Effect of treatment measures on the epidemic dynamics in small-world networks

A nonlinear epidemic model in small-world networks with time-delay is presented to investigate the effect of treatment strength on the epidemic dynamics. Hopf bifurcation is proved to exist during disease spreading. The existence of chaos in a difference epidemic model is also investigated. It is shown that the treatment strength not only determines the stability of the local equilibrium, but also can be applied to stabilize a periodic spreading behavior or a chaotic spreading behavior onto a stable equilibrium. Furthermore, numerical simulations are also provided to illustrate the effectiveness of the theoretical results.