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疾病的广泛传播给人类带来了巨大的损失,因此抑制疾病的传播非常重要.本文考虑了个体接种疫苗意愿的差异性,并结合博弈理论建立了一个基于节点度信息的自愿免疫模型.理论解析结果证明当感染率超过某个阈值时,该模型与忽略个体接种意愿差异性的经典模型(Zhang et al 2010 New J.Phys.12 023015)传播效果(感染节点数)一样.继而考虑疫苗永久有效和有效期有限两种情况,在Baraba′si-Albert网络中利用SIS传播模型对疾病的传播进程进行了数值模拟,发现数值模拟结果与理论解析结果非常符合.实验证明,当感染耗费和接种疫苗耗费相同时,该模型比忽略个体接种意愿差异性的经典模型能够更好的抑制疾病的传播,且感染人数下降比例超过65%,更重要的是,疫苗有效期越长本文的模型(与忽略个体接种意愿差异性的经典模型相比)抑制疾病传播效果越好.
Therefore, it is very important to suppress the spread of the disease.This paper considers the difference of the individual’s willingness to vaccinate, and builds a voluntary immune model based on node degree information with game theory. The results demonstrate that when the infection rate exceeds a certain threshold, the model is the same as the classical model (Zhang et al 2010 New J. Phys. 12 023015) that ignores the difference in the individual’s willingness to inoculate (the number of infected nodes) And finite period of validity, SIS propagation model was used to simulate the spread of the disease in the Baraba’si-Albert network and found that the numerical simulation results are in good agreement with the theoretical analysis.Experiments show that when the infection and vaccination cost At the same time, the model can better suppress the spread of the disease than the classic model, which ignores the difference in the individual’s willingness to vaccinate, and the proportion of infected people declines by more than 65%. More importantly, the longer the vaccine’s duration, the model of this article Compared with the classical model of willingness to differ), the better the effect of inhibiting disease transmission.