Stability Analysis and Optimal Control as Strategies Reducing Smokers in Model of Addicted Smoking with Incident Rate Holling Type Function.

This article discusses the spreading model of addicted smoking involving five compartments, namely susceptible, addicted, temporary quitters, permanent quitters, and not interested in smoking. This model is expressed as a system of nonlinear ordinary differential equations. Parental guidance and anti-nicotine therapy are considered in the model as strategies to control and prevent the spread of addicted smoking. Addicted and non-addicted fixed points of the model are analyzed using linearization, eigenvalues, the Routh-Hurwitz test, and the basic reproduction number. Sensitivity analysis of the model parameters to the basic reproduction number was carried out to determine the influence of the parameters, and it was found that the transmission rate has a significant contribution to the spread of addicted smoking. The model with control is then related to the problem of minimizing the number of individuals addicted to smoking. By using the Pontryagin minimum principle, an optimal path is obtained that minimizes the number of individuals addicted to smoking in a specific time interval. The simulation used several assumptions and model parameter values estimated from actual data. From the optimal path with and without controls, it was found that both controls significantly reduced the number of individuals addicted to smoking.