中文摘要：

研究了一类接触率受到环境噪声干扰的随机SIS流行病模型.利用停时理论及Lyapunov分析方法,证明了该随机模型正解的全局存在唯一性与有界性.当相应的确定性模型基本再生数小于1时,证明了随机模型无病平衡点的随机渐近稳定性;当确定性模型基本再生数大于1时,揭示了随机模型的解围绕相应的确定性模型地方病平衡点的振荡行为;当确定性模型基本再生数大于1并且噪声强度较小时,证明了随机模型的解是平均持续的.另外,得到了强度较大的环境噪声可以导致疾病灭绝的结论.最后,数值模拟验证了所得理论结果的正确性.

英文摘要：

A stochastic SIS epidemic model was analyzed,considering that the contact rate is influenced by environmental noise.The global existence,uniqueness and boundedness of its positive solution were proved by using the stopping time theory and Lyapunov analysis method.The stochastic asymptotical stablility of the disease-free equilibrium point was proved when the corresponding deterministic basic reproduction number is less than 1.It is also shown that the solution of the stochastic model oscillates around the corresponding deterministic endemic equilibrium point when the deterministic basic reproduction number is more than 1,and is of mean persistency when the deterministic basic reproduction number is more than 1 and the noise intensity is small.Besides,it is concluded that the large noise can make the disease extinct.Numerical simulations were carried out to prove the validity of theoretical results.