; and the smoking-present equilibrium is globally asymptotically stable if $R_0 \gt 1$. 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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