Mathematical models of dengue fever epidemiology: multi-strain dynamics, immunological aspects associated to disease severity and vaccines

Maira Aguiar, Nico Stollenwerk


Epidemiological models formulated to describe the transmission of the disease and to predict future outbreaks, can become an interesting tool able to address specific public health questions, guiding public health authorities during implementation of disease control measures such as vector control and vaccination. In this paper, we survey a model framework for dengue fever epidemiology, the most important viral mosquitoborne disease in the world. Here, we discuss the role of number of subsequent infections versus detailed number of dengue serotypes included in the model framework and the human immunological aspects associated to disease severity, identifying the implications for model dynamics and its impact for vaccine implementation.

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Bhatt, S., et al. (2013). The global distribution and burden of dengue. Nature; 496 504-507.

Halstead, S.B. (2003). Neutralization and antibody-dependent enhancement of dengue viruses. Advances in Virus Research; 60:421-467.

Guzman, M.G. et al. (2010). Dengue: a continuing global threat. Nature Reviews Microbiology, 8, S7-S16.

Dejnirattisai, W. et al. (2010). Cross-Reacting Antibodies Enhance Dengue Virus Infection in Humans. Science, 328, 745-748.

Andraud, M., et al. (2012). Dynamic Epidemiological Models for Dengue Transmission: A Systematic Review of Structural Approaches. PLoS ONE 7(11): e49085.

Ferguson, N., Anderson, R. and Gupta, S. (1999). The effect of antibodydependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. Proc. Natl. Acad. Sci. USA; 96:790-94.

Aguiar, M., Stollenwerk, N., & Kooi, B. (2009). Torus bifurcations, isolas and chaotic attractors in a simple dengue fever model with ADE and temporary cross immunity. Int. J. Comput. Math.; 86:1867-77.

Wearing, H.J. & Rohani, P. (2006). Ecological and immunological determinants of dengue epidemics. Proc. Natl. Acad. Sci. USA; 103:11802-11807.

Aguiar, M., et al. (2011). 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. J. Theor. Biol.; 289:181-196.

Aguiar, M., Stollenwerk, N. and Kooi, W. B. (2012). Scaling of stochasticity in dengue hemorrhagic fever epidemics. Math. Model. Nat. Phenom., 7, 1-11.

Messina, J.P., et al., (2015). The many projected futures of dengue. Nature Reviews Microbiology ; 13: 230239.

Kraemer, M., et al. (2015). The global distribution of the arbovirus vectors Aedes aegypti and Ae. Albopictus. ELife; 4:e08347.

Recker, M., et al., (2009). Immunological serotype interactions and their effect on the epidemiological pattern of dengue. Proc. R. Soc. B 276, 25412548.

Coudeville, L., Garnett, G.P.. (2012). Transmission Dynamics of the Four Dengue Serotypes in Southern Vietnam and the Potential Impact of Vaccination. PLoS ONE 7(12): e51244.

Schwartz, I.B., Shaw, L.B., Cummings, D.A.T., Billings, L., McCrary, M., Burke, D.S., (2005). Chaotic desynchronization of multi-strain diseases. Phys. Rev. E 72, 066201066206.

Billings, L., et al., (2007). Instabilities in multiserotype disease models with antibody-dependent enhancement. J. Theor. Biol. 246, 1827.

Nagao, Y., Koelle, K., (2008). Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever. Proc. Natl. Acad. Sci. USA 105, 22382243.

Wikramaratna, P.S., et al., (2010). The effects of tertiary and quaternary infections on the epidemiology of dengue. PLoS ONE 5, e12347.

Aguiar, M., Stollenwerk, N., (2007). A new chaotic attractor in a basic multi-strain epidemiological model with temporary cross-immunity. arXiv:0704.3174v1 [nlin.CD].

Aguiar, M., Kooi, B.W., Stollenwerk, N., (2008). 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. 4, 4870.

