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The Periodic Solution of a SIR Epidemic Model with Periodic Vertical Infection Rate

LI Lu-ping1,2,JIA Jian-wen2(1.School of Mathematical and Computer Science,Shanxi Datong University,Datong 037009,China)(2.School of Mathematical and Computer Science,Shanxi Normal University,Linfen 041004,China)  
A SIR model with periodic vertical infection rate is studied.The dynamical behavior of the model is analyzed.For the model in the small amplitude,we give the approximate expression of the periodic solution and show that the periodic solution is stable.The numerical simulation supports our conjecture.
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