Skip to main content

Advertisement

Log in

An SIR model with infection delay and propagation vector in complex networks

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Based on the SIR (Susceptible-Infected-Removed) model, we propose a novel epidemic model to investigate the impact of infection delay and propagation vector on the spreading behaviors in complex networks. Mean-field approximations and extensive numerical simulations indicate that the infection delay and propagation vector can largely reduce the critical threshold and promote the outbreak of epidemics, and even lead to the case that the infectious diseases transform from the disease-free state to endemic one. The current results are greatly instructive for us to further understand the epidemic spreading and design some effective prevention and containment strategies to fight the epidemics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Proulx, S.R., Promislow, D.E.L., Philips, P.C.: Network thinking in ecology and evolution. Trends Ecol. Evol. 20(6), 345–353 (2005)

    Article  Google Scholar 

  2. Keeling, M.J., Eames, K.T.D.: Networks and epidemic models. J. R. Soc. Interface 2, 295–307 (2005)

    Article  Google Scholar 

  3. Hypponen, M.: Malware goes mobile. Sci. Am. 10, 70–77 (2006)

    Article  Google Scholar 

  4. Kleinberg, J.: The wireless epidemic. Nature 449, 287–288 (2007)

    Article  Google Scholar 

  5. Eubank, S., Guclu, H., Kumar, V.S.A., Marathe, M.V., Srinivasan, A., Toroczkai, Z., Wang, N.: Modeling disease outbreaks in realistic urban social networks. Nature 429, 180–184 (2004)

    Article  Google Scholar 

  6. Wang, X.F., Chen, G.R.: Complex networks: small-world, scale-free and beyond. IEEE Circuits Syst. Mag. 3(1), 6–20 (2003)

    Article  Google Scholar 

  7. Cui, L.Y., Kumara, S., Albert, R.: Complex networks: an engineering view. IEEE Circuits Syst. Mag. 10(3), 10–25 (2010)

    Article  Google Scholar 

  8. Xu, X.L., Chen, Z.Q., Si, G.Y., Hu, X.F., Jiang, Y.Q., Xu, X.S.: The chaotic dynamics of the social behavior selection networks in crowd simulation. Nonlinear Dyn. 64(1–2), 117–126 (2011)

    Article  MathSciNet  Google Scholar 

  9. Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86(13), 3200–3203 (2001)

    Article  Google Scholar 

  10. Moreno, Y., Pastor-Satorras, R., Vespignani, A.: Epidemic outbreaks in complex heterogeneous networks. Eur. Phys. J. B 26, 521–529 (2002)

    Google Scholar 

  11. Barthélemy, M., Barrat, A., Pastor-Satorras, R., Vespignani, A.: Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. Phys. Rev. Lett. 92, 178701 (2004)

    Article  Google Scholar 

  12. Xia, C.Y., Liu, Z.X., Chen, Z.Q., Yu, Z.Z.: Dynamic spreading behaviors of homogeneous and heterogeneous networks. Prog. Nat. Sci. 17(3), 358–365 (2007)

    Article  MATH  Google Scholar 

  13. Xia, C.Y., Liu, Z.X., Chen, Z.Q., Yu, Z.Z.: Epidemic spreading behavior in local-world networks. Prog. Nat. Sci. 18(6), 763–768 (2008)

    Article  Google Scholar 

  14. Li, X., Wang, X.F.: Controlling the spreading in small-world evolving networks: stability, oscillation, and topology. IEEE Trans. Autom. Control 51(3), 534–540 (2006)

    Article  Google Scholar 

  15. Yang, R., Wang, B.H., Ren, J., Bai, W.J., Shi, Z.W., Wang, W.X., Zhou, T.: Epidemic spreading on heterogeneous networks with identical infectivity. Phys. Lett. A 364, 189–193 (2007)

    Article  MATH  Google Scholar 

  16. Wang, J.Z., Liu, Z.R., Xu, J.H.: Epidemic spreading on uncorrelated heterogeneous networks with non-uniform transmission. Physica A 382, 715–721 (2007)

    Article  Google Scholar 

  17. Xia, C.Y., Sun, S.W., Liu, Z.X., Chen, Z.Q., Yu, Z.Z.: Epidemics of SIRS model with nonuniform transmission on scale-free networks. Int. J. Mod. Phys. B 23(9), 2203–2213 (2009)

    Article  MATH  Google Scholar 

  18. Fu, X.C., Small, M., Walker, D.M., Zhang, H.F.: Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization. Phys. Rev. E 77, 036113 (2008)

    Article  MathSciNet  Google Scholar 

  19. Pei, W.D., Chen, Z.Q., Yuan, Z.Z.: Study of epidemic spreading on scale-free networks with finite maximum dissemination. Acta Phys. Sin. 57(11), 6777–6785 (2008) (in Chinese)

    MathSciNet  MATH  Google Scholar 

  20. Xu, D., Li, X., Wang, X.F.: An investigation on local area control of virus spreading in complex networks. Acta Phys. Sin. 56(3), 1313–1317 (2007) (in Chinese)

    Google Scholar 

  21. Huang, W., Li, C.G.: Epidemic spreading in scale-free networks with community structure. J Stat Mech 1, P01014 (2007)

    Article  Google Scholar 

  22. Tang, M., Liu, Z.H., Li, B.W.: Influence of dynamical condensation on epidemic spreading in scale-free networks. Europhys. Lett. 87, 18005 (2009)

    Article  Google Scholar 

  23. Xia, C.Y., Sun, S.W., Rao, F., Sun, J.Q., Wang, J.S., Chen, Z.Q.: SIS model of epidemic spreading on dynamical networks with community. Front. Comput. Sci. China 3(3), 361–365 (2009)

    Article  Google Scholar 

  24. Xia, C.Y., Liu, Z.X., Chen, Z.Q., Yu, Z.Z.: SIRS epidemic model with direct immunization on complex networks. Control Decis. 23(4), 468–472 (2008) (in Chinese)

    MathSciNet  Google Scholar 

  25. Li, X., Cao, L., Cao, G.: Epidemic prevalence on random mobile dynamical networks: individual heterogeneity and correlation. Eur. Phys. J. B 75, 319–326 (2010)

    Article  MATH  Google Scholar 

  26. Yang, Z.Q., Zhang, Q., Chen, Z.Q.: Flocking of multi-agents with nonlinear inner-coupling functions. Nonlinear Dyn. 60(3), 225–264 (2010)

    Article  MathSciNet  Google Scholar 

  27. Xu, X.J., Peng, H.O., Wang, X.M., Wang, Y.H.: Epidemic spreading with time delay in complex networks. Physica A 367, 525–530 (2006)

    Article  Google Scholar 

  28. Li, C.G., Chen, G.R.: Synchronization in general complex dynamical networks with coupling delays. Physica A 343, 263–278 (2004)

    Article  MathSciNet  Google Scholar 

  29. Shi, H.G., Duan, Z.S., Chen, G.: An SIS model with infective medium on complex networks. Physica A 387, 2133–2144 (2008)

    Article  Google Scholar 

  30. Xia, C.Y., Ma, J.H., Chen, Z.Q.: SIR epidemic model with infection medium on complex networks. J. Syst. Eng. 25(6), 818–823 (2010) (in Chinese)

    Google Scholar 

  31. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)

    Article  Google Scholar 

  32. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Chengyi Xia or Juan Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xia, C., Wang, L., Sun, S. et al. An SIR model with infection delay and propagation vector in complex networks. Nonlinear Dyn 69, 927–934 (2012). https://doi.org/10.1007/s11071-011-0313-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-011-0313-y

Keywords

Navigation