Computational and Mathematical Methods in Medicine

Volume 2019, Article ID 8189270, 15 pages

https://doi.org/10.1155/2019/8189270

## The Cost-Effectiveness Analysis and Optimal Strategy of the Tobacco Control

^{1}School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China^{2}School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China^{3}School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China^{4}School of Mathematical Sciences, Monash University, Melbourne, VIC 3800, Australia

Correspondence should be addressed to Liuyong Pang; moc.361@gnoyuilgnap and Sanhong Liu; moc.361@hslyrrej

Received 15 July 2018; Revised 20 November 2018; Accepted 9 January 2019; Published 4 February 2019

Academic Editor: Zoran Bursac

Copyright © 2019 Liuyong Pang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper aims at investigating how the media coverage and smoking cessation treatment should be implemented, for a certain period, to reduce the numbers of smokers and patients caused by smoking while minimizing the total cost. To this end, we first propose a new mathematical model without any control strategies to investigate the dynamic behaviors of smoking. Furthermore, we calculate the basic reproduction number and discuss the global asymptotic stabilities of the equilibria. Then, from the estimated parameter values, we know that the basic reproduction number is more than 1, which reveals that smoking is one of the enduring problems of the society. Hence, we introduce two control measures (media coverage and smoking cessation treatment) into the model. Finally, in order to investigate their effects in smoking control and provide an analytical method for the strategic decision-makers, we apply a concrete example to calculate the incremental cost-effectiveness ratios and analyze the cost-effectiveness of all possible combinations of the two control measures. The results indicate that the combination of media coverage and smoking cessation treatment is the most cost-effective strategy for tobacco control.

#### 1. Introduction

Tobacco use is the single greatest preventable cause of death in the world today. Currently, about 6 million people die from tobacco-related illnesses each year [1]. By 2030, this figure is expected to reach 10 million deaths [2]. If current patterns of smoking continue, about 500 million of the world’s population alive today will eventually be killed by smoking, half of them in productive middle age, losing 20 to 25 years of life [3]. Statistical data indicate that it will be very difficult to reduce tobacco-related deaths over the next 30–50 years, unless adult smokers are encouraged to quit [4]. Hence, smoking control and reducing smoking-related death are priority concerns that government organizations must face in the respective countries. Since tobacco contains nicotine which is addictive, it is very difficult to quit smoking [5]. Many different measures have been used to control smoking, including regulation of the packaging and labelling of tobacco products, higher taxes and prices of cigarettes, setting special smoking areas, mass media campaigns, and psychosocial and pharmacological treatment, all of which aim to enhance public consciousness and help tobacco users to give up smoking and avoid subsequent relapse [6].

Many studies have been conducted to analyze the smoking phenomenon and investigate the effects of different control measures (Ham [7], Yen et al. [8], Ertürk et al. [9], Castillo et al. [10], Sharomi and Gumel [11], and Guerrero et al. [12]). Rowe et al., in 1992 [13], applied a dynamical model to investigate smoking behavior. Zeb et al., in 2013 [14], proposed a model with square-root incidence rate to describe smoking phenomenon. Lahrouz, et al., in 2011 [15], used deterministic and stochastic models to study the dynamic properties of smokers. Guerrero et al., in 2011 [16], used a mathematical model to successfully describe the characteristics of smoking habit in Spain. In 2002, the Canadian Cancer Society released a study which indicated that setting health warning on cigarette packages is very effective in discouraging smoking [17]. In 2015 [18], we proposed a mathematical model with saturated incidence rate to explore the effects of controlling smoking by setting special smoking areas and raising the price of cigarettes. Results indicate that setting special smoking areas and putting up the price of cigarettes are very effective in reducing the number of smokers.

As a continuation of our previous work, we will further investigate the effects of media coverage and smoking cessation treatment in controlling smoking. We will use a concrete example to provide an analytical method for strategic decision-makers, so that we can find out which strategy is the most cost-effective for all possible combinations of the two tobacco control measures. The organization of this paper is as follows. In Section 2, we will present a new mathematical model to describe the dynamic behavior of smokers. In Section 3, we will derive the concrete form of the basic reproduction number and perform stability analysis of the model. In Section 4, we will introduce media coverage and smoking cessation treatment into the model to investigate the effects of two control measures as well as the combination of them. In Section 5, the cost-effectiveness analysis is carried out to gain insight to which strategy is most cost-effective in controlling smoking. Finally, the conclusions are summarized in Section 6.

#### 2. Construction of the Mathematical Model

In order to facilitate discussion, we introduce new occasional smoker class and patient class caused by smoking into our previous model [18]. Hence, we divide the total population into six subpopulations: potential smokers, occasional smokers, smokers, temporary quitters, permanent quitters, and patients caused by smoking, with sizes denoted by , , , , , and , respectively.

The transitions among these subpopulations are shown graphically in Figure 1, which shows that the number of potential smokers is increased at a constant recruitment rate . In addition, potential smokers can become occasional smokers via effective “contact” with smokers. The incidence rate is bilinear (*β* is effective contact rate). The probability that an occasional smoker converts a smoker is assumed as *ω*. The rate of quitting smoking for smokers is *γ*. Smokers with the proportion () are shifted into temporary quitters; nevertheless, smokers with the proportion become permanent quitters. The relapse rate of temporary quitters is *α*. The conversion ratios from occasional smokers, smokers, temporary quitters, and permanent quitters to patients caused by smoking are *τ*, , (), and *η*, respectively. The natural death rates of all the subpopulations are *μ*, and the mortality rate due to the disease caused by smoking is *d*. Hence, we can establish the following model: