复杂网络中具有低易感的疾病传播问题研究

基于真实流行病学中免疫力减弱的特性，提出一个新的疾病传播模型即复杂网络中具有低易感即免疫力减弱的传播模型。 利用平均场理论和计算机仿真对该模型的传播行为进行了详细研究，结果表明该模型的传播阈值主要与网络拓扑结构、免疫丧失率和免疫保留率有关。 小世界网络中存在非零的传播阈值，而无标度网络在网络规模无限大的情况下传播阈值趋于零。 在网络拓扑结构不变的情况下，增大节点的免疫保留率可以增大小世界网络和无标度网络上的传播阈值，降低疾病的传播范围，从而有效控制传染性疾病在复杂网络上传播。

Epidemic Spreading with Lower Susceptibility on Complex Networks

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 was 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 was 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.