Optimal control of a delayed smoking model with immigration

Sun, Changzheng; Jia, Jianwen

doi:10.1080/17513758.2019.1629031

Cited by 17 publications

(4 citation statements)

References 28 publications

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“…From these findings, it will be done optimizing the control of smokers in the community with an effective strategy. We will investigate model (1) to control smoking from cigarettes [13]. The control variable that used in the present model is 1 , 2 , 3 , 4 are represents the education campaigns, vaccination, reducing the pharmacological effects of nicotine and rehabilitation.…”

Section: Discussionmentioning

confidence: 99%

Optimal Control for Smoking Epidemic Model

Ilmayasinta¹,

Anjarsari²,

Ahdi³

2021

Advances in Social Science, Education and Humanities Research

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In this study, we used a mathematical model of the smoking epidemic which was divided into three sub-classes. In this model we provide four optimal controls, namely education campaign about cigarettes, vaccines, treatment and rehabilitation. To solve the problem of optimal control, we use the principle of maximum pontryagin, where the objective function is set to increase the population of individuals who quit smoking and reduce the number of smokers. In the solution, we use the numerical method namely Runge Kutta forward-backward sweep order4 and simulated using MATLAB with the values of initial parameters and conditions are given based on the results of a survey that conducted on high school students in several schools in Lamongan. The control provided in this study shows a decrease in the number of individual population of potential smokers and active smokers, as well as an increase in the number of individual ex-smokers. These results also indicate that the system gets the optimal solution according to certain values of the control level.

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Section: Discussionmentioning

confidence: 99%

Optimal Control for Smoking Epidemic Model

Ilmayasinta¹,

Anjarsari²,

Ahdi³

2021

Advances in Social Science, Education and Humanities Research

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“…Many mathematical models on smoking have been built based on the assumptions of the researchers. In [7], the used mathematical model was divided into four sub-classes, namely potential smokers, individuals who smoke < 20 cigarettes per day, heavy smokers who smoke > 20 cigarettes per day, and people who have stopped smoking. Control was carried out using two optimal controls, namely anti-smoking campaign and media campaign.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control in a Mathematical Model of Smoking

Ilmayasinta

Purnawan

2021

J. Math. Fund. Sci.

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This paper presents a dynamic model of smoking with optimal control. The mathematical model is divided into 5 sub-classes, namely, non-smokers, occasional smokers, active smokers, individuals who have temporarily stopped smoking, and individuals who have stopped smoking permanently. Four optimal controls, i.e., anti-smoking education campaign, anti-smoking gum, anti-nicotine drug, and government prohibition of smoking in public spaces are considered in the model. The existence of the controls is also presented. The Pontryagin maximum principle (PMP) was used to solve the optimal control problem. The fourth-order Runge-Kutta was employed to gain the numerical solutions.

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“…Health-related risky behaviors related to addictions can be regarded as treatable contagious diseases since they can spread through the social interaction [3,4]. It is worth mentioning that health-related risky behaviors such as smoking [5][6][7][8][9][10][11] and drug abuse [12][13][14][15][16] have been explored by mathematical modeling method. In the same way, some drinking models [17][18][19][20][21][22] based on differential equations have been developed to describe the spreading law of drinking dynamics since the pioneering work of [23].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and optimal control analysis of a delayed drinking model

2020

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Alcoholism is a social phenomenon that affects all social classes and is a chronic disorder that causes the person to drink uncontrollably, which can bring a series of social problems. With this motivation, a delayed drinking model including five subclasses is proposed in this paper. By employing the method of characteristic eigenvalue and taking the temporary immunity delay for alcoholics under treatment as a bifurcation parameter, a threshold value of the time delay for the local stability of drinking-present equilibrium and the existence of Hopf bifurcation are found. Then the length of delay has been estimated to preserve stability using the Nyquist criterion. Moreover, optimal strategies to lower down the number of drinkers are proposed. Numerical simulations are presented to examine the correctness of the obtained results and the effects of some parameters on dynamics of the drinking model.

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Optimal control of a delayed smoking model with immigration

Cited by 17 publications

References 28 publications

Optimal Control for Smoking Epidemic Model

Optimal Control for Smoking Epidemic Model

Optimal Control in a Mathematical Model of Smoking

Bifurcation and optimal control analysis of a delayed drinking model

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