含Ornstein-Uhlenbeck过程的随机SIS传染病模型

A Stochastic SIS Epidemic Model with Ornstein-Uhlenbeck Process

本文研究一类含Ornstein-Uhlenbeck过程的随机SIS传染病模型,得到阈值Rs0,并建立了疾病的灭绝性和持久性的判别条件:Rs0<1,疾病灭亡,Rs0>1,疾病持久。结果表明:环境的波动强度和回复速率会影响疾病的爆发,波动强度越大或回复速率越小,会抑制疾病的爆发,并通过数值模拟验证所得结果。

A class of stochastic SIS epidemic model incorporating mean-reverting Ornstein-Uhlenbeck process is investigated.Sufficient conditions for the extinction and permanence of the system are established.The threshold which determines the disease will die out or not is obtained.When Rs0<1,the disease will extinct.While when Rs0>1,the disease will persist.It is found that smaller speed of reversion or bigger intensity of volatility can suppress the disease outbreak.The conclusions are simulated through the numerical method.