The authors have declared that no competing interests exist.
Managed the lab and data: JEQC JGCC VQM JAJ FSMC MZL. Conceived and designed the experiments: CMB MZL DSS AH. Performed the experiments: CMB AH. Analyzed the data: CMB. Contributed reagents/materials/analysis tools: FSMC CN JGCC. Wrote the paper: CMB JMM MZL KS DSS.
With increasing urbanization vectorborne diseases are quickly developing in cities, and urban control strategies are needed. If streets are shown to be barriers to disease vectors, city blocks could be used as a convenient and relevant spatial unit of study and control. Unfortunately, existing spatial analysis tools do not allow for assessment of the impact of an urban grid on the presence of disease agents. Here, we first propose a method to test for the significance of the impact of streets on vector infestation based on a decomposition of Moran's spatial autocorrelation index; and second, develop a Gaussian Field Latent Class model to finely describe the effect of streets while controlling for cofactors and imperfect detection of vectors. We apply these methods to crosssectional data of infestation by the Chagas disease vector
Chagas disease is a major parasitic disease in Latin America. It is transmitted by
In the context of increasing urbanization worldwide
Prevention of vectorborne diseases relies heavily on vector control
Arequipa, Peru, a city of nearly 1 million inhabitants, is currently experiencing an epidemic of infestation by
The impact of known boundaries such as roads or rivers on epidemics or population dynamics has occasionally been assessed using spatiotemporal modeling to describe spatiotemporal presenceabsence data
Here we propose to quantify the impact of known boundaries by measuring their effect on spatial autocorrelation in presenceabsence data. Variations of the autocorrelation over distance have been measured and presented in autocorrelograms
We conducted our study in Paucarpata, the largest district in the city of Arequipa, Peru. The Ministry of Health of Arequipa applied insecticide to 13,917 households in Paucarpata between November 2006 and April 2009. During the insecticide application campaign, householdlevel data on the presence or absence of
We mapped the position of all households and the delimitation of city blocks in the district comparing satellite imagery in Google Earth™
We first assessed the impact of streets on the global spatial autocorrelation of vector infestation as measured by the Moran index (I)
To determine if streets affect the spatial autocorrelation of infestation, we decomposed the autocorrelation into a within cityblock component and an across cityblocks component. We then calculated separate autocorrelograms for pairs of households on the same city block (
We then assessed the significance of the difference
The decomposition of Moran's Index offers a fast, simple way to obtain an estimate of how streets impact the autocorrelation of observations. However, several factors could confound or obscure this estimate. First, wellknown risk factors for
Beyond these two considerations, there is a third, less obvious limitation to the Moran's I. As a pairwise statistic, Moran's I, as well as its derivatives described here, measures indirect and direct correlation together: measured correlation could result either from a direct correlation between households or an indirect correlation mediated by the inbetween households that are strongly correlated on a small distance scale. The effect of streets can be important simply because streets create a gap in a chain of small distance scale autocorrelations between households (hereafter the “gap effect”). In contrast, streets may, above and beyond the gap effect, serve as a barrier to vector migration (hereafter the “barrier effect”). A spatial fieldbased measure of autocorrelation accounts for the autocorrelation of neighbors at all distances simultaneously. Such an approach can then detect a barrier effect linked to the presence of streets and not only to the uneven distribution of households induced by streets.
We built a Bayesian generalized linear model describing household infestation status as a discrete manifestation of a continuous predictor of infestation. The predictor of infestation includes a spatial field component
Working backward, we consider the infestation data
Spatial component. The spatial component
We introduce the effect of streets in a similar way as in the decomposition of the Moran's I – by distinguishing between neighbors within a city block and proximate households separated by streets. The spatial weight
We consider four oneparameter kernels describing a wide range of shapes (
Name  Equation, 
Shape  DIC  Shape factor 
Streets factor, 
Same Block Index 
Exponential 

