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Conceived and designed the experiments: ST. Analyzed the data: YN WS MT PC CD. Contributed reagents/materials/analysis tools: WS. Wrote the paper: ST YN PC CD. Organized collaboration and collected data: YN. Conducted entomological surveys: SS.

The authors have declared that no competing interests exist.

Dengue is the most prevalent mosquito-borne virus, and potentially fatal dengue hemorrhagic fever (DHF) occurs mainly in secondary infections. It recently was hypothesized that, due to the presence of cross-immunity, the relationship between the incidence of DHF and transmission intensity may be negative at areas of intense transmission. We tested this hypothesis empirically, using vector abundance as a surrogate of transmission intensity.

House Index (HI), which is defined as the percentage of households infested with vector larvae/pupae, was obtained from surveys conducted on one million houses in Thailand, between 2002 and 2004. First, the utility of HI as a surrogate of transmission intensity was confirmed because HI was correlated negatively with mean age of DHF in the population. Next, the relationship between DHF incidence and HI was investigated. DHF incidence increased only up to an HI of about 30, but declined thereafter. Reduction of HI from the currently maximal level to 30 would increase the incidence by more than 40%. Simulations, which implemented a recently proposed model for cross-immunity, generated results that resembled actual epidemiological data. It was predicted that cross-immunity generates a wide variation in incidence, thereby obscuring the relationship between incidence and transmission intensity. The relationship would become obvious only if data collected over a long duration (e.g., >10 years) was averaged.

The negative relationship between DHF incidence and dengue transmission intensity implies that in regions of intense transmission, insufficient reduction of vector abundance may increase long-term DHF incidence. Further studies of a duration much longer than the present study, are warranted.

An infection with dengue virus may lead to dengue hemorrhagic fever (DHF), a dangerous illness. There is no approved vaccine for this most prevalent mosquito-borne virus, which infects tens of millions (or more) people annually. Therefore, health authorities have been putting an emphasis on reduction of vector mosquitoes, genus

Dengue is the most prevalent vector-borne viral disease, the distribution of which has been expanding continually

Although the periodicity of highly oscillatory DHF outbreaks has been under intensive study

In contrast to DF, children seemed to be more prone to manifest DHF than are adults

The present study aims to provide an empirical example of this non-monotonic relationship between the incidence of DHF and transmission intensity, with transmission intensity represented by vector abundance. Vector abundance is one of the major determinants for transmission intensity of a vector-borne disease

Here, we describe the empirical relationship between DHF incidence and transmission intensity, as represented by HI. The age-specific structure of this relationship also was characterized to support findings obtained for the entire population. The epidemiological characteristics of DHF were compared with predictions made by simulation of an individual-based model based upon the above mentioned mathematical modelling study. Our findings have major implications for future epidemiological surveys and dengue control programs.

In Thailand, the highest incidence of DHF occurs between June and August. Hence, entomological surveys mainly are conducted in the pre-epidemic season (

The Bureau of Epidemiology, Ministry of Public Health, provided the annual number of cases of DHF (including Dengue Shock Syndrome) in nine age categories (0–4, 5–9, 10–14, 15–24, 25–34, 35–44, 45–54, 55–64, ≥65 years) for each district, for the years between 1994 and 2004. Age-stratified population data, based upon five yearly censuses/surveys and yearly projections, were obtained from the National Statistics Office of Thailand (

Subsequent statistical analyses were performed using R 2.6.2 and Stata 9.2. We used non-parametric statistical methods, Spearman's rank correlation analysis and the generalized additive model (GAM), so that analyses did not have to assume any fixed distribution

To ensure that HI could be used as a reliable surrogate of transmission intensity, we compared the mean age of DHF cases to HI using rank correlation analysis. A high mean age of DHF cases was used as an indicator of low transmission intensity, because the mean age of infected individuals generally is negatively correlated with the transmission intensity of an acute infectious disease

We examined the quantitative relationship between incidence of DHF and HI using GAM. Logarithm was used as the link function. First, we tested this relationship by incorporating only HI as the independent variable (univariate analysis). Then, we adjusted for possible confounding by socioeconomic and climatic variables. Socioeconomic factors may affect reported incidence in diverse fashions. For example, incidence may be biased by (a) the prevalence of health offices, which are responsible for DHF case reporting in each district. Abundance of breeding places is affected by local water storage practices (reviewed by

