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《Mathematics in Practice and Theory》 2018-18
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Analysis of Delay Dynamic Model of Brucellosis Based on Disease Testing

NAN Yao-yao;HOU Qiang;YANG Xiao-feng;School of Science, North University of China;  
Testing and killing measures play an important role in the prevention and control of animal diseases, especially the brucella. Due to the influence of testing behavior standards,time lag and other factors on the transmission dynamics of brucella, detection behavior is very significant. In this paper, the time lag dynamic model is established based on the specific features of brucellosis detection. First, the basic reproduction number and the equilibrium point are calculated, when R_0 ≤1, the system(1) has one disease free equilibrium point E_0;when R_01 R_c, the system(1) has an endemic equilibrium point E_1~*; when R_c 1, the system(1) has an endemic equilibrium point E_2~*.Secondly, the stability of the equilibrium point is analyzed. And by the method of numerical analysis it is found when the τ exceeded the critical value, the model would have periodic oscillations, which indicated that the delay in detection time could lead to the periodic fluctuation of the epidemic disease.
【Fund】: 国家自然科学青年基金(11501528);; 山西省自然科学青年基金(2015021018)
【CateGory Index】: S855.12
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