中国物理B ›› 2009, Vol. 18 ›› Issue (4): 1306-1311.doi: 10.1088/1674-1056/18/4/002

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Effect of incubation period on epidemic spreading in complex networks

黄炜, 姜锐, 胡茂彬, 吴清松   

  1. School of Engineering Science, University of Science and Technology of China, Hefei 230026, China
  • 收稿日期:2008-08-02 修回日期:2008-08-22 出版日期:2009-04-20 发布日期:2009-04-20

Effect of incubation period on epidemic spreading in complex networks

Huang Wei(黄炜), Jiang Rui(姜锐), Hu Mao-Bin(胡茂彬), and Wu Qing-Song(吴清松)   

  1. School of Engineering Science, University of Science and Technology of China, Hefei 230026, China
  • Received:2008-08-02 Revised:2008-08-22 Online:2009-04-20 Published:2009-04-20

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摘要： We study the effect of incubation period on epidemic spreading in the Barabasi--Albert scale-free network and the Watts--Strogatz small world network by using a Suspectable-Incubated-Infected-Suspectable model. Our analytical investigations show that the epidemic threshold is independent of incubation period in both networks, which is verified by our large-scale simulation results. We also investigate the effect of incubation period on the epidemic dynamics in a supercritical regime. It is found that with the increase of incubation period Ω , a damped oscillation evolution of ρT(the ratio of persons in incubated state) appears and the time needed to reach a saturation value increases. Moreover, the steady value of ρT increases and approaches to an asymptotic constant with the value of {\it\Omega} increasing. As a result, the infected ratio ρI decreases with the increase of Ω according to a power law.

关键词: epidemic spreading, incubation period, complex network

Abstract: We study the effect of incubation period on epidemic spreading in the Barabasi--Albert scale-free network and the Watts--Strogatz small world network by using a Suspectable-Incubated-Infected-Suspectable model. Our analytical investigations show that the epidemic threshold is independent of incubation period in both networks, which is verified by our large-scale simulation results. We also investigate the effect of incubation period on the epidemic  dynamics in a supercritical regime. It is found that with the increase of incubation period ${\it\Omega} $, a damped oscillation evolution of $\rho_T$ (the ratio of persons in incubated state) appears and the time needed to reach a saturation value increases. Moreover, the steady value of $\rho _T $ increases and approaches to an asymptotic constant with the value of ${\it\Omega} $ increasing. As a result, the infected ratio $\rho _I$ decreases  with the increase of ${\it\Omega}$ according to a power law.

Key words: epidemic spreading, incubation period, complex network

中图分类号:  (Networks and genealogical trees)

  • 89.75.Hc
87.18.Sn (Neural networks and synaptic communication) 87.19.X- (Diseases) 87.10.-e (General theory and mathematical aspects)