中文摘要：

讨论了随机与异质网络共存的SEIRS传染病模型,通过正平衡点的存在性给出基本再生数R0=（（1-η）Aλ＋ηβ）/μ.结果表明,当R0〈1时,无病平衡点（1,0,0,0）局部稳定;当R0〉1时,无病平衡点（1,0,0,0）不稳定,此时系统存在唯一的地方病平衡点,并且一致持续存在.最后通过数值仿真,验证了理论结果的正确性.

英文摘要：

In this paper, we investigate an SEIRS epidemic model based on homogeneous and heterogeneous networks. The existence of endemic equilibrium is determined by the basic reproduction number R0 -- （1-η）Aλ＋ηβ. The results show that if R0 〈 1, then the disease free equilibrium （1, 0, 0, 0） is locally asymptotically stable. Otherwise, if R0 〉 1, then the disease free equilibrium is unstable, and there exists a unique endemic equilibrium which is uniformly persistent in the time limit. Our simulation results verify the theory.