Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand


Dengue fever is a mosquito-borne virus that infects 50–100 million people each year1. Of these infections, 200,000–500,000 occur as the severe, life-threatening form of the disease, dengue haemorrhagic fever (DHF)2. Large, unanticipated epidemics of DHF often overwhelm health systems3. An understanding of the spatial–temporal pattern of DHF incidence would aid the allocation of resources to combat these epidemics. Here we examine the spatial–temporal dynamics of DHF incidence in a data set describing 850,000 infections occurring in 72 provinces of Thailand during the period 1983 to 1997. We use the method of empirical mode decomposition4 to show the existence of a spatial–temporal travelling wave in the incidence of DHF. We observe this wave in a three-year periodic component of variance, which is thought to reflect host–pathogen population dynamics5,6. The wave emanates from Bangkok, the largest city in Thailand, moving radially at a speed of 148 km per month. This finding provides an important starting point for detecting and characterizing the key processes that contribute to the spatial–temporal dynamics of DHF in Thailand.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Example of the EMD sifting process.
Figure 2: Monthly DHF incidence in each of the 72 provinces of Thailand.
Figure 3: The 3-yr periodic mode for each of the 72 provinces of Thailand.
Figure 4: Spatial synchrony of DHF incidence (blue) and the 3-yr periodic mode of variance (red) across 72 provinces of Thailand with 95% C.I. envelopes (see Methods).
Figure 5: Cross-correlation coefficients between the 3-yr oscillatory mode of DHF incidence in Bangkok and the same mode of DHF incidence in the 71 other provinces of Thailand.


  1. 1

    Gubler, D. J. Dengue and dengue hemorrhagic fever. Clin. Microbiol. Rev. 11, 480–496 (1998)

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  2. 2

    Gubler, D. J. The global pandemic of dengue/dengue haemorrhagic fever: current status and prospects for the future. Ann. Acad. Med. Singapore 27, 227–234 (1998)

    CAS  PubMed  Google Scholar 

  3. 3

    DeRoeck, D., Deen, J. & Clemens, J. D. Policymakers' views on dengue fever/dengue haemorrhagic fever and the need for dengue vaccines in four southeast Asian countries. Vaccine 22, 121–129 (2003)

    Article  PubMed  Google Scholar 

  4. 4

    Huang, N. E. et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A 454, 903–995 (1998)

    ADS  MathSciNet  Article  Google Scholar 

  5. 5

    Ferguson, N., Anderson, R. & Gupta, S. The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. Proc. Natl Acad. Sci. USA 96, 790–794 (1999)

    ADS  CAS  Article  PubMed  Google Scholar 

  6. 6

    Hay, S. I. et al. Etiology of interepidemic periods of mosquito-borne disease. Proc. Natl Acad. Sci. USA 97, 9335–9339 (2000)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Chareonsook, O., Foy, H. M., Teeraratkul, A. & Silarug, N. Changing epidemiology of dengue hemorrhagic fever in Thailand. Epidemiol. Infect. 122, 161–166 (1999)

    CAS  Article  PubMed  PubMed Central  Google Scholar 

  8. 8

    Watts, D. M., Burke, D. S., Harrison, B. A., Whitmire, R. E. & Nisalak, A. Effect of temperature on the vector efficiency of Aedes aegypti for dengue 2 virus. Am. J. Trop. Med. Hyg. 36, 143–152 (1987)

    CAS  Article  PubMed  Google Scholar 

  9. 9

    Tun-Lin, W., Burkot, T. R. & Kay, B. H. Effects of temperature and larval diet on development rates and survival of the dengue vector Aedes aegypti in north Queensland, Australia. Med. Vet. Entomol. 14, 31–37 (2000)

    CAS  Article  PubMed  Google Scholar 

  10. 10

    Gubler, D. J. & Rosen, L. Quantitative aspects of replication of dengue viruses in Aedes albopictus (Diptera: Culicidae) after oral and parenteral infection. J. Med. Entomol. 13, 469–472 (1977)

