一类分数阶SIR流行病模型的稳定性研究  

Study on the Stability of a Kind of Fractional Order SIR Epidemic Model

作　　者：原三领[1] 李小月[1] 许超群[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《生物数学学报》2016年第1期71-82,共12页Journal of Biomathematics

基　　金：国家自然科学基金资助项目(11271260);上海市教委重点创新项目(13ZZ116);中国沪江基金(B14005);上海市一流学科资助项目(XTKX2012)

摘　　要：本文讨论了一类分数阶SIR流行病模型的稳定性问题.对不考虑疾病治疗的情形,利用特征值分析的方法分析了其平衡点的稳定性,并在一定条件下证明了模型一致稳态正解的存在唯一性;在此基础上,进一步考虑了具有治疗的分数阶SIR流行病模型的平衡点的稳定性,得到了其后向分支发生的条件.最后通过数值仿真验证了所得结论的正确性.In this paper, the stability of a kind of fractional order SIR epidemic model is investigated. For the case with no disease treatment, the stabilities of the equilibria are obrained by analyzing the eigenwlues of the model, and under certain conditions the existence and uniqueness of the uniformly steady-state solution is proved. Basis on above, we further consider the stabilities of the equilibria of the fractional order SIR epidemic model with treatment and obtain the condition for the occurring of backward bifurcation. Numerical simulations have been performed to verify the correctness of the obtained results.

关 键 词：分数阶SIR模型 平衡点 一致稳态解 稳定性 后向分支 

分 类 号：Q332[生物学—遗传学]