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Volume 2, Issue 3
Analysis of a Kind of Quitting Smoking Model with Beddington-DeAngelis Function

Zhimin Li, Tailei Zhang, Jianzhong Gao & Shu Fang

DOI: 10.12150/jnma.2020.447

J. Nonl. Mod. Anal., 2 (2020), pp. 447-465.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we discuss the dynamics of quitting smoking with Beddington-DeAngelis function. Firstly, the basic reproduction number of the model is obtained by establishing the basic reproduction matrix. Then, by using the Routh-Hurwitz criterion and Lyapunov functionals and LaSalle's Invariant Principle and the second additive compound matrix, local and global dynamics of the model are analyzed. Based on the partial rank correlation coefficients (PRCCs), we discuss some biological implications and focus on the impact of some key model parameters. Finally, the numerical simulations show the theoretical analysis more intuitively, and we give some strategies to control the spread of smokers.

  • Keywords

Beddington-DeAngelis function, Quitting smoking model, Local stability, Global stability.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-2-447, author = {Li , ZhiminZhang , TaileiGao , Jianzhong and Fang , Shu}, title = {Analysis of a Kind of Quitting Smoking Model with Beddington-DeAngelis Function}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {2}, number = {3}, pages = {447--465}, abstract = {

In this paper, we discuss the dynamics of quitting smoking with Beddington-DeAngelis function. Firstly, the basic reproduction number of the model is obtained by establishing the basic reproduction matrix. Then, by using the Routh-Hurwitz criterion and Lyapunov functionals and LaSalle's Invariant Principle and the second additive compound matrix, local and global dynamics of the model are analyzed. Based on the partial rank correlation coefficients (PRCCs), we discuss some biological implications and focus on the impact of some key model parameters. Finally, the numerical simulations show the theoretical analysis more intuitively, and we give some strategies to control the spread of smokers.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2020.447}, url = {http://global-sci.org/intro/article_detail/jnma/18821.html} }
TY - JOUR T1 - Analysis of a Kind of Quitting Smoking Model with Beddington-DeAngelis Function AU - Li , Zhimin AU - Zhang , Tailei AU - Gao , Jianzhong AU - Fang , Shu JO - Journal of Nonlinear Modeling and Analysis VL - 3 SP - 447 EP - 465 PY - 2021 DA - 2021/04 SN - 2 DO - http://doi.org/10.12150/jnma.2020.447 UR - https://global-sci.org/intro/article_detail/jnma/18821.html KW - Beddington-DeAngelis function, Quitting smoking model, Local stability, Global stability. AB -

In this paper, we discuss the dynamics of quitting smoking with Beddington-DeAngelis function. Firstly, the basic reproduction number of the model is obtained by establishing the basic reproduction matrix. Then, by using the Routh-Hurwitz criterion and Lyapunov functionals and LaSalle's Invariant Principle and the second additive compound matrix, local and global dynamics of the model are analyzed. Based on the partial rank correlation coefficients (PRCCs), we discuss some biological implications and focus on the impact of some key model parameters. Finally, the numerical simulations show the theoretical analysis more intuitively, and we give some strategies to control the spread of smokers.

Zhimin Li, Tailei Zhang, Jianzhong Gao & Shu Fang. (1970). Analysis of a Kind of Quitting Smoking Model with Beddington-DeAngelis Function. Journal of Nonlinear Modeling and Analysis. 2 (3). 447-465. doi:10.12150/jnma.2020.447
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