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

考虑一类跳扩散SEIR流行病模型并确定其疾病发生与否的阈值.首先,通过一个简化的极限系统从理论上确定阈值Ξ;其次,用比较原理证明当Ξ<0时,疾病将依指数灭绝;最后,通过构造合适的Lyapunov函数证明当Ξ>0时,随机系统解的转移概率函数将收敛到唯一的不变测度,其收敛速度为任意阶多项式收敛.

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

参考文献

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基金资助

吉林省科技发展计划项目(YDZJ202201ZYTS648)