Collectively, these socioeconomic/climatic variables were averaged for the period for which the dependent variable, incidence, was averaged. We enrolled districts from which socioeconomic and climatic variables have been available from 1994 to 2004. Consequently, 785 districts were enrolled. This dataset (incidence linked with covariates) is available on request from the corresponding author. Multivariate analyses were conducted using the following procedure. First, HI and all socioeconomic/climatic factors were incorporated as independent variables, with ^{6} combinations of

The relationship between DHF incidence and HI was examined within different age classes for which original age categories were aggregated into the following three age classes: 0–4, 5–24, and ≥25 years. GAM was applied similarly to these age-class specific incidences.

We employed computer simulations to see whether (and to what extent) the observed epidemiological pattern could be explained based upon a theoretical framework. The assumption of the above mentioned mathematical model was expressed equivalently by an individual-based model (see

In addition, this individual-based model can incorporate the age-dependency in the probability to manifest DHF (categorical parameter “_{0}) of dengue virus. The present study parameterized simulations with the following three scenarios. (I) Cross-immunity scenario: the duration of cross-serotype protection (“_{0} was selected by extrapolating the mean age of DHF obtained between 2002 and 2004 from each of the 785 districts, through the relationship between R_{0} and mean age of DHF (_{0} values was used as the input for all three scenarios. Each simulation was run for 150 years.

At different durations for averaging (_{0} using GAM.

On the other hand, actual incidences were averaged for the recent

The national-level mean age of DHF cases was 16 years during 2002 to 2004. The mean HI recorded each April during 2002 to 2004 was 23. As shown in

Each point corresponds to one district in this and subsequent figures.

During 2002 to 2004, the annual DHF incidence was 83 per 100,000 individuals. HI showed a statistically significant contribution to the log incidence of DHF, both in univariate and multivariate regression models (

The annual incidence of DHF (per 100,000 individuals) averaged between 2002 and 2004 is plotted against House Index in the entire population (A, B), at 0–4 years (C), 5–24 years (D), and ≥25 years (E). Y-axis is original scale (A) or log scale (B–E). The lines correspond to the univariate regression model presented in

The smoothing function obtained from GAM analysis, which regressed the log of DHF incidence reported between 2002 and 2004 against House Index, is presented as the solid line. Dashed line represents the 95% confidence interval, while the spikes on the horizontal axis represent the frequency of data points (or districts) in this and the next figure.

N = 785 | |||

1. univariate regression model (^{†} = 2) | |||

Variable | |||

House Index | 0.006 | ||

Deviance | 2,092,809 | ||

AIC ^{‡} | 8,428 | ||

2. multivariate regression model | |||

full regression model for | smallest regression model for | final regression model with mixed | |

variables ^{§} | |||

House Index | 0.028 | 0.035 | 0.031 ( |

APET | <0.001 | <0.001 | <0.001 ( |

winter temperature | <0.001 | <0.001 | <0.001 ( |

summer temperature | 0.003 | <0.001 | <0.001 ( |

public large wells | 0.004 | <0.001 | <0.001 ( |

birth rate | <0.001 | <0.001 | <0.001 ( |

AVP | 0.651 | ||

health stations | 0.468 | ||

high schools | 0.301 | ||

public small wells | 0.846 | ||

private small wells | 0.401 | ||

land ownership | 0.714 | ||

Deviance | 1,558,853 | 1,572,931 | 1,566,715 |

AIC | 8,240 | 8,224 | 8,223 |

In multivariate analysis, the following six variables remained in the final regression model (

The final regression model obtained from the multivariate GAM analysis (

Although incorporation of socioeconomic/variables improved the goodness of fit, this multivariate predictive model still failed to reproduce the very wide variation in the observed incidence (compare

Incidence of DHF was predicted based upon the final regression model (

Further analysis of the age-specific associations between incidence of DHF and HI was conducted, as shown in

