复杂网络上具有多感染阶段的传染病传播模型

针对传染病传播模型缺乏多感染阶段的不足,结合SIR和SEIR两种传播模型的特性,提出了一种改进的具有多感染阶段的SIR传染病传播模型(即SInR模型)。该模型充分考虑了不同感染阶段的非均匀感染力对不同网络结构上传染病传播及传播阈值的影响；同时引入相对感染力及传播时间尺度的概念,从网络结构、网络规模及相对感染力方面进行了仿真研究。仿真中无标度网络采用BA模型的生成算法,而小世界网络采用WS模型的生成算法。由仿真可知,感染节点在整个感染过程中大致服从泊松分布,因此在SInR模型下无标度网络的传播速度更快,范围更广；相对感染力对于传染病的大规模爆发存在着一个阈值,当感染力大于阈值时传染病才能大范围地爆发传播,而小于阈值时传染病只会局域小范围传播直至消失,无标度网络的感染力阈值为0.2,小世界网络的感染力阈值为0.24；随着网络规模的增大,传播时间尺度也在增大,相应的传播速度就会降低。仿真结果表明:该模型下无标度网络传染病传播速度更快且影响范围更大;无标度网络的相对传染力的传播阈值小于小世界网络,设置合理阈值有利于降低传染病的传播影响力。

Epidemic model with multiple infections stages on complex networks

For the deficiency of the epidemic propagation models lacking of multiple infections stages, referring to the characteristics of two traditional propagation models including SIR and SEIR, an improved SIR epidemic propagation model with multiple infections stages, named SInR model, was put forward. Different infectious stages with non-uniform infectiousness which impacts on the spread of the epidemic in different network structures and the spread threshold were considered; meanwhile, relative infectiousness and propagation time were introduced to the model, and the simulations on network construction, network scale and relative infectiousness were also given. In the simulation, scale-free networks and small-world networks respectively used BA model generation algorithm and WS model generation algorithm. The infected nodes obeyed Poisson distribution in process of infection, thus the propagation speed of scale-free networks was faster as well as wider transmission under SInR model. There was a spread threshold of relative infectiousness for massive outbreak, when the relative infectiousness was greater than the threshold, the epidemic would outbreak in a wide range; otherwise, the epidemic would only spread in a local small range until it disappeared. The threshold of scale-free networks was 0.2, while that of small-world networks was 0.24. The propagation time scale increased and the corresponding propagation speed decreased while the network scale increased. The simulation results show that epidemic disease spreads faster and the influence range is larger on scale-free network under this model. In addition, the spread threshold value of relative infectiousness of scale-free network is less than the small world's and setting a reasonable threshold is beneficial to reduce the influence of the propagation of epidemic disease.