一类具有非线性发生率的SIR模型的稳定性和Hopf分支
发布时间：2019-07-30 11:28
【摘要】：【目的】研究了一类具有非线性发生率的SIR传染病模型,分析该系统在非平凡平衡点处的稳定性和Hopf分支。【方法】运用正规形理论和中心流形投影定理,讨论了该系统在平衡点处的稳定性。【结果】得到第一Laypunov系数,当l1(0)0时,该系统是不稳定的亚临界分支;当l1(0)0时,该系统是稳定的超临界分支。【结论】得到了系统在非平凡平衡点附近会产生唯一、稳定的极限环,此时传染病会发生但不会大规模流行。
[Abstract]:[Objective]To study a kind of SIR infectious disease model with non-linear incidence rate. [Method]The stability of the system at equilibrium point is discussed by using normal shape theory and central manifold projection theorem. [Results]The first Laypunov coefficient was obtained. When l1(0)0, the system was an unstable subcritical branch. When l1(0)0, the system is a stable supercritical branch. [Conclusion]The system will produce the only and stable limit ring near the non-ordinary equilibrium point. At this time, the infectious disease will occur but will not be spread on a large scale.
【作者单位】： 重庆工商大学融智学院;重庆商务职业学院财务处;
【基金】：国家自然科学基金(No.11304403)
【分类号】：O175
，
本文编号：2520869
[Abstract]:[Objective]To study a kind of SIR infectious disease model with non-linear incidence rate. [Method]The stability of the system at equilibrium point is discussed by using normal shape theory and central manifold projection theorem. [Results]The first Laypunov coefficient was obtained. When l1(0)0, the system was an unstable subcritical branch. When l1(0)0, the system is a stable supercritical branch. [Conclusion]The system will produce the only and stable limit ring near the non-ordinary equilibrium point. At this time, the infectious disease will occur but will not be spread on a large scale.
【作者单位】： 重庆工商大学融智学院;重庆商务职业学院财务处;
【基金】：国家自然科学基金(No.11304403)
【分类号】：O175
，
本文编号：2520869
本文链接：https://www.wllwen.com/kejilunwen/yysx/2520869.html
