小世界网络V.S.均匀混合网络中的SIRS型传染病模型  

Comparison of SIRS Epidemic Model in Small-world Network and in Uniformly Mixed World

作　　者：孙有发[1] 梁肖肖[1] 郭旭冲[1] 刘彩燕[1] 张成科[2] 

机构地区：[1]广东工业大学管理学院,广州510520 [2]广东工业大学经济与贸易学院,广州510520

出　　处：《系统仿真学报》2012年第3期669-676,共8页Journal of System Simulation

基　　金：国家自然科学基金(70801019;71171061);广东省自然科学基金(S2011010004970)

摘　　要：在现实复杂情形下(包含非线性传染率、有隔离措施、群外个体迁入、生育与死亡以及疾病可水平和垂直传播等),比较研究小世界网络中的SIRS型传染病模型与均匀混合SIRS型传染病模型的疾病动态传播行为,以及相同疾病控制策略在两种传染病模型上的效果。数值仿真研究发现:1)动态行为特征仅与模型参数有关的均匀混合SIRS型传染病模型不能准确刻画小世界网络中的传染病传播行为。2)源于均匀混合SIRS型传染病模型的控制策略(如强化隔离染病个体、限制易感群体迁入、提高染病个体死亡率以及控制疾病垂直传播等)适用于控制小世界网络中的传染病,但效果有显著差异。3)小世界网络中的SIRS型传染病的控制策略中,存在一个最佳的染病个体死亡率阈值。The dynamic behaviors and performances of control strategies of SIRS epidemic model in small-world and in uniformly mixed world were investigated and compared in details,under such real complex circumstances that the transmission rate of disease is non-linear;quarantine measures were partially taken for infectious individuals;immigrations,fertility and death of individuals were permitted;and finally diseases could be both directly and vertically transmitted.Numerical simulations researches find that： 1） The SIRS epidemic model in uniformly mixed world whose dynamic behavior is fully determined by the model＇s parameters,cannot characterize the SIRS epidemic model in small-world.2） Those control strategies derived from SIRS epidemic model in uniformly mixed world,such as quarantining infectious individuals,restricting immigrants,raising death rate of the infectious and controlling vertical transmissions,are suitable for controlling the SIRS epidemic in small-world despite of their significantly different effects.3） There exists an optimal death rate of the infectious for controlling the epidemic in small world.

关 键 词：SIRS型传染病模型 小世界网络 数值仿真 疾病控制 死亡率阈值 树生长算法 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术] Q-332[自动化与计算机技术—计算机科学与技术]