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《College Mathematics》 2018-01
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Analysis of a Nonlinear SIR Epidemic Model with Pulse Vaccination and Treatment

ZHU Fang-fang;TANG Xue-ning;MENG Xin-zhu;College of Mathematics and Systems Science,Shandong University of Science and Technology;  
This paper proposes a novel SIR epidemic model with twice pulse process which considers the pulse vaccination and pulse treatment.By using stroboscopic map and Floquet theory,we investigate the existence and local stability of the disease-free periodic solution,which implies the epidemic disease may go to extinction ultimately.In addition,we show that the disease may be persistent and epidemic under some conditions,and we obtain the basic reproduction number which determines whether or not epidemics occur.Finally,numerical simulation analysis is applied to illustrate the influences of pulse vaccination and pulse treatment on disease control.
【Fund】: 国家自然科学基金(11371230);; 山东省自然科学基金(ZR2015AQ001)
【CateGory Index】: O175
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