不同阶次下分数阶SIR传染病模型的稳定性分析

建立一类考虑Logistic增长与饱和传染率的不同阶次分数阶时滞传染病模型. 首先, 利用Jacobi矩阵和特征根轨迹法, 分析该模型的局部稳定性, 并给出基本再生数; 其次, 选取分岔参数作为时滞, 给出地方病平衡点发生Hopf分岔的充分条件； 最后, 利用数值仿真验证理论分析的正确性. 研究结果表明, 分数阶次的改变会影响系统的稳定性.

Stability Analysis of Fractional-Order SIR Epidemic Models with Different Orders

Considering Logistic growth and saturated infection rate, we established a class of fractional-order time delay epidemic models with different orders. Firstly, by using Jacobi matrix and eigenvalue trajectory method, we analyzed the local stability of the model and gave the basic reproduction number. Secondly, we selected the bifurcation parameter as the time delay, and gave the sufficient condition for the occurrence of Hopf bifurcation at the endemic equilibrium point. Finally, the correctness of theoretical analysis was verified by numerical simulations. The research results show that the change of fractional-order may affect the stability of the system.