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- W2016144004 abstract "We consider SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratio<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:msub><mml:mrow><mml:mi>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle=italic>0</mml:mn></mml:mrow></mml:msub><mml:mo><</mml:mo><mml:mn fontstyle=italic>1</mml:mn></mml:math>, we discuss the global asymptotical stability of the disease-free equilibrium by constructing a Lyapunov functional. If<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:msub><mml:mrow><mml:mi>ℛ</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle=italic>0</mml:mn></mml:mrow></mml:msub><mml:mo>></mml:mo><mml:mn fontstyle=italic>1</mml:mn></mml:math>, we obtain sufficient conditions under which the endemic equilibrium<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:msup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>of system is locally asymptotically stable. And we also have discussed the stability and direction of Hopf bifurcations. Numerical simulations are carried out to explain the mathematical conclusions." @default.
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- W2016144004 date "2014-01-01" @default.
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- W2016144004 title "Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources" @default.
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- W2016144004 doi "https://doi.org/10.1155/2014/109372" @default.
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