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Dynamical diversity induced by individual responsive immunization

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  • Wu, Qingchu
  • Liu, Huaxiang
  • Small, Michael

Abstract

A voluntary vaccination allows for a healthy individual to choose vaccination according to the individual’s local information. Hence, vaccination has the potential to provide a complex negative feedback (non-infection decreases propensity for vaccination, hence increasing infection and vice versa). In this paper, we investigate a kind of SIS epidemic model with a deterministic and voluntary vaccination scheme in scale-free networks. We first study a threshold model with no historical information. By using the comparative method we confirm that under some conditions there exist two critical values of infection rates to determine three kinds of epidemic dynamical behaviors: the epidemic spread, the asymptotical decay and the exponential decay. Furthermore, a mean-field approximation model can predict the maximal infection level but cannot predict the existence of two critical infection rates. In numerical simulations, we observe a maximum in epidemic duration as a function of the model parameter. A similar phenomenon has been found in the model with historical information. Finally, we study a degree-weighted model with a nonnegative exponent α where α=0 corresponds to the threshold model. We find that at the steady state the infection density increases with α, while the variation of the vaccination fraction is less straightforward.

Suggested Citation

  • Wu, Qingchu & Liu, Huaxiang & Small, Michael, 2013. "Dynamical diversity induced by individual responsive immunization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(12), pages 2792-2802.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:12:p:2792-2802
    DOI: 10.1016/j.physa.2013.02.014
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    References listed on IDEAS

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    1. Wang, Yubo & Xiao, Gaoxi & Hu, Jie & Cheng, Tee Hiang & Wang, Limsoon, 2009. "Imperfect targeted immunization in scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2535-2546.
    2. Timothy C Reluga, 2010. "Game Theory of Social Distancing in Response to an Epidemic," PLOS Computational Biology, Public Library of Science, vol. 6(5), pages 1-9, May.
    3. Nyabadza, Farai & Mukwembi, Simon & Rodrigues, Bernardo Gabriel, 2009. "A tuberculosis model: The case of ‘reasonable’ and ‘unreasonable’ infectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(10), pages 1995-2000.
    4. Tsimring, Lev S & Huerta, Ramón, 2003. "Modeling of contact tracing in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 33-39.
    5. Bai, Wen-Jie & Zhou, Tao & Wang, Bing-Hong, 2007. "Immunization of susceptible–infected model on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 656-662.
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    Cited by:

    1. Wu, Qingchu & Fu, Xinchu & Jin, Zhen & Small, Michael, 2015. "Influence of dynamic immunization on epidemic spreading in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 566-574.
    2. Wang, Xiaoyang & Wang, Ying & Zhu, Lin & Li, Chao, 2016. "A novel approach to characterize information radiation in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 94-105.

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