Stability analysis of a giving up smoking model

Abstract

In this paper we present and analyze a generalization of the giving up smoking model that was introduced by Sharomi and Gumel [4], in which quitting smoking can be temporary or permanent. In our model, we study a population with peer pressure effect on temporary quitters and we consider also the possibility of temporary quitters becoming permanent quitters and the impact of this transformation on the existence and stability of equilibrium points. Numerical results are given to support the results.

Mathematical Model of Drinking Epidemic

“…We determine the global stability of the endemic equilibrium in this section, by using the first three equations of the system (1) − (4) that is: in the region Γ * = {(ܵ, ‫,ܪ‬ ܶ)ܴ߳ ା ଷ : ܵ + ‫ܪ‬ + ܶ ≤ 1, ܵ 0 , ‫ܪ‬ ≥ 0 , ܶ ≥ 0}, Γ * is positively invariant, i.e. every solution of the model (15), with initial conditions in Γ * remains there for time ‫ݐ(‬ 0).…”

“…Also Γ * * is positively invariant subset of Γ * and the ߱-limit set of each solution of model (14) is a single point in Γ * * since there is no periodic solutions, homoclinic loops and oriented phase polygons inside Γ * * if ∅ ≤ ߙ. Therefore ‫ܧ‬ * is globally asymptotically stable [15,16].…”

Smoking model with cravings to smoke

“…Smoking is renowned to be the immense cause of both treatable and premature worldwide. According to World Health Organization (WHO), smoking-associated diseases are cause of nearly 5 million deaths annually all over the world and this figure is expected to double by 2025 [3]. Despite of the fact that smoking is extensively recognized as a treatable cause of death and total number of new smokers rise, intrusive tobacco control can halt a large number of deaths from smoking.…”

“…They analyzed the qualitative behavior of a mathematical model in which the total population is partitioned into four compartments. In 2014, Zainab Alkhudhari et al [3] extended the model [4,5], and investigated that mathematical model in which the total population was break down into four compartments: Potential smokers (P ), smokers (S), temporary quitters (Q t ) and permanent quitters (Q p ). They studied the impact of smokers (S) on temporary quitters (Q t ).…”

Optimal intervention strategy for prevention tuberculosis using a smoking-tuberculosis model

“…Little work has been done on the mathematical modeling of tobacco smoking compared with the modeling of epidemic diseases. Since Castillo-Garsow et al [10] proposed simple models describing the acquisition and cessation of smoking, the mathematical models developed in later studies [3,4,17,40,56,57] have been based on SIR or SEIR model, while some use finer compartmental decompositions. Stability analyses and optimal control theory have been applied to smoking models using numerical simulations, although the connection with real data is not always clear.…”