N = 785 | |||

Age class | 0–4 years | 5–24 years | ≥25 years |

1. univariate regression model (^{†} = 2) | |||

variable | |||

House Index | 0.044 | 0.001 | 0.008 |

Deviance | 5,592,654 | 12,851,371 | 290,947 |

AIC ^{‡} | 9,200 | 9,852 | 6,879 |

2. multivariate regression model (final regression model with mixed | |||

variables ^{§} | |||

House Index | 0.031 ( | 0.002 ( | |

APET | <0.001 ( | <0.001 ( | 0.006 ( |

winter temperature | <0.001 ( | <0.001 ( | 0.003 ( |

summer temperature | <0.001 ( | <0.001 ( | 0.005 ( |

public large wells | 0.002 ( | <0.001 ( | |

birth rate | <0.001 ( | ||

AVP | <0.001 ( | ||

health stations | |||

high schools | 0.008 ( | ||

public small wells | |||

private small wells | <0.001 ( | ||

land ownership | 0.001 ( | <0.001 ( | |

Deviance | 4,592,236 | 10,128,066 | 165,907 |

AIC | 9,058 | 9,689 | 6,476 |

As shown in _{0}, which greatly resembled the empirical relationship (compare with

Incidence of DHF generated by simulations are plotted over Basic Reproductive Number (R_{0}). The used scenarios are: two-year cross-immunity (A–D); age-dependency which assumed a higher probability of manifesting DHF in the older individuals (E–H); and control scenario without cross-immunity or age-dependency (I–L). Incidences in the last “

GAM was applied to examine the relationship between incidences generated by simulations and R_{0} (

Age-stratified incidence of DHF in the last three years from each simulation were averaged. The parameters inputted to simulations were: two-year cross-immunity (A–D); age-dependency which assumes a higher probability of manifesting DHF in older individuals (E–H); control scenario without cross-immunity or age-dependency (I–L). DHF incidence presented for the entire population (A, E, I) or stratified into 0–4 years (B, F, J), 5–24 years (C, G, K), and ≥25 years (D, H, L). Y-axis is log scale.

The goodness of fit in predicting incidence by R_{0} showed remarkable differences between simulation with cross-immunity and those without cross-immunity (

The goodness of fit in the regression models for incidence of DHF is plotted over the window length (“_{0} with

The predictability of DHF incidence was inversely measured by deviance and plotted to

The goodness of fit in predicting actual incidence, either by HI only or by HI and covariates, showed a similarly complex response to

N = 785 | |||||||||

window for averaing (years) | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |

1. univariate regression model (^{†} = 2) | |||||||||

variable | level of | ||||||||

House Index | ** | ** | ** | * | * | * | ** | ** | * |

AIC ^{‡} | 8,428 | 8,767 | 8,477 | 8,239 | 8,250 | 8,183 | 8,040 | 8,069 | 7,993 |

2. multivariate regression model (final regression model with mixed | |||||||||

variables ^{§} | level of | ||||||||

House Index | * | * | * | * | * | * | * | ||

APET | *** | *** | *** | *** | *** | *** | ** | * | |

winter temperature | *** | *** | *** | *** | *** | *** | *** | *** | *** |

summer temperature | *** | ** | *** | * | * | *** | * | ||

public large wells | *** | ** | ** | ** | * | ||||

birth rate | *** | *** | *** | *** | *** | *** | *** | *** | *** |

AIC | 8,223 | 8,497 | 8,180 | 7,932 | 8,037 | 8,011 | 7,908 | 7,913 | 7,905 |

Our analysis demonstrates that HI is a reliable indicator of transmission intensity, at least at the district level. The usefulness of HI is evident by its highly significant, inverse relationship to mean age, otherwise equivalent to a positive correlation between HI and transmission intensity. Our findings are consistent with observations from Singapore, where an increase in the mean age of patients with dengue infection was preceded by a substantial reduction in HI

Analysis of DHF incidence among the entire Thai population revealed that incidence rose up to HI of about 30 and gradually declined thereafter. This non-monotonic relationship appears to be consistent with a state of endemic stability. However, the age-dependency in the probability to manifest DHF may not simply satisfy the condition for endemic stability, because DHF occurs more frequently in children than in adults. On the other hand, cross-immunity explains not only this non-monotonic relationship (_{0} predicted incidence from simulations with cross-immunity (

Stratification of data according to age revealed a positive association between DHF incidence and HI among the youngest population. In contrast, a negative association was observed in the oldest population. These contrasting correlations may be explained as follows. Under low transmission intensity, the majority of individuals in the youngest age class do not possess antibodies against any serotype and are relatively resistant to DHF. As the transmission intensity increases, a larger number of individuals in this age class possess antibodies to only one serotype, making them predisposed to DHF. Therefore, the correlation between DHF incidence and transmission intensity becomes positive in the youngest age class, as observed here. In contrast, when transmission intensity is low, many in the oldest age class possess antibodies against only one serotype and are predisposed to DHF. As transmission intensity increases, more members of this age class possess antibodies against almost all serotypes, conferring resistance to DHF. Importantly, these age-stratified relationships could be reproduced by simulations of any scenarios examined. Therefore, this analysis did not differentiate whether cross-immunity or age-dependency determined the epidemiological characteristics of DHF.

