Stability and Hopf Bifurcation of a Delayed Drug Abstinence Model

doi:10.13438/j.cnki.jdzk.2024.05.001

Abstract

Abstract: A class of delayed Susceptible-Light-Heavy-Mentally ill-Treated-Quitted (SLHMTQ)drug rehabilitation model with bilinear contact rate was studied.The bifurcation parameter as the time delay of drug addiction relapse,the local asymptotic stability of the model and the existence of local Hopf bifurcation were investigated using the eigenvalue method.The critical time delay value for the model to generate local Hopf bifurcation was derived,and the properties of the bifurcation periodic solution were studied using the central manifold theorem.

Key words: drug rehabilitation model, Hopf bifurcation, time delay, bilinear contact rate, stability

ZHANG Zizhen, ZHANG Yixue. Stability and Hopf Bifurcation of a Delayed Drug Abstinence Model[J]. Journal of Jishou University(Natural Sciences Edition), 2024, 45(5): 1-10.

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