Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics

M. Aguiar; B.W. Kooi; J. Martins; N. Stollenwerk

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 3, page 1-11
  • ISSN: 0973-5348

Abstract

top
In this paper we analyze the stochastic version of a minimalistic multi-strain model, which captures essential differences between primary and secondary infections in dengue fever epidemiology, and investigate the interplay between stochasticity, seasonality and import. The introduction of stochasticity is needed to explain the fluctuations observed in some of the available data sets, revealing a scenario where noise and complex deterministic skeleton strongly interact. For large enough population size, the stochastic system can be well described by the deterministic skeleton gaining insight on the relevant parameter values purely on topological information of the dynamics, rather than classical parameter estimation of which application is in general restricted to fairly simple dynamical scenarios.

How to cite

top

Aguiar, M., et al. "Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics." Mathematical Modelling of Natural Phenomena 7.3 (2012): 1-11. <http://eudml.org/doc/222190>.

@article{Aguiar2012,
abstract = {In this paper we analyze the stochastic version of a minimalistic multi-strain model, which captures essential differences between primary and secondary infections in dengue fever epidemiology, and investigate the interplay between stochasticity, seasonality and import. The introduction of stochasticity is needed to explain the fluctuations observed in some of the available data sets, revealing a scenario where noise and complex deterministic skeleton strongly interact. For large enough population size, the stochastic system can be well described by the deterministic skeleton gaining insight on the relevant parameter values purely on topological information of the dynamics, rather than classical parameter estimation of which application is in general restricted to fairly simple dynamical scenarios.},
author = {Aguiar, M., Kooi, B.W., Martins, J., Stollenwerk, N.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {dengue fever epidemiology; multi-strain model; external infections; deterministic skeleton; stochastic system},
language = {eng},
month = {6},
number = {3},
pages = {1-11},
publisher = {EDP Sciences},
title = {Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics},
url = {http://eudml.org/doc/222190},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Aguiar, M.
AU - Kooi, B.W.
AU - Martins, J.
AU - Stollenwerk, N.
TI - Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/6//
PB - EDP Sciences
VL - 7
IS - 3
SP - 1
EP - 11
AB - In this paper we analyze the stochastic version of a minimalistic multi-strain model, which captures essential differences between primary and secondary infections in dengue fever epidemiology, and investigate the interplay between stochasticity, seasonality and import. The introduction of stochasticity is needed to explain the fluctuations observed in some of the available data sets, revealing a scenario where noise and complex deterministic skeleton strongly interact. For large enough population size, the stochastic system can be well described by the deterministic skeleton gaining insight on the relevant parameter values purely on topological information of the dynamics, rather than classical parameter estimation of which application is in general restricted to fairly simple dynamical scenarios.
LA - eng
KW - dengue fever epidemiology; multi-strain model; external infections; deterministic skeleton; stochastic system
UR - http://eudml.org/doc/222190
ER -

