中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3309-3317.doi: 10.1088/1674-1056/18/8/035

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Epidemic spreading on networks with vaccination

史红静1, 段志生1, 李嵘1, 陈关荣2   

  1. (1)State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China; (2)State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China;Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR
  • 收稿日期:2009-02-10 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60674093, 10832006) and the Hong Kong Research Grants Council under Grant CityU 1117/08E.

Epidemic spreading on networks with vaccination

Shi Hong-Jing(史红静)a)†, Duan Zhi-Sheng(段志生)a), Chen Guan-Rong(陈关荣)a)b), and Li Rong(李嵘)a)   

  1. a State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China; b Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, China
  • Received:2009-02-10 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 60674093, 10832006) and the Hong Kong Research Grants Council under Grant CityU 1117/08E.

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摘要： In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.

Abstract: In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.

Key words: complex network, disease spreading, SIS model, epidemic modeling, vaccination, epidemic threshold

中图分类号:  (Diseases)

  • 87.19.X-
02.60.Cb (Numerical simulation; solution of equations) 87.10.-e (General theory and mathematical aspects)