【摘要】：【目的】研究了一類具有非線性發(fā)生率的SIR傳染病模型,分析該系統(tǒng)在非平凡平衡點(diǎn)處的穩(wěn)定性和Hopf分支�！痉椒ā窟\(yùn)用正規(guī)形理論和中心流形投影定理,討論了該系統(tǒng)在平衡點(diǎn)處的穩(wěn)定性�！窘Y(jié)果】得到第一Laypunov系數(shù),當(dāng)l1(0)0時(shí),該系統(tǒng)是不穩(wěn)定的亞臨界分支;當(dāng)l1(0)0時(shí),該系統(tǒng)是穩(wěn)定的超臨界分支�！窘Y(jié)論】得到了系統(tǒng)在非平凡平衡點(diǎn)附近會(huì)產(chǎn)生唯一、穩(wěn)定的極限環(huán),此時(shí)傳染病會(huì)發(fā)生但不會(huì)大規(guī)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.
【作者單位】： 重慶工商大學(xué)融智學(xué)院;重慶商務(wù)職業(yè)學(xué)院財(cái)務(wù)處;
【基金】：國家自然科學(xué)基金(No.11304403)
【分類號(hào)】：O175
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本文編號(hào)：2520869