Asymptotic behavior of stochastic multi-group epidemic models with distributed delays

作者：Liu, Qun; Jiang, Daqing^*; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

来源：Physica A: Statistical Mechanics and Its Applications , 2017, 467: 527-541.

DOI：10.1016/j.physa.2016.10.034

• Stochastic multi-group epidemic model
• Distributed delay
• Disease-free equilibrium
• Endemic equilibrium
• Lyapunov functional

In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R-0. If R-0 <= 1, the solution of the stochastic system oscillates around the disease-free equilibrium E-0, while if R-0 > 1, the solution of the stochastic model fluctuates around the endemic equilibrium E*. Moreover, we also establish sufficient conditions of these results.

• 出版日期2017-2-1
• 单位东北师范大学; 中国石油大学（华东）; 玉林师范学院