Abstract
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.
Highlights
The SIR epidemic model is one of the most popular epidemic models in epidemiology; it was initially proposed by Kermack and Mckendrick
The SIR models have been considered by many researchers [ – ]
For more details of a simple SIR model, we can refer to the books of Hethcote [ ] and Anderson and May [ ]
Summary
The SIR (susceptible, infectious, recovered) epidemic model is one of the most popular epidemic models in epidemiology; it was initially proposed by Kermack and Mckendrick [ – ]. Gao et al [ ] have investigated a delayed SIR epidemic model with pulse vaccination. They conclude that the infection-free periodic solution is globally attractive and the system is permanent. Impulsive equations are found in almost every domain of applied science and have been studied in many investigations [ , , – ]. Motivated by the above studies, our study is to investigate transmission dynamics of an SIR epidemic model with stage structure and pulse vaccination. The present paper is to introduce birth pulse of the population, state structure and pulse vaccination into SIR epidemic model and obtain some important qualitative properties for the investigated system. To the best of our knowledge, no such research has been conducted
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