Qualitative behavior of a smoking model

Din, Qamar; Ozair, Muhammad; Hussain, Takasar; Saeed, Umer

doi:10.1186/s13662-016-0830-6

Cited by 25 publications

(19 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Based on the discussion in [21], it can be concluded that all the roots of Eq. (6) have negative real parts.…”

Section: Local Stability and Existence Of Hopf Bifurcationmentioning

confidence: 99%

“…Thus, it is reasonable to consider the smokers associated with some illness compartment in giving up smoking model. Based on this point, the following smoking model has been proposed by Din et al [21]:…”

Section: Introductionmentioning

confidence: 99%

“…α is the recruitment rate of the potential smoker; β is the transmission coefficient; γ is the natural death rate; δ(1η) is the temporarily quit rate of smoking; δη is the permanently quit rate of smoking; ε is the developing rate of the smokers associated with some illness; ζ is the relapse rate from the temporarily quit smokers to the smokers; ϑ is the death rate related to smoking illness. Din et al [21] investigated stability of system (1).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamical analysis of a giving up smoking model with time delay

2019

View full text Add to dashboard Cite

In this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh-Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.

show abstract

“…Based on the discussion in [21], it can be concluded that all the roots of Eq. (6) have negative real parts.…”

Section: Local Stability and Existence Of Hopf Bifurcationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical analysis of a giving up smoking model with time delay

2019

View full text Add to dashboard Cite

show abstract

“…For example, Ma et al developed different forms of heroin epidemic models [3,[6][7][8][9][10] to study the transmission of heroin epidemics. Sharomi et al formulated different smoking models [11][12][13][14][15][16][17] for giving up smoking. There were also some drinking models [18][19][20][21] proposed by Mushayabasa et al to analyze the influence of binge drinking to public health.…”

Section: Introductionmentioning

confidence: 99%

Influence of time delay on bifurcation of a synthetic drug transmission model with psychological addicts

2020

View full text Add to dashboard Cite

A synthetic drug transmission model with psychological addicts and time delay is proposed in this paper. By analyzing the corresponding characteristic equation and choosing the time delay as the bifurcation parameter, a set of sufficient criteria guaranteeing local stability of the synthetic drug addiction equilibrium and the appearance of a Hopf bifurcation of the model is established. Further, the direction and stability of the Hopf bifurcation are investigated with the aid of normal form theory and center manifold theory. Finally, numerical simulations are performed to support the analytical results.

show abstract

“…In [1], a smoking model that considers the number of individuals who are aware of the bad effects of smoking through education or media campaign was presented. Din [8] studied a smoking model considering non-smokers, smokers, people who temporarily or permanently quit smoking and people who are associated with illness due to smoking.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

Morales‐Delgado¹,

Gómez‐Aguilar²,

Taneco-Hernández³

et al. 2018

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

In this paper, we analyze the fractional modeling of the giving up the smoking using the definitions of Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives. Applying the homotopy analysis method and the Laplace transform with polynomial homotopy, the analytical solution of the smoking dynamics has obtained. Furthermore, using an iterative scheme by the Laplace transform, and the Atangana-Baleanu fractional integral, special solutions of the model are obtained. Uniqueness and existence of the solutions by the fixed-point theorem and Picard-Lindelof approach are studied. Finally, some numerical simulations are carried out for illustrating the results obtained.

show abstract

Qualitative behavior of a smoking model

Cited by 25 publications

References 11 publications

Dynamical analysis of a giving up smoking model with time delay

Dynamical analysis of a giving up smoking model with time delay

Influence of time delay on bifurcation of a synthetic drug transmission model with psychological addicts

Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

Contact Info

Product

Resources

About