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. 2019 Feb 4:2019:8189270.
doi: 10.1155/2019/8189270. eCollection 2019.

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

Liuyong Pang  1 , Sanhong Liu  2 , Xinan Zhang  3 , Tianhai Tian  4
Affiliations

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

Liuyong Pang et al. Comput Math Methods Med. .

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 ℛ 0 and discuss the global asymptotic stabilities of the equilibria. Then, from the estimated parameter values, we know that the basic reproduction number ℛ 0 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.

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Figures

Figure 1
Figure 1
Flow chart of system (1).
Figure 2
Figure 2
Time series plots with different initial values of S(t) when ℛ0=1.4840 > 1.
Figure 3
Figure 3
(a) Optimal control variable u1∗(t) for strategy a; (b) optimal control variable u2∗(t) for strategy a; (c) optimal state variable S∗(t) for strategy a; (d) optimal state variable C∗(t) for strategy a.
Figure 4
Figure 4
(a) Efficacy function EaS(t) for strategy a; (b) efficacy function EaC(t) for strategy a.
Figure 5
Figure 5
(a) Optimal control u1∗(t) for strategy b; (b) optimal control u2∗(t) for strategy c; (c) optimal state variables S∗(t) for strategies b and c, respectively; (d) optimal state variables C∗(t) for strategies b and c, respectively.
Figure 6
Figure 6
(a) Efficacy functions of EkS(t) (k = b and c) for strategies b and c; (b) efficacy functions of EkC(t) (k = b and c) for strategies b and c.
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References

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