复杂网络上两城市之间疾病传播的建模与分析

Modeling and Analyzing the Disease Propagation Between Two Cities on Complex Networks

针对两城市间不同的迁入迁出对于疾病传播的影响,建立了复杂网络上的两城市疾病传播SIS(Susceptible-Infected-Susceptible)模型,证明了无病平衡点的存在性和全局吸引性.通过数值模拟和参数的敏感性分析发现:当R_0>1时,在城市之间的往返出行可以将一个城市的局部疫情很快传到另一个城市;当R_0<1时,疾病在有移民的迁入和人口迁出的城市更容易灭绝,而当R_0>1时,疾病在有移民迁入和人口迁出的城市传播更慢且疾病规模更小;进一步得到移民的迁入对疾病传播的基本再生数比较敏感,从而可以通过增加移民迁入的方式达到控制疾病的目的.

In order to find out the effect of different patterns of immigrations and emigrations on the spread of diseases,a susceptible-infected-susceptible（SIS）model of the disease spread between two cities on complex networks was proposed.The existence of the disease free equilibrium was proved and it is globally attractive.Numerical simulations and sensitivity analysis were performed.If R_01,it is observed that the short-time traveling between two cities can quickly spread the disease from one city to another.The disease is easier to die out in the city with immigration and emigration if R_01,and the disease spread is slower in the city with immigration and emigration if R_01.Moreover,the immigration is sensitive to the basic reproductive number,and the disease can be controlled by means of increasing the immigration.