无标度网络上分片线性传染力与免疫作用下的流行病动力学

EPIDEMIC DYNAMICS OF SIR MODEL WITH PIECEWISE LINEAR INFECTIVITY AND IMMUNIZATIONS ON SCALE-FREE NETWORKS

本文研究了含有免疫作用的易感染者-感染者-移出者传染病模型(即SIR模型)在复杂网络上的动力学行为,讨论了免疫作用对疾病传播的影响.当接种比例大于零时,传染率需要跨越更大的传染临界值疾病才能流行,且随着时间的增大传染临界值也增大.所以通过接种疫苗确实可以起到预防和控制疾病在复杂网络上传播的作用.具体讨论了具有分片线性传染力的SIR模型在无标度网络上的流行病传播阈值,并运用分片线性传染力得到了传播阈值为正的条件.接着分析了各种免疫策略的SIR模型,得出各类免疫后的传播阈值,并进行了数值模拟和比较.在相同的免疫概率下,目标免疫比随机免疫、近邻免疫、主动免疫更为有效.

The Susceptible-Infected-Removed （SIR） model~ epidemic dynamics on complex networks with immunizations were studied, and the effects of immunizations on the spread of epidemic were discussed. When vaccinal ratio is greater than zero, the critical infection value becomes greater with the time increasing. Therefore vaccination can indeed prevent and control the spreading of diseases on complex networks. In further details, this paper discussed the epidemic threshold for disease spreading using SIR model with piecewise linear infectivity on scale-free networks. And with this nonlinear infectivity, the conditions for positive epidemic threshold were derived. Then various immunization strategies for the SIR model and the corresponding thresholds were discussed. Numerical simulations and comparisons show that the targeted immunization is more effective than random immunization, acquaintance immunization and active immunization strategies.