Dynamics of a smoking model with smoking death rate

Gul Zaman¹ ; Young Han Kang² ; Il Hyo Jung³

¹ Department of Mathematics University of Malakand Chakdara, Dir Lower Khyber Pakhtunkhawa, Pakistan
² Institute of Liberal Education Catholic University of Daegu Gyeongsan-Si Gyeongbuk 712-702, South Korea
³ Department of Mathematics Pusan National University Busan 609-735, South Korea

Applicationes Mathematicae, Tome 44 (2017) no. 2, pp. 281-295

Résumé

In this work, we derive and analyze a smoking model by taking into account hospitalized smokers and smoke quitters of two types: temporary and permanent, which is one of the possible extensions of the giving-up smoking model. Temporary quitters may become smokers again, while permanent quitters, once they quit, never smoke again in the entire life span. The existence and stability of the possible equilibria of the model are examined in terms of a certain threshold condition ${\mathcal R}$, the smoking generation number (the basic reproduction number). Numerical simulations are carried out to investigate the influence of the key parameters on the spread of smoking, to support the analytical conclusion and illustrate possible behavioral scenarios.

Détail

DOI : 10.4064/am2249-8-2017

Keywords: work derive analyze smoking model taking account hospitalized smokers smoke quitters types temporary permanent which possible extensions giving up smoking model temporary quitters may become smokers again while permanent quitters once quit never smoke again entire life span existence stability possible equilibria model examined terms certain threshold condition mathcal smoking generation number basic reproduction number numerical simulations carried out investigate influence key parameters spread smoking support analytical conclusion illustrate possible behavioral scenarios