Modeling the Chaotic Dynamics of Early Worm Propagation

A chaotic worm propagation model is proposed to analyze early worm propagation process in this paper. Worm propagation is very complex, whose major transitions are between regular cycles and irregular, possibly chaotic epidemics. This paper deals with a discrete mathematical model of early worm propagation systems: Chaotic Susceptible-Infected (CSI) model. In the CSI model, three threshold values of a control parameter depending on the ratio of infection rate to removal rate share the behavior of early worm propagation in four zones: no infection, increase of infection, bifurcation and then chaos. It is shown that for the same total number of hosts in the network, the ratio of infection rate to removal rate shares the dynamics of the infection: for low ratio, infection disappears and for high ratio, the infection increases but the number of infected hosts first remains at a positive constant value and then multiple period-doubling bifurcation route to chaos. It is proved that the bifurcation and chaos of early worm propagation can be predicted by the CSI model according to the numerical and simulation results.