References

top
  1. Centers for Disease Control and Prevention. Dengue, (2011). Retrieved from  URIhttp://www.cdc.gov/dengue/
  2. D. Alonso, A. McKane, M. Pascual. Stochastic Amplification in Epidemics. Journal of the Royal Society Interface, (2006), 4, 575-582.  
  3. D. J. Gubler. Epidemic dengue/dengue hemorrhagic fever as a public health, social and economic problem in the 21st century. Trends in Microbiology, (2002), 10, 100–103.  
  4. D. T. Gillespie. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics, (1976), 22, 403–434.  
  5. D. T. Gillespie. Monte Carlo simulation of random walks with residence time dependent transition probability rates. Journal of Computational Physics, (1978), 28, 395–407.  Zbl0397.65004
  6. J. D. Gubler, W. Suharyono, R. Tan, M. Abidin, A. Sie. Viraemia in patients with naturally acquired dengue infection. Bull. World Health Organ., (1981), 59, 623–630.  
  7. J. E. Doedel, B. Oldeman. AUTO 07P - Continuation and bifurcation software for ordinary differential equations. Technical Report : Concordia University, Montreal, Canada, (2009). Retrieved from  URIhttp://indy.cs.concordia.ca/auto/
  8. J. S. Mackenzie, D. J. Gubler, L. R. Petersen. Emerging flaviviruses : the spread and resurgence of Japanese encephalitis, West Nile and dengue viruses. Nature Medicine Review, (2004), 12, S98–S109.  
  9. M. Aguiar, B. W. Kooi, N. Stollenwerk. Epidemiology of Dengue Fever : A Model with Temporary Cross-Immunity and Possible Secondary Infection Shows Bifurcations and Chaotic Behaviour in Wide Parameter Regions. Math. Model. Nat. Phenom., (2008), 4, 48–70.  Zbl1337.92126
  10. M. Aguiar, N. Stollenwerk, B. W. Kooi. Torus bifurcations, isolas and chaotic attractors in a simple dengue model with ADE and temporary cross immunity. International Journal of Computer Mathematics, (2009), 86, 1867–1877.  Zbl1173.92023
  11. M. Aguiar, S. Ballesteros, B. W. Kooi, N. Stollenwerk. The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections : complex dynamics and its implications for data analysis. Accepted for publication in Journal of Theoretical Biology, (2011).  
  12. M. G. Guzmánet al.Dengue : a continuing global threat. Nature Reviews Microbiology, (2010), 8, S7–S16.  
  13. M. J. Keeling, J. V. Ross. On methods for studying stochastic disease dynamics. Journal of the Royal Society Interface, (2008), 5, 171–181.  
  14. N. Ferguson, R. Anderson, S. Gupta. The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. Proc. Natl. Acad. Sci. USA, (1999), 96, 790–94.  
  15. N. G. van Kampen. Stochastic Processes in Physics and Chemistry. (North-Holland, Amsterdam, 1992).  Zbl0511.60038
  16. N. Stollenwerk, V. A. A. Jansen. Evolution towards criticality in an epidemiological model for meningococcal disease. Physics Letters A, (2003b), 317, 87–96.  Zbl1030.92026
  17. N. Stollenwerk, M. C. J. Maiden, V. A. A. Jansen, V.A.A.Diversity in pathogenicity can cause outbreaks of menigococcal disease. Proc. Natl. Acad. Sci. USA, (2004), 101, 10229–10234.  
  18. N. Stollenwerk, V. V. A. Jansen. Population biology and criticality (Imperial College Press, London, 2010).  
  19. O. Chareonsooket al.Changing epidemiology of dengue hemorrhagic fever in Thailand. Epidemiol. Infect., (1999), 122, 161–166.  
  20. Pediatric Dengue Vaccine Initiative. International Vaccine Institute (IVI). Global Burden of Dengue, (2011). Retrieved from  URIhttp://www.pdvi.org/about_dengue/GBD.asp
  21. Pers comm. : Francisco Lemos, Secretaria de Estado de Saúde de Minas Gerais, Brazil ; Sônia Diniz, Fundação Ezequiel Dias, Minas Gerais, Brazil and Scott Halstead, Pedriatic Dengue Vaccine Initiative, Maryland, USA.  
  22. United Nations Population Division World Urbanization Prospects : The 2009 Revision Population Database, (2011). Retrieved from  URIhttp://www.un.org/esa/population/unpop.htm
  23. S. B. Halsteadet al.Dengue and chikungunya virus infection in man in Thailand, 1962–1964. V. Epidemiologic observations outside Bangkok. Am. J. Trop. Med. Hyg., (1969), 18, 1022–33.  
  24. S. B. Halstead. Antibody-dependent Enhancement of Infection : A Mechanism for Indirect Virus Entry into Cells. Cellular Receptors for Animal Viruses, 28, Chapter 25, 493–516. (Cold Spring Harbor Laboratory Press, 1994).  
  25. S. B. Halstead. Immune enhancement of viral infection. Progress in Allergy, (1982), 31, 301–364.  
  26. S. B. Halstead. Neutralization and antibody-dependent enhancement of dengue viruses. Advances in Virus Research, (2003), 60, 421–467.  
  27. S. Matheuset al.Discrimination between Primary and Secondary Dengue Virus Infection by an Immunoglobulin G Aviditnoy Test Using a Single Acute-Phase Serum Sample. Journal of Clinical Microbiology, (2005), 43, 2793–2797.  
  28. W. Dejnirattisaiet al.Cross-Reacting Antibodies Enhance Dengue Virus Infection in Humans. Science, (2010), 328, 745–748.  
  29. Wikipedia contributors. Wikipedia, The Free Encyclopedia. Provinces of Thailand, (2011). Retrieved from  URIhttp://en.wikipedia.org/wiki/Provinces_of_Thailand
  30. World Health Organization. Dengue and Dengue Hemorrhagic Fever, Fact sheet 117, (2009). Retrieved from  URIhttp://www.who.int/mediacentre/factsheets/fs117/en/
  31. Y. Nagao, K. Koelle. Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever. Proc. Natl. Acad. Sci, (2008), 105, 2238–2243.  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.