Threshold dynamics and optimal control of an age-structured giving up smoking model

被引：34

作者：

Rahman, Ghaus Ur ^{[1
,4
]}

Agarwal, Ravi P. ^{[2
]}

Liu, Lili ^{[3
]}

Khan, Asaf ^{[1
]}

机构：

[1] Univ Swat, Dept Math & Stat, Swat, Kpk, Pakistan

[2] Texas A&M Univ Kingsville, Dept Math, Kingsville, TX USA

[3] Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Shanxi, Peoples R China

[4] Pak Austria Fachhsch, Inst Appl Sci & Technol, Haripur Kpk, Pakistan

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2018年 / 43卷

关键词：

Giving up smoking model; Age factor; Smoking generation number; Global stability; Optimal control; Gateaux derivative; GLOBAL STABILITY; CESSATION; SYSTEMS; HIV;

D O I：

10.1016/j.nonrwa.2018.02.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new giving up smoking model is proposed by incorporating the continuous age-structure in the chain smokers class, which is known as a class of age-structured giving up smoking model. Smoking generation number is defined and proved to be a classic threshold parameter. Two steady states of the model are found. The corresponding characteristic equations are analyzed, and the proper Lyapunov functionals are constructed to show the local and global stability of both steady states. Optimal control strategy is presented and numerical simulations are made to support the main results. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：96 / 120

页数：25

共 34 条

[1]

Alkhudhari Z., 2014, ISRN APPL MATH, V2014

[2]

[Anonymous], 2003, SOBOLEV SPACES

[3]

[Anonymous], 2007, BEST PRACT COMPR TOB

[4]

[Anonymous], 2010, WHO

[5] Global analysis of HIV-1 dynamics with Hill type infection rate and intracellular delay [J].

Bairagi, N. ;

Adak, D. .

APPLIED MATHEMATICAL MODELLING, 2014, 38 (21-22) :5047-5066

[6] GLOBAL ANALYSIS OF AGE-STRUCTURED WITHIN-HOST VIRUS MODEL [J].

Browne, Cameron J. ;

Pilyugin, Sergei S. .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (08) :1999-2017

[7]

Castanedo Cristina., 2000, Temas de enfermeria gerontologica, P1

[8] Discrete Approximations and Optimization of Evolution Inclusions [J].

Din, Qamar ;

Donchev, Tzanko .

SET-VALUED AND VARIATIONAL ANALYSIS, 2012, 20 (01) :15-30

[9] Mass media campaigns to promote smoking cessation among adults: an integrative review [J].

Durkin, Sarah ;

Brennan, Emily ;

Wakefield, Melanie .

TOBACCO CONTROL, 2012, 21 (02) :127-138

[10] Solving a model for the evolution of smoking habit in Spain with homotopy analysis method [J].

Guerrero, F. ;

Santonja, F. J. ;

Villanueva, R. J. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2013, 14 (01) :549-558

← 1 2 3 4 →