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Chin. Phys. B, 2009, Vol. 18(8): 03309    DOI: 10.1088/1674-1056/18/8/035
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Epidemic spreading on networks with vaccination

Shi Hong-Jinga, Duan Zhi-Shenga, Li Ronga, Chen Guan-Rongb
a State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China; b 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
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.
Keywords:  epidemic modeling      vaccination      complex network      disease spreading      SIS model      epidemic threshold     
Received:  10 February 2009      Published:  20 August 2009
PACS:  87.19.X- (Diseases)  
  02.60.Cb (Numerical simulation; solution of equations)  
  87.10.-e (General theory and mathematical aspects)  
Fund: 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.

Cite this article: 

Shi Hong-Jing, Duan Zhi-Sheng, Chen Guan-Rong, Li Rong Epidemic spreading on networks with vaccination 2009 Chin. Phys. B 18 03309

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