Journal of Jishou University(Natural Sciences Edition) ›› 2022, Vol. 43 ›› Issue (1): 1-9.DOI: 10.13438/j.cnki.jdzk.2022.01.001

• Mathematics •     Next Articles

A Time-Delayed Giving up Smoking Model with  Relapse

ZHANG Zizhen,ZHANG Weishi   

  1. (School of Management Science and Engineering,Anhui University of Finance and Economics,Bengbu 233030,Anhui China)
  • Online:2022-01-25 Published:2022-05-16

Abstract: A time-delayed giving up smoking model with relapse is studied.The model includes five subgroups:potential smokers,occasional smokers,heavy smokers,temporary quitters and permanent quitters.Firstly,the basic reproduction number and smoking equilibrium of the model are calculated.Then the existence of Hopf bifurcation is discussed by taking the time delay of the period experienced by occasional smokers to heavy smokers as the bifurcation parameter,and the critical point of the delay for the occurrence of Hopf bifurcation is calculated.Finally,a simulation example is given to verify the correctness of the results.

Key words: time-delay, giving up smoking model, Hopf bifurcation, basic reproduction number, smoking equilibrium

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