Dynamics of an SIR epidemic model with stage structure and pulse vaccination. (English) Zbl 1418.92215
Summary: Pulse vaccination is an important strategy to eradicate an infectious disease. In this paper, we investigate an SIR epidemic model with stage structure and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, we obtain the conditions for the global asymptotical stability of the infection-free periodic solution of the studied system. The permanent conditions of the investigated system are also given. The results indicate that a large pulse vaccination rate is a sufficient condition to eradicate the disease. It provides a reliable tactic basis for preventing the epidemic outbreak.
MSC:
| 92D30 | Epidemiology |
| 92C60 | Medical epidemiology |
| 34K20 | Stability theory of functional-differential equations |
| 34A37 | Ordinary differential equations with impulses |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 92D25 | Population dynamics (general) |
Keywords:
SIR epidemic model; stage structure; global asymptotical stability; permanence; pulse vaccinationReferences:
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