Nicholas G. Reich et al. (2013). Interactions between serotypes of dengue highlight epidemiological impact of cross-immunity. J R Soc Interface 10: 20130414.

Aguiar, M., et al. (2013). How much complexity is needed to descri be the fluctuations observed in dengue hemorrhagic fever incidence data? Ecol. Complex.; 16:31-40.

World Health Organization Strategic Advisory Group of Experts (SAGE) on Immunization. Background paper on Dengue Vaccines prepared by the SAGE working group on dengue vaccines and the WHO secretariat. (2016). Retrieved from docs/en/

Scott B. Halstead. (2016). Protective and Immunological Behavior of Yellow Fever Dengue Chimeric Vaccine. Vaccine, 34(14), 1643-647.

Aguiar M, Stollenwerk N, Halstead SB. (2016). The risks behind Dengvaxia recommendation. Lancet Infect Dis. 2016;16:882.

Ferguson N, Rodrguez-Barraquer I, Dorigatti I, et al. (2016). Benefits and risks of the Sanofi-Pasteur dengue vaccine: modeling optimal deployment. Science. 2016;353:10331036.

Flasche S. et al. (2016) The Long-Term Safety, Public Health Impact, and Cost-Effectiveness of Routine Vaccination with a Recombinant, Live-Attenuated Dengue Vaccine (Dengvaxia): A Model Comparison Study. PLoS Med 13(11): e1002181.

Aguiar M, Stollenwerk N, Halstead SB. (2016). The impact of the newly licensed dengue vaccine in endemic countries. PLoS Negl Trop Dis. 2016;10(12):e0005179. doi:10.1371/journal.pntd.0005179

Robert V. Gibbons et al. (2007). Analysis of repeat hospital admissions for dengue to estimate the fre- quency of third or fourth dengue infections resulting in admissions and dengue hemorrhagic fever, and serotype sequences Am. J. Trop. Med. Hyg., 77(5), 910913.

Rocha F., Aguiar M.,Souza M., and Stollenwerk N.. (2013). Time-scale separation and center manifold analysis describing vector-borne disease dynamics, Int. J. Comput. Math., 90(10), 21052125.

Duong, V. et al. (2015). Asymptomatic humans transmit dengue virus to mosquitoes. Proc. Natl. Acad. Sci. USA, 112, 14688-93.

Ma´ıra Aguiar, Scott B. Halstead and Nico Stollenwerk. (2017). Consider stopping dengvaxia administration without immunological screening. Expert Review of Vaccines, 16 (4), 301-302.

Ma´ıra Aguiar, Luis Mateus and Nico Stollenwerk. (2016). The currently best estimate for worldwide dengue vaccine efficacy. AIP Conference Proceedings, 1738, 390014.

Capeding, M.R., et al. (2014). Clinical efficacy and safety of a novel tetravalent dengue vaccine in healthy children in Asia:a phase 3, randomised, observer-masked, placebo-controlled trial. Lancet; 384:1358-65.

Villar, L., et al. (2015). Efficacy of a tetravalent dengue vaccine in children in Latin America. New Engl. J. Med. ; 372:113-123.

Stollenwerk, N., Aguiar, M., Ballesteros, S., Boto, J., Kooi, W. B., & Mateus, L. (2012). Dynamic noise, chaos and parameter estimation in population biology, J. Royal Soc. Interface Focus 2, 156169.

Mateus, L., Stollenwerk, N., & Zambrini, J.C. (2013) Stochastic Models in Population Biology: From Dynamic Noise to Bayesian Description and Model Comparison for Given Data Sets, Int. Journal. Computer Math. 90, 21612173.

Hadinegoro S.R., Arredondo-Garcia J.L., Capeding M.R., Deseda C., Chotpitayasunondh T., Dietze R., et al. (2015). Efficacy and Long-Term Safety of a Dengue Vaccine in Regions of Endemic Disease. N. Engl. J. Med., 373, 1195206.



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