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Global dynamics and bifurcation in delayed SIR epidemic model. (English) Zbl 1235.34216

The authors extend the work of J.-Z. Zhang et al. [Discrete Dyn. Nat. Soc. 2008, Article ID 636153 (2008; Zbl 1159.92037)] by incorporating a new variable into the model denoting the information about the current state of disease and formulate an SIR epidemic model with time delay. Then, they discuss the existence of transcritical bifurcation, Hopf bifurcation, and the local and global stability of the endemic equilibrium. Finally, numerical simulations are carried out to explain the mathematical conclusions.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K18 Bifurcation theory of functional-differential equations
92D30 Epidemiology
34K20 Stability theory of functional-differential equations

Citations:

Zbl 1159.92037
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References:

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