Randomness of Dengue Outbreaks on the Equator

Technical Appendix

Yirong Chen, Alex R. Cook

, and Alisa X.L. Lim

Author affiliations: National University of Singapore, Singapore (Y. Chen, A.R. Cook, A.X.L. Lim); National University Health System, Singapore (Y. Chen, A.R. Cook); Yale–NUS College, Singapore (A.R. Cook)

Abstract

A simple mathematical model without seasonality indicated that the apparently chaotic dengue epidemics in Singapore have characteristics similar to epidemics resulting from chance. Randomness as a sufficient condition for patterns of dengue epidemics in equatorial regions calls into question existing explanations for dengue outbreaks there.

Dengue, a vectorborne infectious disease, has complex epidemiologic dynamics (1). The recent expansion of the range of dengue makes this disease a considerable public health concern worldwide (2). In the city-state of Singapore, the number of dengue cases has increased dramatically since the 1990s, and all 4 serotypes of the dengue virus are endemic (3). Cyclical outbreaks of dengue of increasing magnitude have been observed with a cycle of 5–6 years (4), but this pattern appeared to cease in 2005, and no obvious cycle has occurred since then. Although other tropical and subtropical countries in Southeast Asia have distinct seasonality (5) so that dengue epidemics occur at distinct and predictable times of the year (6), Singapore’s proximity to the equator gives it an aseasonal climate, and the timing of dengue epidemics is irregular (7,8).

Many factors have been postulated to contribute to dengue’s spread in Singapore, such as a consistently warm and humid climate that favors year-round vector proliferation, high urbanization, and a tendency for vectors to live in human residences (9). The extent to which these factors affect dengue epidemics in aseasonal Singapore, if they do at all, is unclear. Competing explanations for the timing of large dengue outbreaks in Singapore can be found in the literature. One study attributes dengue epidemics to conducive temperatures and precipitation variations (10); another attributes them to variable maximum and minimum temperatures (11). Rainfall and temperature have been shown to be related to dengue outbreaks in Brazil, another equatorial country (12).

The tendency to see patterns where none exists has been well recognized. When 2 events happen contemporarily and a plausible story connects the events, the tendency to assume that 1 causes the other is strong (13). Cancer cases cluster around mobile phone masts (base stations), not because the radiation from a mast is carcinogenic at typical exposures but because numerous masts exist and occasionally cancer cases cluster together, similarly to spilled grains of rice (14). A study in the heuristics and biases program discusses a famous example from sports (15), which are notorious for stories being concocted around essentially chance outcomes. Basketball fans, coaches, and pundits often believe that players have “hot hand” streaks when they have a run of good form, making many shots in succession and playing above their usual level during a match. The study systematically deconstructed this belief by a series of statistical tests that showed that the patterns of actual hits and misses was consistent with mere chance—analogous to sequences of coin tosses rather than an illusory hot hand (15).

In probabilistic models, chance is represented by error terms, or noise, encompassing all the many complicating factors that are not worth including in the systematic signal. Past models for dengue in Singapore have accounted for chance alongside systematic effects of the weather and other factors (10,11). However, is chance alone sufficient to explain the frequent, large, and ostensibly chaotic outbreaks we observe? We sought to assess whether the rise and fall of dengue outbreaks from week to week in Singapore come in runs or are indistinguishable from random noise and thereby whether it is necessary to consider other possible drivers of these epidemics.

Ms. Chen is a research assistant and doctoral student at the National University of Singapore. Her main research interest is modelling of endemic diseases such as dengue and hand, foot and mouth disease.

Acknowledgments

This study was funded by the Center for Infectious Disease Epidemiology and Research in the Saw Swee Hock School of Public Health, and additional funding was provided by Singapore's Health Services Research grant number HSRG-0040-2013.

Data used in this paper are available at http://www.moh.gov.sg.

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Figures

Technical Appendix

Technical Appendix. Statistical modeling approach used for aseasonal modeling of dengue incidence in Singapore. 389 KB

Suggested citation for this article: Chen Y, Cook AR, Lim AXL. Randomness and dengue outbreaks on the equator. Emerg Infect Dis. 2015 Sep [date cited].http://dx.doi.org/10.3201/eid2109.141030

DOI: 10.3201/eid2109.141030