### AIMS Mathematics

2018, Issue 4: 584-599. doi: 10.3934/Math.2018.4.584
Research article Topical Sections

# Smoking dynamics with health education effect

• 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.

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

### Related Papers:

• 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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• © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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沈阳化工大学材料科学与工程学院 沈阳 110142

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