Optimal Control for Smoking Epidemic Model

Abstract

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.

An Optimal Control Analysis of Dengue Fever

“…We prove the existence of an optimal control with an initial condition of 𝑡 = 0 in this section by stating and proving the following theorem and studying the properties of the model ( 9)-( 16) with all non-negative initial circumstances 𝑡 > 0. We'll also utilize model ( 9)-( 16) to examine if there's an optimal control that meets all of Pontryagin's Maximum Principle's requirements [37]- [41]. By using Pontryagin's Maximum Principle, Eqs.…”

Curbing the Menace of Re-Cycling Smokers in a Population through Mathematical Modeling Approach

“…There are around 1 billion smokers on the globe. Due to the poor quality of available treatment and long-term smoking cessation, some people still smoke (Ilmayasinta et al, 2021). When smokers and non-smokers were compared, smokers were 70% more likely to have a heart attack.…”

“…When smokers and non-smokers were compared, smokers were 70% more likely to have a heart attack. The risk of developing lung cancer is ten times higher for smokers, and one in ten deaths are related to smoking (Ilmayasinta et al, 2021;Morales-Delgado et al, 2018). Even without this illness, smoking can result in cancer.…”

“…Even without this illness, smoking can result in cancer. All of this is not unexpected considering that cigarette smoke includes more than 4000 chemicals and poisons, all of which are extremely hazardous to human health (Ilmayasinta et al, 2021;Sharma, 2020;Veeresha et al, 2019). In some circumstances, smoking may be seen as a contagious form of agony brought on by addiction.…”

“…Because cigarettes contain tens of thousands of chemicals and toxins, they are the direct cause of all these dangerous diseases. Mathematicians sought to create many practical smoking models to provide the best depiction of the cigarette smoking phenomenon (Awan et al, 2021;Ilmayasinta et al, 2021;Morales-Delgado et al, 2018;Sharma, 2020;Veeresha et al, 2019).…”