The negative response of incidence to transmission intensity at areas of intense transmission has important public health implications, regardless of its underlying mechanism. The incidence of DHF is affected by the dominant virus serotype, which shifts from period to period

Theoretically, sufficiently radical reduction of vector mosquitoes can achieve a decrease of the entire incidence of DHF. However, it is unclear whether such radical vector control is possible at a nation-wide scale in developing countries. Instead, reduction of the vector population may become stagnant as the vector abundance decreases. Furthermore, even substantial vector reduction (for example, from HI = 60 to10) would not necessarily decrease the final incidence (extrapolate the HI values to incidence in

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Definition and values of scenario parameters assigned to each simulation of Dengue Hemorrhagic Fever (DHF)

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Individual-Based Model for Dengue Hemorrhagic Fever (DHF). A. Diagram of the transition between immunological states caused by infections with wild type virus. The transition between immunological states was a result of either viral inoculation (solid arrow) or expiration of time from the most recent inoculation (broken arrow). The serotype(s) that an individual has experienced is recorded as the existence of protective antibodies to this serotype(s). B. Age-dependent probability for a secondary infection to manifest as DHF in a DHF-predisposed individual. Four hypothetical possibilities of age-dependency are defined: no age-dependency (

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Relationship between DHF incidence and transmission intensity (R_{0}) generated by cross-serotype immunity. Results from simulations, which assumed the cross-protective period (“

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Relationship between DHF incidence and transmission intensity generated by age-dependent manifestation of DHF. The results of simulation are presented for four age-dependencies (

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Relationship between DHF incidence and transmission intensity generated by transmission enhancement. Transmission enhancement (

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Temporal pattern of alternating serotypes in the presence of cross immunity and effects of a sudden drop in transmission intensity. Examples of serotype-specific incidence of DHF are presented. The last 40 years are presented.

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Relationship between mean age of DHF cases and Dengue transmission intensity (R_{0}) Mean age of DHF cases is plotted against transmission intensity (R_{0}). The result for a parameter setting (_{0}.

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Periodicity profile (periodogram) for incidence generated by simulations for Dengue Hemorrhagic Fever (DHF). Individual-based simulation for DHF (described in the accompanying manuscript) was executed for 150 years, from which monthly incidence for the last 40 years was analyzed by fast Fourier transform with Daniell smoothing (provided in R 2.6.2). Parameters for simulations are as follows: cross-immunity of 0.5 year (A–C), one year (D–F), two years (G–I), three years (J–L), and four years (M–O); age-dependency, which attributes a higher probability of manifesting DHF to the older population [defined as _{0} = 3 (A, D, G, J, M, P, S), R_{0} = 6 (B, E, H, K, N, Q, T), or R_{0} = 12 (C, F, I, L, O, R, U). We executed each parameter setting in duplicate, and confirmed that the resulting periodograms were very similar. The highest spectrum intensity was presented as 1, for each parameter setting.

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Standard deviation in the asynchronous sinusoidal incidences. One hundred sinusoidal curves, with asynchronous phases, were generated, to emulate the incidence of DHF. The sinusoidal incidence was averaged for diverse window lengths (“

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Translation of the Abstract into Japanese by Yoshiro Nagao

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We thank the community volunteers as well as the staff of vector control units and regional vector-borne disease control offices. We thank Professor Takashi Mashimo, Dr. Katia Koelle, Dr. Joseph Egger, Mrs. Ladda Likityingwara, Dr. Usavadee Thavara, Ms. Pensri Chitnumsup, Dr. Ichiro Kurane, Dr. Diarmid Campbell-Lendrum, and Professor Susumu Hotta for their advice and assistance. We are grateful to a reviewer for suggesting the use of GAM.