复杂网络上随机SEIR模型的最终染病规模  

Final Epidemic Size of Stochastic SEIR Model on Complex Networks

作　　者：刘桂荣[1] 张刘雄 LIU Guirong;ZHANG Liuxiong(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2022年第3期599-605,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11971279)。

摘　　要：基于个体间接触的异质性和疾病传播环境的随机性,利用随机过程理论建立了复杂网络上随机SEIR模型。通过随机时间变换,将随机SEIR模型进行变形,并利用大数定律证明了最终染病规模的收敛性;利用中心极限定理给出传染病最终染病规模的分布。最后通过数值模拟验证了理论结果。理论结果可以为传染病最终染病规模的精确预测提供依据。Based on the heterogeneity of the contact between individuals and the randomness of the environment in which infectious diseases spread,a stochastic SEIR model on complex networks is established by using stochastic process theory.The stochastic SEIR model is transformed by random time transformation,and the convergence of the final epidemic size is proved by the law of large numbers.The distribution of the final epidemic size is given by using the central limit theorem.Finally,the theoretical results are verified by numerical simulation.The theoretical results can provide a basis for accurate prediction of the final epidemic size.

关 键 词：SEIR模型 复杂网络 随机过程 最终染病规模 

分 类 号：O29[理学—应用数学]