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Travelling waves and spatial hierarchies in measles epidemics

Author

Listed:
  • B. T. Grenfell

    (University of Cambridge)

  • O. N. Bjørnstad

    (University of Cambridge
    501 ASI Building, Penn State University)

  • J. Kappey

    (University of Cambridge)

Abstract

Spatio-temporal travelling waves are striking manifestations of predator–prey and host–parasite dynamics. However, few systems are well enough documented both to detect repeated waves and to explain their interaction with spatio-temporal variations in population structure and demography. Here, we demonstrate recurrent epidemic travelling waves in an exhaustive spatio-temporal data set for measles in England and Wales. We use wavelet phase analysis, which allows for dynamical non-stationarity—a complication in interpreting spatio-temporal patterns in these and many other ecological time series. In the pre-vaccination era, conspicuous hierarchical waves of infection moved regionally from large cities to small towns; the introduction of measles vaccination restricted but did not eliminate this hierarchical contagion. A mechanistic stochastic model suggests a dynamical explanation for the waves—spread via infective ‘sparks’ from large ‘core’ cities to smaller ‘satellite’ towns. Thus, the spatial hierarchy of host population structure is a prerequisite for these infection waves.

Suggested Citation

  • B. T. Grenfell & O. N. Bjørnstad & J. Kappey, 2001. "Travelling waves and spatial hierarchies in measles epidemics," Nature, Nature, vol. 414(6865), pages 716-723, December.
  • Handle: RePEc:nat:nature:v:414:y:2001:i:6865:d:10.1038_414716a
    DOI: 10.1038/414716a
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    Cited by:

    1. Sourya Shrestha & Aaron A King & Pejman Rohani, 2011. "Statistical Inference for Multi-Pathogen Systems," PLOS Computational Biology, Public Library of Science, vol. 7(8), pages 1-14, August.
    2. Nicola Bellomo & Richard Bingham & Mark A.J. Chaplain & Giovanni Dosi & Guido Forni & Damian A. Knopoff & John Lowengrub & Reidun Twarock & Maria Enrica Virgillito, 2020. "A multi-scale model of virus pandemic: Heterogeneous interactive entities in a globally connected world," LEM Papers Series 2020/16, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    3. Yusuf Amuda Tajudeen & Habeebullah Jayeola Oladipo & Iyiola Olatunji Oladunjoye & Mutiat Oluwakemi Mustapha & Sheriff Taye Mustapha & Adam Aberi Abdullahi & Rashidat Onyinoyi Yusuf & Samuel Olushola A, 2022. "Preventing the Next Pandemic through a Planetary Health Approach: A Focus on Key Drivers of Zoonosis," Challenges, MDPI, vol. 13(2), pages 1-14, September.
    4. Ngamsa Tegnitsap, J.V. & Fotsin, H.B., 2022. "Multistability, transient chaos and hyperchaos, synchronization, and chimera states in wireless magnetically coupled VDPCL oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    5. Mohan, Nishith & Kumari, Nitu, 2021. "Positive steady states of a SI epidemic model with cross diffusion," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    6. Campi, Gaetano & Bianconi, Antonio, 2022. "Periodic recurrent waves of Covid-19 epidemics and vaccination campaign," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Chryssi Giannitsarou & Stephen Kissler & Flavio Toxvaerd, 2021. "Waning Immunity and the Second Wave: Some Projections for SARS-CoV-2," American Economic Review: Insights, American Economic Association, vol. 3(3), pages 321-338, September.
    8. Goldwyn, Eli E. & Hastings, Alan, 2008. "When can dispersal synchronize populations?," Theoretical Population Biology, Elsevier, vol. 73(3), pages 395-402.
    9. Wang, Yi & Cao, Jinde & Sun, Gui-Quan & Li, Jing, 2014. "Effect of time delay on pattern dynamics in a spatial epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 137-148.
    10. Yujie Yuan & Yantao Wang & Xiushan Jiang & Chun Sing Lai, 2024. "An Innovative Multi-Objective Rescheduling System for Mitigating Pandemic Spread in Aviation Networks," Clean Technol., MDPI, vol. 6(1), pages 1-16, January.
    11. Chun-Hsiang Chan & Tzai-Hung Wen, 2021. "Revisiting the Effects of High-Speed Railway Transfers in the Early COVID-19 Cross-Province Transmission in Mainland China," IJERPH, MDPI, vol. 18(12), pages 1-17, June.
    12. Wladimir J Alonso & Maia A Rabaa & Ricardo Giglio & Mark A Miller & Cynthia Schuck-Paim, 2015. "Modeling the Impact of Alternative Immunization Strategies: Using Matrices as Memory Lanes," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-11, October.
    13. Jose Angulo & Hwa-Lung Yu & Andrea Langousis & Alexander Kolovos & Jinfeng Wang & Ana Esther Madrid & George Christakos, 2013. "Spatiotemporal Infectious Disease Modeling: A BME-SIR Approach," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-12, September.
    14. Wan Yang & Liang Wen & Shen-Long Li & Kai Chen & Wen-Yi Zhang & Jeffrey Shaman, 2017. "Geospatial characteristics of measles transmission in China during 2005−2014," PLOS Computational Biology, Public Library of Science, vol. 13(4), pages 1-21, April.
    15. Dirk Douwes‐Schultz & Alexandra M. Schmidt, 2022. "Zero‐state coupled Markov switching count models for spatio‐temporal infectious disease spread," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 589-612, June.
    16. Frey, Erwin, 2010. "Evolutionary game theory: Theoretical concepts and applications to microbial communities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(20), pages 4265-4298.
    17. Suresh, R. & Senthilkumar, D.V. & Lakshmanan, M. & Kurths, J., 2016. "Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 235-245.
    18. Munro, Alastair D. & Smallman-Raynor, Matthew & Algar, Adam C., 2021. "Long-term changes in endemic threshold populations for pertussis in England and Wales: A spatiotemporal analysis of Lancashire and South Wales, 1940-69," Social Science & Medicine, Elsevier, vol. 288(C).

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