# 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

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topAguiar, 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- Centers for Disease Control and Prevention. Dengue, (2011). Retrieved from URIhttp://www.cdc.gov/dengue/
- D. Alonso, A. McKane, M. Pascual. Stochastic Amplification in Epidemics. Journal of the Royal Society Interface, (2006), 4, 575-582.
- 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.
- 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.
- 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
- 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.
- 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/
- 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.
- 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
- 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
- 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).
- M. G. Guzmánet al.Dengue : a continuing global threat. Nature Reviews Microbiology, (2010), 8, S7–S16.
- M. J. Keeling, J. V. Ross. On methods for studying stochastic disease dynamics. Journal of the Royal Society Interface, (2008), 5, 171–181.
- 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.
- N. G. van Kampen. Stochastic Processes in Physics and Chemistry. (North-Holland, Amsterdam, 1992). Zbl0974.60020
- 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
- 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.
- N. Stollenwerk, V. V. A. Jansen. Population biology and criticality (Imperial College Press, London, 2010).
- O. Chareonsooket al.Changing epidemiology of dengue hemorrhagic fever in Thailand. Epidemiol. Infect., (1999), 122, 161–166.
- Pediatric Dengue Vaccine Initiative. International Vaccine Institute (IVI). Global Burden of Dengue, (2011). Retrieved from URIhttp://www.pdvi.org/about_dengue/GBD.asp
- 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.
- United Nations Population Division World Urbanization Prospects : The 2009 Revision Population Database, (2011). Retrieved from URIhttp://www.un.org/esa/population/unpop.htm
- 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.
- 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).
- S. B. Halstead. Immune enhancement of viral infection. Progress in Allergy, (1982), 31, 301–364.
- S. B. Halstead. Neutralization and antibody-dependent enhancement of dengue viruses. Advances in Virus Research, (2003), 60, 421–467.
- 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.
- W. Dejnirattisaiet al.Cross-Reacting Antibodies Enhance Dengue Virus Infection in Humans. Science, (2010), 328, 745–748.
- Wikipedia contributors. Wikipedia, The Free Encyclopedia. Provinces of Thailand, (2011). Retrieved from URIhttp://en.wikipedia.org/wiki/Provinces_of_Thailand
- World Health Organization. Dengue and Dengue Hemorrhagic Fever, Fact sheet 117, (2009). Retrieved from URIhttp://www.who.int/mediacentre/factsheets/fs117/en/
- 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.

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