A stochastic SIS epidemic model with vaccination

作者：Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming^*

来源：Physica A: Statistical Mechanics and Its Applications , 2017, 486: 127-143.

DOI：10.1016/j.physa.2017.05.083

• Epidemic model
• Vaccination
• Stochastic reproduction number
• Markov semigroup
• Stationary distribution

In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R-0(s) which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R-0(s) < 1, under some mild extra conditions, there exists a disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R-0(s) > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.

• 出版日期2017-11-15
• 单位宁夏大学; 淮阴师范学院; 华东政法大学