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Alcoholism is a social phenomenon that affects all social classes and is a chronic disorder that causes the person to drink uncontrollably, which can bring a series of social problems. With this motivation, a delayed drinking model including five subclasses is proposed in this paper. By employing the method of characteristic eigenvalue and taking the temporary immunity delay for alcoholics under treatment as a bifurcation parameter, a threshold value of the time delay for the local stability of drinking-present equilibrium and the existence of Hopf bifurcation are found. Then the length of delay has been estimated to preserve stability using the Nyquist criterion. Moreover, optimal strategies to lower down the number of drinkers are proposed. Numerical simulations are presented to examine the correctness of the obtained results and the effects of some parameters on dynamics of the drinking model. [ABSTRACT FROM AUTHOR]

Taking the delay due to the latent period of computer viruses and the delay due to the period that the anti-virus software uses to clean the computer viruses as the bifurcation parameters, local Hopf bifurcation of an epidemic model over the Internet is studied. We discuss the existence of the Hopf bifurcation under four conditions: (1) τ1>0, τ2=0, (2) τ1=0, τ2>0, (3) τ1=τ2=τ>0, and (4) τ1>0, τ2∈(0,τ20). Properties of the Hopf bifurcation about condition (4) are investigated by means of the center manifold theorem and the normal form theory. Finally, some simulations are presented to support our obtained results. [ABSTRACT FROM AUTHOR]