含可变感染率的SIRS模型在复杂网络上的传播分析

摘要

In real-world networks of disease transmission, the probability of infection is different for individuals contacted with the source of infection. This may be due to many factors, such as constitution or resistance.Based on SIRS (susceptible infected removed susceptible) model in the complex networks, an epidemic model with variable infection is proposed. By the mean-field theory, in our study the epidemic threshold of the model is proved to be concerned with the topology of networks and variable infection function. Finally, the correctness of theoretical analysis is confirmed by numerical simulations.%在疾病传播的现实网络中,每个个体与感染源接触而被感染的概率并不是一样,这与个体的体质、抵抗力及接触程度等因素有关.基于复杂网络上SIRS模型,提出了一个可变感染率的疾病传播模型.利用平均场原理,分析得到该传播模型的传染临界阈值主要与网络的拓扑结构和可变感染函数有关.数值模拟验证了理论分析的正确性.