Based on the weakened immunity property of real epidemiology, a new epidemic model with lower susceptibility,i.e. weakened immunity, was proposed.The propagation behavior of the model was studied in detail through the mean field theory and computer simulation.The results showed that the epidemic threshold of the model is concerned with the topology of networks, loss rate of immunity and retention rate of immunity.There would exist a nonzero epidemic threshold on small-world networks and the threshold could be null if the size of scale-free networks is sufficiently large. If the topology of networks does not change,increasing the retention rate of immunity of nodes can increase the epidemic threshold on complex networks and reduce the prevalence of disease,thus control the disease spreading on complex networks effectively.
