个体在随机和异质网络相互转化的传染病模型研究

Epidemic Model Based on Individual Transferring Between Random and Heterogeneous Networks

利用将人群分为随机和异质的两个子网,且个体可以在这两个子网之间相互转化的方法,建立了随机和异质接触传播模式不能同时在每个个体身上发生的一类多途径传染病模型.利用极限系统以及Gershgorin圆盘定理证明了模型的无病平衡点的唯一性,并利用下一代矩阵方法计算得到了模型的基本再生数,得到无病平衡点的稳定性,进而得到了在基本再生数小于1时疾病最终消亡的结论.

A new epidemic model with multiple routes was established by dividing the population into random and heterogeneous subnetworks, and each individual can transfer from one subnetwork to another at any time, in which the transmission mechanisms of random and heterogeneous can＇t occur on each individual simulta- neously. The uniqueness of the disease-free equilibrium was obtained by using the limit system and the Gersh- gorin disk theorem. And then according to the method of next generation matrix, the basic reproduction num- ber of the model was derived. Finally, the local stability of the disease-free equilibrium was proved. It draws the conclusion that the epidemic will extinct if the basic reproduction number is less than one.