带有接种的随机SIS传染病模型研究

Stochastic SIS Epidemic Model with Vaccination

研究了一类带有接种的随机SIS传染病模型.利用非负半鞅收敛定理这种简单而有效的方法找到了随机模型的阈值R_0.R_0决定了疾病的灭绝和流行.当R_0<1时,疾病灭绝;当R_0>1时,模型的解在时间均值意义下趋于一点,即此时疾病将流行.

A stochastic version of the delayed SIS epidemic model with vaccination was concerned.A simple but effective method was provided for estimating the threshold of a class of stochastic epidemic models by use of the nonnegative semimartingale convergence theorem.The threshold of the stochastic delayed model,denoted by R^0,completely determines the extinction and prevalence of the disease.If R^0<1,the disease ultimately vanishes from the population with probability one.If R^0>1,the system is proved to be convergent to a point in the meaning of time mean.