吉林大学学报（理学版）2026，Vol.64Issue(3)：551-558,8.DOI:10.13413/j.cnki.jdxblxb.2025239
一类跳扩散SEIR流行病模型渐近行为的分类
Classification of Asymptotic Behavior of a Class of Jump-Diffusion SEIR Epidemic Models
摘要
Abstract
We considered a class of jump-diffusion SEIR epidemic models and determined the threshold for the disease to occur or not.Firstly,the threshold Ξ was theoretically determined through a simplified limiting system.Secondly,by using comparison principle,we proved that when Ξ＜0,the disease became exponentially extinct.Finally,by constructing an appropriate Lyapunov function,we proved that when Ξ＞0,the transition probability function of the solution of a stochastic system converged to the unique invariant measure,with the convergence speed of arbitary order polynomial convergence.关键词
阈值/遍历性/灭绝/不变测度Key words
threshold/ergodicity/extinction/invariant measure分类
数理科学引用本文复制引用
林玉国,郭丽..一类跳扩散SEIR流行病模型渐近行为的分类[J].吉林大学学报（理学版）,2026,64(3):551-558,8.基金项目
吉林省科技发展计划项目(批准号:YDZJ202201ZYTS648). （批准号:YDZJ202201ZYTS648）
