双层网络上考虑人口流动的传染病建模及分析

Modeling and Analysis of Duplex Network Infectious Disease Dynamics Considering Population Mobility

基于复杂网络传染病传播动力学理论,考虑不同城市间的人口流动,提出了一类双层网络上的传染病数学模型,进而分析了此模型的复杂动力学性态。利用下一代矩阵法给出了模型的基本再生数,同时借助李雅普诺夫函数方法,研究了模型的无病平衡点、地方平衡点及其稳定性。最后,通过数值仿真讨论模型参数对传染病传播过程的影响,并且验证了理论结果的正确性。结果表明,个体在不同城市之间的流动以及在流动过程中与有传染性的个体接触对传染病传播有很大的影响,流动性越强,传染病传播速度越快。

To describe the impact of population mobility between twocities on the spread of infectious diseases,a new dual city infectious disease complex dynamical model is proposed.We obtain the basic regeneration number of the model based onapplied spectral analysis(next generation matrix method),while the Lyapunov function method was used,Moreover,the disease-free equilibrium points and local equilibrium points of the model were discussed,and it was found that thesetwo equilibrium points are globally asymptotically stable.Furthermore,the impact of population mobility on the spread of infectious diseases via numerical simulations is analyzed.The results show that the increase of population mobility between two cities leads to more intense disease transmission.Finally,the influence of media effects on the spread of infectious diseases is investigated.It is shown that the spread of diseases is suppressed because of the increase of individual's self-isolation rate.Therefore,controlling the population mobilityis an effective initiative to curb outbreaks of infectious diseases throughout the network.The results can provide a theoretical basis for preventing and controlling the spreading of infectious diseases,the stronger the mobility,the faster the spread of infectious diseases.