Skip to main content

Advertisement

SpringerLink
Log in

Epidemics with short and long-range interactions: role of vector dispersal patterns

  • Interdisciplinary Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We study the properties of the SIDRV (Susceptible-Infectious-Detected-Recovered-Vaccinated) model of the epidemic spread with local and non-local infection spread. The local spread is introduced by the nearest neighbors’ interactions while the non-local spread is produced by vectors performing a random walk onto the system topology. Within the model we focus on a study of vectors’ properties and on the interplay between vectors’ characteristics and their dispersal patterns. We search for a type of a random walk which maximizes the time for which vectors are in the infectious state and consequently contribute to the (non-local) infection spread for the longest time. We also search for a type of a random walk which leads to the highest severity of epidemics. On the basis of numerical simulations we can conclude that from the whole considered class of random walks some are favored over others. We also show a very different performance and sensitivity of efficiency measures related to time and epidemics severity. Finally, we assess the role of assumptions taken within the model and discuss its relevance in designing elimination strategies, showing crucial role of local control strategies.

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

Access this article

Log in via an institution

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. A.J. Stacey, J.E. Truscott, M.J.C. Asher, C.A. Gilligan, Phytopathology 94, 209 (2004)

    Article  Google Scholar 

  2. D.M. Rizzo, M. Garbelotto, E.M. Hansen, Annu. Rev. Phytopathol. 43, 309 (2005)

    Article  Google Scholar 

  3. J. Swinton, C.A. Gilligan, Proc. R. Soc. London Ser. B 351(1340), 605 (1996)

    ADS  Google Scholar 

  4. M.F. Shlesinger, J. Klafter, Lévy walks versus Lévy flights, in On Growth and Form: Fractal and Non-Fractal Patterns in Physics, edited by H.E. Stanley, N. Ostrowsky (Springer Verlag, Berlin, 1986), p. 279

    Google Scholar 

  5. A.M. Reynolds, C.J. Rhodes, Ecology 90, 877 (2009)

    Article  Google Scholar 

  6. A.M. Edwards, R.A. Phillips, N.W. Watkins, M.P. Freeman, E.J. Murphy, V. Afanasyev, S.V. Buldyrev, M.G.E. da Luz, E.P. Raposo, H.E. Stanley et al., Nature (London 449, 1044 (2007)

    Article  ADS  Google Scholar 

  7. D. Boyer, G. Ramos-Fernandez, O. Miramontes, J.L. Mateos, G. Cocho, H. Larralde, H. Ramos, F. Rojas, Proc. R. Soc. London Ser. B 273, 1743 (2006)

    Article  Google Scholar 

  8. D.W. Sims, E.J. Southall, N.E. Humphries, G.C. Hays, C.J.A. Bradshaw, J.W. Pitchford, A. James, M.Z. Ahmed, A.S. Brierley, M.A. Hindell et al., Nature (London) 451, 1098 (2008)

    Article  ADS  Google Scholar 

  9. D. Brockmann, L. Hufnagel, T. Geisel, Nature (London) 439, 462 (2006)

    Article  ADS  Google Scholar 

  10. R.M. Anderson, R.M. May, Infectious Diseases of Humans: Dynamics and Control (Oxford University Press, Oxford, 1991)

    Google Scholar 

  11. M.J. Keeling, M.E.J. Woolhouse, R.M. May, G. Davies, B.T. Grenfell, Nature (London) 421, 136 (2003)

    Article  ADS  Google Scholar 

  12. M.J. Tildesley, N.J. Savill, D.J. Shaw, R. Deardon, S.P. Brooks, M.E.J. Woolhouse, B.T. Grenfell, M.J. Keeling, Nature (London) 440, 83 (2006)

    Article  ADS  Google Scholar 

  13. S. Barrett, M. Hoel, Environ. Devel. Econ. 12, 627 (2007)

    Google Scholar 

  14. B. Dybiec, A. Kleczkowski, C.A. Gilligan, J. R. Soc. Interface 6, 941 (2009)

    Google Scholar 

  15. H.W. Hethcote, SIAM Rev. 42, 599 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. B. Dybiec, A. Kleczkowski, C.A. Gilligan, Phys. Rev. E 70, 066145 (2004)

    Article  ADS  Google Scholar 

  17. B. Dybiec, A. Kleczkowski, C.A. Gilligan, Acta Phys. Pol. B 36, 1509 (2005)

    ADS  Google Scholar 

  18. A. Kleczkowski, B. Dybiec, C.A. Gilligan, Acta Phys. Pol. B 37, 3017 (2006)

    ADS  Google Scholar 

  19. A. Janicki, A. Weron, Simulation and Chaotic Behavior of α-Stable Stochastic Processes (Marcel Dekker, New York, 1994)

    Google Scholar 

  20. A. Weron, R. Weron, Lect. Not. Phys. 457, 379 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  21. R.M. Haynes, Geografiska Annaler B 56, (1974)

  22. W. Feller, An Introduction to Probability Theory and its Applications (John Wiley, New York, 1968)

    MATH  Google Scholar 

  23. R. Weron, Statist. Probab. Lett. 28, 165 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  24. R.S. Greenberg, S.R. Daniels, W.D. Flanders, J.W. Eley, J.R. Boring, Medical epidemiology (McGraw-Hill Medical, 2004)

  25. G.M. Viswanathan, V. Afanasyev, S.V. Buldyrev, E.J. Murphy, P.A. Prince, H.E. Stanley, Nature (London) 381, 413 (1996)

    Article  ADS  Google Scholar 

  26. Z. Dezso, A.L. Barabasi, Phys. Rev. E 65, 055103 (2002)

    Article  ADS  Google Scholar 

  27. K.J. Sharkey, R.G. Bowers, K.L. Morgan, S.E. Robinson, R.M. Christley, Proc. R. Soc. London Ser. B 275, 19 (2008)

    Article  Google Scholar 

  28. K.T.D. Eames, M.J. Keeling, Proc. R. Soc. London Ser. B 270, 2565 (2003)

    Article  Google Scholar 

  29. B. Dybiec, Physica A 387, 4863 (2008)

    Article  ADS  Google Scholar 

  30. T.C. Germann, K. Kadau, I.M. Longini, C.A. Macken, Proc. Natl. Acad. Sci. U.S.A. 103, 5935 (2006)

    Article  ADS  Google Scholar 

  31. M. Ajelli, S. Merler, PLoS ONE 3, e1519 (2008)

    Article  Google Scholar 

  32. P. Wang, M.C. Gonzalez, C.A. Hidalgo, A.L. Barabasi, Science 324, 1071 (2009)

    Article  ADS  Google Scholar 

  33. World Health Organization, Influenza A(H1N1), http://www.who.int/csr/disease/swineflu (2009)

Download references

Author information

Authors and Affiliations

  1. Marian Smoluchowski Institute of Physics, and Mark Kac Center for Complex Systems Research, Jagellonian University, ul. Reymonta 4, 30–, 059, Kraków, Poland

    B. Dybiec

  2. Center for Models of Life, Niels Bohr Institute, Blegdamsvej 17, 2100, Copenhagen Ø, Denmark

    B. Dybiec

Authors
  1. B. Dybiec
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Dybiec.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dybiec, B. Epidemics with short and long-range interactions: role of vector dispersal patterns. Eur. Phys. J. B 72, 685–693 (2009). https://doi.org/10.1140/epjb/e2009-00403-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2009-00403-1

Keywords

Search

Navigation