we reviewed data on the weekly incidence of clinically diagnosed dengue in singapore during 20032012 . we compared the number of dengue cases per week to a simple simulation model ( technical appendix ) with no environmental drivers other than the dependence of weekly number of cases from up to 4 weeks before . summaries of observed incidence and of the simulated aseasonal model were compared for assessing proximity of the behavior of observed cases to the behavior of simulated cases . the simulation model used was a standard autoregressive time series model in which the number of cases during any week affects the mean number of cases for the 4 weeks that follow . we allowed the simulated number to have a random variation around that mean ; data were log - transformed to ensure that incidence was positive . the fitted autoregressive model was used to simulate synthetic dengue outbreaks over multiple decades , and incidence of simulated outbreaks was compared with observed incidence . hot hand  in basketball study ( 15 ) and that might falsify the model that accounted for chance alone . this model included correlation between dengue incidence by week and the preceding week ( the autocorrelation function ) , the probability distribution for the weekly incidence aggregated over 10 years , the distribution of the annual number of cases , the maximum number of cases observed over the previous decade , and the probability of a rise in incidence each week following a series of rises ( i.e. , the possible beginning of an epidemic ) or a series of declines ( i.e. , the possible ending of an epidemic ) . d ) three randomly generated simulated scenarios from the aseasonal model described in the text and the technical appendix . although the peaks are not synchronized , similar patterns can be discerned ; large and small outbreaks of similar scale and frequency occur in all 4 scenarios . for all metrics considered , the actual scenario ( i.e. , the observed dengue incidence ) was fully consistent with the aseasonal model ; both the autocorrelation function ( figure 2 , panel a ) and the cumulative probability of dengue incidence ( figure 2 , panel b ) from the historical incidence data lie within the distribution resulting from the aseasonal model . the probabilities of an increase in incidence each week that follows a series of rises or falls and corresponding 95% cis calculated on the basis of simulations from the aseasonal model all include the proportions observed historically ( figure 2 , panel c ) . furthermore , the distribution of the annual incidence ( figure 2 , panel d ) and the maximum observed incidence over the decade ( figure 2 , panel e ) are consistent with the aseasonal model . similarly , the number of successive increases or decreases over the decade was consistent with chance ( p = 0.18 ) . comparison of observed dengue incidence and incidence from simulated aseasonal models , 20032012 , singapore . a ) distribution of actual and simulated autocorrelation functions at different time lags ( e.g. , this week versus next week ; last week versus next week , etc . ) b ) distribution of cumulative distribution function of the simulated weekly number of dengue cases and cumulative density function of the actual numbers of cases . c ) conditional probabilities of an increase in number of dengue cases and 95% cis for simulated scenario and actual data , given 13 consecutive decreases or increases . e ) density plot of simulated 10-year maximum number of cases and actual 10-year number of cases . these metrics are not conventional measures of dengue surveillance data ; they capture more complex , emergent properties of the epidemic process . however , our findings show that , for dengue incidence in equatorial singapore , where average monthly temperatures vary only from 26c28c , randomness alone is sufficient to explain the apparent epidemics of dengue . although seasonal factors may have a role , as the literature suggests ( 10,11 ) , seasonality or other temporal drivers such as fluctuation in the intensity of the country s vector control program are not necessary to explain the qualitative and quantitative patterns of dengue in this equatorial city - state . as our results suggest , the possibility that dengue outbreaks occur in aseasonal locations because of chance should be considered .
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 .