具有年龄结构随机SIRS模型的持久性分析

Persistence analysis of a stochastic SIRS model with age structure

在确定型SIRS传染病模型的基础上,加入随机扰动项得到具有年龄结构的随机传染病模型。由持久性的含义,利用It0公式及强大数定律得出了I(t)上、下极限的范围,并在此基础上得出了R(t)的上、下极限。结果表明,当白噪声强度较小时,疾病将持续存在。

On the basis of the deterministic SIRS epidemic model,the random disturbance term was added to obtain a stochastic infectious disease model with age structure.From the meaning of persistence,the upper and lower limits of I(t)were obtained by using Ito formula and the law of strong large numbers,and on this basis,the upper and lower limits of R(t)were obtained.The results show that the disease will persist when the intensity of white noise is small.