Bifurcation in a delayed worm propagation model with birth and death rates

In this paper, a delayed worm propagation model with birth and death rates is discussed. The number of system reinstallations may be increased when the hosts get unstable (infected or quarantined). In view of such situation, dynamic birth and death rates are introduced. Afterwards, the stability of the positive equilibrium is studied. Through the theoretical analysis, it is proved that the model is locally asymptotically stable without time delay. Moreover, a bifurcation appears when time delay t passes a constant value which means that the worm propagation system is unstable and uncontrollable. Thus, the time delay should be decreased in order to predict or eliminate the worm propagation. Finally, a numeric simulation is presented which fully supports our analysis.