一类具有潜伏期的随机禽流感模型的渐近性分析

Asymptotic Analysis of a Stochastic Viral Infection Model with a Latent Period

研究了一类禽类患病系统具有潜伏期而人类染病系统受到随机白噪声干扰的随机禽流感模型的渐近性质.首先通过构造停时和Lyapunov函数及伊藤引理的方法得到了随机模型全局正解的存在唯一性.其次证明了在禽类患病种群灭绝的情形下,人类患病种群必将灭绝的结果;再次得到了禽类患病种群长期存在的前提下,由于随机因素的干扰,人类患病种群终将趋于灭绝的充分条件.最后通过数值模拟比较了人类染病种群在确定性和随机性系统中的发展趋势.

Asymptotic analysis of an avian influenza model with a latent period and human infection system disturbed by random white noise was investigated.Firstly,the existence and uniqueness of global positive solutions was proved by constructing stopping time,Lyapunov functions and Ito’s lemma.Then,it was proved that the human infected population would be extinct in the case of avian infected population going extinction.Even though the avian disease population existed in a long time,the human infected population would be extinct due to the random disturbances,and the sufficient conditions were obtained.Finally,development tendency of the human infected population in determinate and random system was compared by simulations.