A delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response

AIMS Mathematics

article

A Pratap¹  Ranjit Kumar Upadhyay²  Anwar Zeb³  Yougang Wang⁴ 

[1] Department of Mathematics, Alagappa University Alagappapuram;Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines);Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus;School of Management Science and Engineering, Anhui University of Finance and Economics

关键词: delay;    Hopf bifurcation;    synthetic drugs model;    stability;    periodic solution;   

DOI  :  10.3934/math.2021001

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

This paper gropes the stability and Hopf bifurcation of a delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response. The critical point at which a Hopf bifurcation occurs can be figured out by using the escalating time delay of psychologically addicts as a bifurcation parameter. Directly afterwards, properties of the Hopf bifurcation are explored with aid of the central manifold theorem and normal form theory. Specially, global stability of the model is proved by constructing a suitable Lyapunov function. To underline effectiveness of the obtained results and analyze influence of some influential parameters on dynamics of the model, some numerical simulations are ultimately addressed.

【 授权许可】

CC BY