    CAS  Article  PubMed  Google Scholar 

  11. 11

    Rosen, L., Roseboom, L. E., Gubler, D. J., Lien, J. C. & Chaniotis, B. N. Comparative susceptibility of mosquito species and strains to oral and parenteral infection with dengue and Japanese encephalitis viruses. Am. J. Trop. Med. Hyg. 34, 603–615 (1985)

    CAS  Article  PubMed  Google Scholar 

  12. 12

    Grenfell, B. T., Bjornstad, O. N. & Kappey, J. Travelling waves and spatial hierarchies in measles epidemics. Nature 414, 716–723 (2001)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Bjornstad, O. N., Peltonen, M., Liebhold, A. M. & Baltensweiler, W. Waves of larch budmoth outbreaks in the European alps. Science 298, 1020–1023 (2002)

    ADS  CAS  Article  PubMed  Google Scholar 

  14. 14

    Bacon, P. J. Population Dynamics of Rabies in Wildlife (Academic, London, 1985)

    Google Scholar 

  15. 15

    Sherratt, J. A. Periodic travelling waves in cyclic predator–prey systems. Ecol. Lett. 4, 30–37 (2001)

    Article  Google Scholar 

  16. 16

    Mollison, D. Modeling biological invasions—chance, explanation, prediction. Phil. Trans. R. Soc. Lond. B 314, 675–693 (1986)

    ADS  Article  Google Scholar 

  17. 17

    Bjornstad, O. N., Ims, R. A. & Lambin, X. Spatial population dynamics: analyzing patterns and processes of population synchrony. Trends Ecol. Evol. 14, 427–432 (1999)

    CAS  Article  PubMed  Google Scholar 

  18. 18

    Bjornstad, O. N. & Falck, W. Nonparametric spatial covariance functions: estimation and testing. Environ. Ecol. Stat. 8, 53–70 (2001)

    MathSciNet  Article  Google Scholar 

  19. 19

    Lambin, X., Elston, D. A., Petty, S. J. & MacKinnon, J. L. Spatial asynchrony and periodic travelling waves in cyclic populations of field voles. Proc. R. Soc. Lond. B 265, 1491–1496 (1998)

    CAS  Article  Google Scholar 

  20. 20

    de Roos, A. M., McCauley, E. & Wilson, W. G. Pattern formation and the spatial scale of interaction between predators and their prey. Theor. Popul. Biol. 53, 108–130 (1998)

    Article  PubMed  Google Scholar 

  21. 21

    Coulson, T. et al. Age, sex, density, winter weather, and population crashes in Soay sheep. Science 292, 1528–1531 (2001)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Nisalak, A. et al. Serotype-specific dengue virus circulation and dengue disease in Bangkok, Thailand from 1973 to 1999. Am. J. Trop. Med. Hyg. 68, 191–202 (2003)

    Article  PubMed  Google Scholar 

  23. 23

    Gubler, D. J. et al. Virological surveillance for dengue hemorrhagic-fever in Indonesia using the mosquito inoculation technique. Bull. WHO 57, 931–936 (1979)

    CAS  PubMed  Google Scholar 

  24. 24

    Anderson, R. M., Grenfell, B. T. & May, R. M. Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination: time series analysis. J. Hyg. (Lond.) 93, 587–608 (1984)

    CAS  Article  PubMed Central  Google Scholar 

Download references


We thank O. Bjornstad for making R code available.This work was supported by grants from the National Oceanic and Atmospheric Administration's Joint Program on Climate Variability and Human Health (a consortium including the EPA, NASA, NSF and EPRI), and the Bill and Melinda Gates Foundation.

Author information



Corresponding author

Correspondence to Donald S. Burke.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Supplementary information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Cummings, D., Irizarry, R., Huang, N. et al. Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand. Nature 427, 344–347 (2004).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing