1. A delayed synthetic drug transmission model with two stages of addiction and Holling Type-II functional response
- Author
-
Anwar Zeb, Ranjit Kumar Upadhyay, A. Pratap, and Yougang Wang
- Subjects
Lyapunov function ,Hopf bifurcation ,delay ,General Mathematics ,Addiction ,media_common.quotation_subject ,lcsh:Mathematics ,Functional response ,periodic solution ,stability ,lcsh:QA1-939 ,Two stages ,Critical point (mathematics) ,Synthetic drugs ,symbols.namesake ,symbols ,Applied mathematics ,synthetic drugs model ,hopf bifurcation ,Bifurcation ,media_common ,Mathematics - Abstract
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.
- Published
- 2021