具有Beddington-DeAngelis发生率的随机SIS传染病模型的定性分析

Qualitative Analysis of Stochastic SIS Epidemic Model with Beddington-DeAngelis Incidence Rate

建立并研究了一类具有Beddington-DeAngelis发生率的随机SIS传染病动力学模型。首先对于对应的确定性模型,研究了模型平衡点的稳定性,得到了决定疾病消除或者流行的基本再生数。然后针对随机SIS传染病模型,利用随机微分方程的比较定理和伊藤公式,研究了疾病的传播动力学,在噪声较小的情况下得到类似于确定性模型的决定疾病消除或者流行的阈值。结果显示,大的随机噪声能抑制疾病的流行。最后,给出了数值模拟去验证理论结果。

In this paper,a stochastic SIS epidemic model with Beddington-DeAngelis incidence rate was proposed and investigated.Firstly,for the deterministic model,the stability of the equilibrium points was studied and the basic reproduction number which determines the extinction or persistence of the epidemic disease was obtained.Then for the stochastic model,the transmission dynamics of the disease was investigated by using the comparison theorem of stochastic differential equation and It8 formula,and the threshold which determines the extinction or persistence of the epidemic disease was got when the noise was small.The results show that large stochastic noise will suppress the spread of the epidemic.Lastly,numerical simulations were carried out to illustrate the theoretical results.