Research article Special Issues

The impact of media converge on complex networks on disease transmission

  • Received: 26 March 2019 Accepted: 03 July 2019 Published: 09 July 2019
  • In this paper, we propose an epidemic disease model about the effect of media coverage on complex networks, where the contacts between nodes are treated as a social network. We calculate the basic reproduction number R0 and get that the disease-free equilibrium is locally and globally asymptotically stable if R0 < 1, otherwise disease-free equilibrium is unstable and there exists a unique endemic equilibrium, and the disease is permanent. And two immunization strategies are considered: proportional and target immunization. By comparing two immunization strategies, it is found that the target immunization is better than the proportional immunization. Finally, numerical simulations verify our results and some discussions of vaccination strategies are done in the control of infectious dseases.

    Citation: Maoxing Liu, Shushu He, Yongzheng Sun. The impact of media converge on complex networks on disease transmission[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6335-6349. doi: 10.3934/mbe.2019316

    Related Papers:

  • In this paper, we propose an epidemic disease model about the effect of media coverage on complex networks, where the contacts between nodes are treated as a social network. We calculate the basic reproduction number R0 and get that the disease-free equilibrium is locally and globally asymptotically stable if R0 < 1, otherwise disease-free equilibrium is unstable and there exists a unique endemic equilibrium, and the disease is permanent. And two immunization strategies are considered: proportional and target immunization. By comparing two immunization strategies, it is found that the target immunization is better than the proportional immunization. Finally, numerical simulations verify our results and some discussions of vaccination strategies are done in the control of infectious dseases.
    加载中


    [1] M. E. J. Newman, Spread of epidemic disease on networks, Phys. Rev. E, 66 (2002), 016128.
    [2] M. E. J. Newman, The structure and function of complex networks, SIAM Rev., 45 (2003), 167–256.
    [3] M. J. Keeling, The implications of network structure for epidemic dynamics, Theor. Popul. Biol., 67 (2005), 1–8.
    [4] R. Pastor-Satorras and A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001), 3200–3203.
    [5] T. Zhou, J. G. Liu, W. J. Bai, et al., Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity, Phys. Rev. E, 74 (2006), 056109.
    [6] M. Liu and Y. Chen, An SIRS model with differential susceptibility and infectivity on uncorrelated networks, Math. Biosci. Eng., 12 (2015), 415–429.
    [7] J. Liu and T. Zhang, Epidemic spreading of an SEIRS model in scale-free networks, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 3375–3384.
    [8] R. Pastor-Satorras and A. Vespignani, Immunization of complex networks, Phys. Rev. E, 65 (2002), 036104.
    [9] A. d'Onofrio, A note on the global behaviour of the network-based SIS epidemic model, Nonlinear Anal., 9 (2008), 1567–1572.
    [10] J. Lou and T. Ruggeri, The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network, J. Math. Anal. Appl., 365 (2010), 210–219.
    [11] W. J. Reed, A stochastic model for the spread of a sexually transmitted disease which results in a scale-free network, Math. Biosci., 201 (2006), 3–14.
    [12] M. Liu and J. Ruan, Modelling the spread of sexually transmitted diseases on scale-free networks, Chinese Physics B, 18 (2009), 2115–2120.
    [13] S. Funk, M. Salathé and V. A. A. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: a review, J. R. Soc. Interf., 7 (2010), 1247–1256.
    [14] R. Liu, J. Wu and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infec-tious diseases, Comput. Math. Methods Med., 8 (2007), 153–164.
    [15] J. Tchuenche, N. Dube, C. Bhunu, et al., The impact of media coverage on the transmission dynamics of human influenza, BMC Public Health, 11 (2011), S5.
    [16] M. Liu, E. Liz and G. Röst, Endemic bubbles generated by delayed behavioral response–global stability and bifurcation switches in an SIS model, SIAM J. Appl. Math., 75 (2015), 75–91.
    [17] L. Zuo, M. Liu and J. Wang, The impact of awareness programs with recruitment and delay on the spread of an epidemic, Math. Prob. Eng., 2014 (2014), 235935.
    [18] S. Collinson and J. M. Heffernan, Modelling the effects of media during an influenza epidemic, BMC Public Health, 14 (2014), 1–10.
    [19] K. A. Pawelek, A. Oeldorf-Hirsch and L. Rong, Modeling the impact of twitter on influenza epidemics, Math. Biosci. Eng., 11 (2014), 1337–1356.
    [20] D. Greenhalgh, S. Rana, S. Samanta, et al., Awareness programs control infectious disease-Multiple delay induced mathematical model, Appl. Math. Comput., 251 (2015), 539–563.
    [21] Y. Wang, J. Cao, Z. Jin, et al., Impact of media coverage on epidemic spreading in complex networks, Phys. A, 392 (2013), 5824–5835.
    [22] X. Yuan, Y. Xue and M. Liu, Analysis of an epidemic model with awareness programs by media on complex networks, Chaos Soli. Frac., 48 (2013), 1–11.
    [23] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equi-libria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
    [24] P. De Leenheer and H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math., 63 (2003), 1313–1327.
    [25] H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993), 407–435.

    © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
  • Reader Comments
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(539) PDF downloads(592) Cited by(0)

Article outline

Figures and Tables

Figures(3)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog