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The only way for dengue to spread in the human population is through the human-mosquito-human cycle. Most research in this field discusses the dengue-mosquito or dengue-human relationships over a particular study area, but few have explored the local spatial variations of dengue-mosquito and dengue-human relationships within a study area. This study examined whether spatial heterogeneity exists in these relationships. We used Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) models to analyze spatial relationships and identify the geographical heterogeneities by using the information of entomology and dengue cases in the cities of Kaohsiung and Fengshan in 2002. Our findings indicate that dengue-mosquito and dengue-human relationships were significantly spatially non-stationary. This means that in some areas higher dengue incidences were associated with higher vector/host densities, but in some areas higher incidences were related to lower vector/host densities. We demonstrated that a GWR model can be used to geographically differentiate the relationships of dengue incidence with immature mosquito and human densities. This study provides more insights into spatial targeting of intervention and control programs against dengue outbreaks within the study areas.

Dengue is the most rapidly spreading mosquito-borne viral disease in the World [

The dengue viruses (DENVs) are transmitted to humans by

The relationships of the dengue incidence–mosquito abundance and dengue incidence-human density are still not well understood. Since the density of adult mosquitoes is difficult to estimate, immature vector data were widely used for evaluating the incidence–mosquito relationship [

Until now, most studies of dengue-mosquito or dengue-human relationships have presented a global perspective by which any relationship was assumed to be spatially constant across the whole study area, thereby ignoring local variations. However, this assumption may be inappropriate since the dengue-mosquito or dengue-human relationships could be positively correlated in some study areas, but negatively or not correlated at all in other areas. For example, a small number of female mosquitoes in a very dense area is sufficient to cause an outbreak. This study was conducted to evaluate the hypothesis that spatial heterogeneity existed for dengue-mosquito and dengue-human relationships. We demonstrated that the variation of dengue incidences among study areas was reflected by the densities of both immature vectors and hosts. By capturing the local relationships across the space, the authorities can design more effective, locally-specific strategies. This understanding is especially important where the control and prevention resources are limited.

Kaohsiung city has been the epicenter where most of the dengue outbreaks have been recorded in Taiwan [^{2}, is the most densely populated urban centre in Taiwan. The neighboring Fengshan city, located directly to its east, has a population of 330,000 within an area of 27 km^{2}. Piped water is available for 99% of the city households and household waste is removed daily throughout both cities by the government. The 2002 dengue epidemic in which Kaohsiung and Fengshan cities were the major foci was the largest outbreak in recent years in Taiwan (

The “Li”, the lowest administrative unit in Taiwan, was used as the spatial mapping unit in this study. There were a total of 542 Lis and 12 districts in the two cities during the study period of 2002. On average each Li had a population of 3,366 and 1138.41 households in an area of 0.36 km^{2}. The study area is shown in

All information on dengue cases was provided by the Centers for Disease Control-Taiwan (Taiwan CDC). Laboratory confirmation was obtained for all suspected cases identified through passive, active and passive-based active surveillance activities. Passive surveillance involved the mandatory referral of suspected dengue cases within 24 h of presentation at any of 231 health clinics or hospitals (both private and public), school-based reports of absence due to fever as well as individual self-reporting [

Larval habitats of

Breteau index was used to estimate the density of immature ^{2}) was taken from 2002 census data as an indicator of human population density (POPden) estimated for each Li.

In this study, the dengue annual cumulative incidence (IR), given as cases per 100,000 populations, was used as the measure of disease severity, and as the dependent variable; independent variables were POPden and the monthly maximum BI detected in each Li in 2002 (BI_{max}). A summary of the variables in both Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) models are shown in _{0} + β_{1} BI_{max}+ β_{2} POPden + ɛ. β_{0} and β_{1} were the regression coefficients whereas

The diagnoses of an OLS model were approached by assessing multicollinearity and the residuals. The multicollinearity was assessed through variance inflation factor (VIF) values, and if VIFs were greater than 10, this indicated multicollinearity existed [

where _{i}_{ij}

The values of Moran's

A GWR local model was applied to analyze how the IR-BI_{max} and POPden relationships changed from one Li to another. It was a localized multivariate regression that allowed the parameters of a regression estimation to change locally. Unlike conventional regression, which produced a single regression equation to summarize global relationships among the independent and dependent variables, GWR detected spatial variation of relationships in a model and produced maps for exploring and interpreting spatial non-stationarity [

Within the matrix, _{gn}_{gn}

The spatial variability of an estimated local regression coefficient was examined to determine whether the underlying process exhibited spatial heterogeneity [_{i}_{0}_{i}_{1}_{i}_{max}_{i}_{2}_{i}_{i}_{i}

We also examined the local collinearity as well as the independency and normality of residuals of GWR model to evaluate the fit of the model. The local collinearity was assessed by scatter plots of the local coefficient estimates for BI_{max} and POPden and condition number. The condition number is the square root of the largest eigenvalue divided by the smallest eigenvalue. If the condition numbers are greater than 30, multicollinearity would be a very serious concern. The adjusted coefficient of determination (Adjusted R^{2}), and ANOVA were used for comparing OLS and GWR models. Akaike Information Criterion (AIC) generated for OLS and corrected Akaike Information Criterion (AICc) calculated for GWR were also used for model comparison [

Our analysis in this article was based on Li-level data. All analyses were implemented using ESRI^{®}ArcGIS^{TM}9.3 and GWR 3.0 with 0.05 significance level. In the GWR model, the adaptive kernel with AICc estimated bandwidth was chosen. The adaptive kernel was chosen because the distribution of Li was inhomogeneous in the study area (

The spatial distributions of the IR, BI_{max} and POPden were mapped in

The results of applying OLS regression showed that holding the variable of population density fixed, ceteris paribus, one BI_{max} increase is significantly associated with 947.93 increase of average IR (_{max} and POPden relationships.

The summary results of GWR are listed in

^{2} between the observed and fitted values, which indicated how well the GWR model replicated the local IR around BI_{max} and POPden. It was obvious that the value of R^{2} was not homogeneously distributed in all Lis, and the overall GWR regression fitted best in districts 1, 5, 10 and 11. This model did not fit well in district 12, and this could imply additional covariates were needed to explain the IR in district 12.

The condition number shown in

The spatial variations in parameter estimations for intercept, maximum Breteau index and population density are shown in _{max} and POPden equaled zero. It was observed that higher intercept values were located around the borders of two cities [districts 9, 10 and 11, _{max} shown in _{max}. However, in the remaining districts, higher IR associated with lower BI_{max} and

This study provides further indications that the relationships of dengue incidence-maximum BI and dengue incidence-population density were spatially non-stationary in Kaohsiung and Fengshan cities. In regression maps, it is clear that the intensity and directions of the influence of maximum BI and population density on dengue incidence were different in the study area. This result gives the policy makers more ideas how to better adopt specific control and prevention strategies to specific areas [

The spatial heterogeneity of intercept results in

In the northern part of the study area, higher human densities were shown to contribute to higher dengue incidence rates. This positive relationship was expected as higher human density may lead to higher vector-host contact rates. A previous finding in Taiwan showed that the relative risk of accumulated dengue incidence for areas with more than 10,000 people/km^{2} was 10-fold compared to areas with less than 1,000 people/km^{2} [

The relationship between vector abundance (both immature and mature stages) and dengue occurrence has been discussed in many studies [

To improve the understanding of incidence-vector and incidence-host relationships, the followings could be further examined. First of all, the researchers could adopt GWR space-time analyses, such as stratifying the year of 2002 into different periods, or analyzing more than one epidemic year. This approach could provide more detailed patterns of spatial autocorrelation changes of incidence-vector and incidence-host associations. Secondly, the researchers could use other BI calculations such as minimum BI or average BI to see whether different incidence-BI relationships would be generated. Threshold effect of BI could also be considered. Thirdly, categorizing human by different age groups in the GWR model could assist policy makers to determine which actions are suitable for different populations. Finally, researchers could also separate

The geographical heterogeneity was detected by the GWR method in the relationships of dengue incidence with immature mosquito and human density (^{2}, AIC/AICc and ANOVA all indicated GWR was a better model to explain this dataset. GWR approaches have been applied in a lot of areas, such as public health and demography, as an exploring method for identifying the spatial variations [

This paper underlines the spatial variations of incidence-immature mosquito density and incidence-human density relationships in a local scale. Exploring the heterogeneity of spatial relationships could provide more insights into spatial targeting of intervention against dengue epidemics.

The research was supported by the grants of National Science Council (NSC 98-2410-H-002-168-MY2) in Taiwan. The authors also acknowledge the financial support provided by Infectious Diseases Research and Education Center, Department of Health and National Taiwan University. The funder had no role in study design, data collection and analysis, or preparation of the manuscript.

The epidemic curve of confirmed dengue cases as cumulated by weeks of onset in Kaohsiung and Fengshan cities, 2002–2009.

The distribution of 542 Lis and 12 districts in Kaohsiung (district 1–10 and 12) and Fengshan cities (district 11) in Taiwan. Each small polygon represents each Li.

Spatial distributions of (_{max}); and (^{2}. Li was the basic administrative unit in Taiwan, and there were 542 Lis in the study area.

Spatial mapping of the locally weighed coefficient of determination (R^{2}) between the observed and fitted values by geographically weighted regression (GWR) modeling. The data presented here were the 2002 dengue incidence, the maximum Breteau index and population density in each Li in Kaohsiung and Fengshan cities.

Spatial mapping of pseudo _{max}) and population density (POPden) for each Li by geographically weighted regression (GWR) modeling. The dependent variable was dengue incidence (per 100,000 populations) taken from 2002 dengue epidemic data in Kaohsiung and Fengshan cities. Each polygon represents each district.

Scatter plot of the GWR coefficients of population density (POPden) and maximum Breteau index (BI_{max}) with R^{2} = 0.01. The dashed lines were the levels of the OLS estimations.

Normal quantile-quantile plot of the residuals from GWR estimations.

Summary of BI_{max} and POPden impact on incidence using GWR in each district. BI_{max} (+) means BI_{max} had positive impact on incidence while BI_{max} (−) means BI_{max} had negative impact on incidence; POPden (+) means POPden had positive impact on incidence whereas POPden (−) means POPden had negative impact on incidence.

Summary of dependent and independent variables used in OLS and GWR.

Variable | Numerator | Denominator | |
---|---|---|---|

Dependent: | IR | 100,000 × number of cases | Populations |

Independent: | BI_{max} |
100 × number of positive containers | Number of premises inspected |

POPden | Populations | The area of Li (km^{2}) |

IR: cumulative incidence of dengue; BI_{max}: Maximum Breteau index; POPden: Population density.

Ordinary Least Squares (OLS) results.

Parameter | Estimated Value | Standard Error | VIF | |
---|---|---|---|---|

Intercept | 115.52 | 34.73 | 0.003 | |

BI_{max} |
947.93 | 202.48 | 0.013 | 1.02 |

POPden | 0.00 | 0.00 | 0.111 | 1.02 |

Adjusted R^{2} |
0.04 | |||

AIC | 7,902.12 |

Geographical weighted regression (GWR) results.

Parameter | Minimum | 25% quartile | 50 % quartile | 75 % quartile | Maximum |
---|---|---|---|---|---|

Intercept | −272.60 | 78.46 | 166.09 | 320.92 | 1,088.31 |

BImax | −2980.43 | −262.53 | 100.40 | 838.91 | 5,797.87 |

POPden | −0.02 | −0.00 | 0.00 | 0.00 | 0.02 |

Condition number | 2.96 | 4.67 | 5.83 | 7.32 10.39 | |

Adjusted R^{2} |
0.59 | ||||

AICc | 7,715.17 |