Sagar Vikram, Zhao Yi
Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China.
Chaos. 2017 Feb;27(2):023115. doi: 10.1063/1.4976953.
In the present work, the effect of personal behavior induced preventive measures is studied on the spread of epidemics over scale free networks that are characterized by the differential rate of disease transmission. The role of personal behavior induced preventive measures is parameterized in terms of variable λ, which modulates the number of concurrent contacts a node makes with the fraction of its neighboring nodes. The dynamics of the disease is described by a non-linear Susceptible Infected Susceptible model based upon the discrete time Markov Chain method. The network mean field approach is generalized to account for the effect of non-linear coupling between the aforementioned factors on the collective dynamics of nodes. The upper bound estimates of the disease outbreak threshold obtained from the mean field theory are found to be in good agreement with the corresponding non-linear stochastic model. From the results of parametric study, it is shown that the epidemic size has inverse dependence on the preventive measures (λ). It has also been shown that the increase in the average degree of the nodes lowers the time of spread and enhances the size of epidemics.
在本研究中，研究了个人行为引发的预防措施对疾病在具有不同疾病传播速率特征的无标度网络上传播的影响。个人行为引发的预防措施的作用通过变量λ进行参数化，该变量调节节点与相邻节点一部分同时进行接触的数量。疾病的动态变化由基于离散时间马尔可夫链方法的非线性易感-感染-易感模型描述。网络平均场方法得到推广，以考虑上述因素之间的非线性耦合对节点集体动态的影响。从平均场理论获得的疾病爆发阈值的上限估计值与相应的非线性随机模型结果吻合良好。从参数研究结果可知，疫情规模与预防措施（λ）呈反比关系。研究还表明，节点平均度的增加会缩短传播时间并扩大疫情规模。