Sharp top, thin tail  2526  9.00 (7.04–11.8)  0.30 
94.0% (89.8–96.9) 
Gaussian 

Flat top, thin tail  2553  17.3 (14.4–21.2)  0.52 
93.7% (88.1–97.3) 
Cauchy 

Flat top, fat tail  2553  8.25 (5.30–13.0)  0.08 
94.7% (91.4–97.3) 
Geometric 

Sharp top, fat tail  2609  7.64 (2.08–26.3)  0.03 
95.1% (91.6–98.2) 
The shape factor
Same Block Index: Percent of the spatial component of infestation explained by same city block neighbors (see Section 2 in
To assess the relevance of the cityblock as a spatial unit of infestation we calculate the “Same Block Index” which we define as the mean percentage of the spatial component of infestation explained by neighbors on the same city block (Section 2 in
Local component. We include in a local component
Link function. We relate our outcome data, the observed infestation,
When infestation data are not available (noninspected houses), the sensitivity is set to 0 (see Section 4 in
Fitting and validation. We fit the Gaussian Field Latent Class model on a fraction of the map consisting of all of the households inspected between September and December 2007 (
Map of the study area. Black indicates infested households, white noninfested households, and grey noninspected households. The area encircled by dashes was used to fit the Gaussian Field Latent Class model; the remaining area was used as a validation dataset. The closeup shows the urban grid underneath and the aggregation of vectors within city blocks.
We used the validation dataset to determine how well our parameterized model predicted the presence of vectors in unobserved households. To do so, we randomly selected 5% of the houses in the validation set and removed them. We set the sensitivity of inspectors and the spatial parameters to their estimated means, remove the cofactors from the model and refit the spatial component, predicting the observation of infestation in the withheld households. We repeated the process 20 times, without replacement, so that all houses had been selected for prediction exactly once. We then evaluated the predictions using the McFadden index
As a second check, we verified that the Gaussian Field Latent Class model properly reproduced the global autocorrelation of the observed infestation by generating
All analyses were performed in R
During the vector control campaign in Paucarpata, the Ministry of Health sprayed 9,654 houses, among which 1,791 (18.5%) were infested with
For all distance classes up to 120 m, the autocorrelation among houses within the same city block was significantly greater than that among houses separated by streets (
Left: autocorrelation of the infestation status as a function of the distance. Solid line: Global Moran's index. DotDashed line: Moran's Index for within blocks household pairs. Dashed line: Moran's Index for household pairs across streets. All Moran's I values are significantly different from the expected value under hypothesis of no spatial autocorrelation (
Notably the expected difference
Controlling for the spatial distribution of cofactors and inspectors, we estimated the barrier effect of streets on infestation to induce a two to thirty fold decrease (
As a part of the fitting process of the Gaussian Field Latent Class model, we assessed the effect of cofactors on the presence of vector infestation. We found that the presence of guinea pigs and the presence of dogs were significant risk factors for vector infestation. Conversely, we found that the presence of plastered walls inside of the house was strongly and significantly protective against infestation. The degree of the effect of these cofactors varied across the four kernels considered (detailed results in
Interestingly, for all four kernels, the standard deviation of the continuous infestation predictor induced by the joint effect of all the cofactors and the random effect (0.44–0.54) was threefold less than the standard deviation of the estimated spatial component across households (1.64–1.93).
We also assessed the quality of inspectors in terms of their sensitivity—the probability that an inspector detects vectors in households that are indeed infested. The mean inspector sensitivity was 70%, with extremes at 41 and 90% (
The Gaussian Field Latent Class model allowed us to make generally accurate predictions in holdout households across the four kernels (McFadden index
The autocorrelation of infestation in the generated data is compared to the autocorrelation in observed data. Infestation data were generated on the validation map using the estimated parameters for each of the kernels: exponential (first column), Cauchy (second column), Gaussian (third column), and geometric (fourth column). We calculated the standard Moran's I (first row) and the difference
We observed a significant effect of streets on the spatial pattern of Chagas disease vectors in Arequipa, Peru, and show that greater than 90% of the spatial component of infestation is determined by neighbors on the same city block. In addition, the difference of autocorrelation in the same block and between blocks indicate that the crossing of streets is grossly equivalent to an added distance of 30–45 m in terms of spatial autocorrelation. The limiting effect of streets was consistent across two methodological approaches: a pairwise analysis (decomposed Moran's I) and a field based model (Gaussian Field Latent Class). The latter approach accounted for known cofactors and imperfect detection, further confirming that streets constitute an important barrier to aggregation of triatomine infestation above and beyond the uneven spatial distribution of urban households.
The underlying cause of the barrier effect of streets on
Several authors have commented on the need to assess the role of landscape heterogeneity in the context of epidemiological
We have shown previously that the presence of guinea pigs, the presence of dogs and the presence of other animals are risk factors for triatomine infestation and that fully cemented plaster walls are protective
There are several limitations to our study. The effect of streets detected in our approach could be confounded by unmeasured cofactors strongly clustered within blocks. Two reasons nevertheless limit the probability of such a scenario. First our Gaussian Field Latent Class model explicitly accounts for the main known cofactors of infestation by Chagas vectors as identified previously
We were only able to obtain binary data on the presence or absence of vectors; data on vector densities could provide more information with which to assess the effect of streets. While our analysis is tailored to binary observations, it could be extended to consider discrete measurements. Our Gaussian Field Latent Class model can be applied to a wide variety of datasets without adaptation of the priors; however, care should be taken to correctly choose the order of magnitude when assigning a prior on the shape factor of the spatial autocorrelation kernel. The use of 100m as a threshold distance beyond which correlation is assumed to be null is a simplification needed to lessen computation time; we assessed the effect of this simplification and determined that our findings were not affected by it.
The flat prior used here for inspector sensitivity may shrink the posterior towards the mean of the prior, 50%. The true sensitivity is then likely greater than the estimate provided here, 70%. However, the strong estimated effect of streets is robust to variations of the prior (Section 4 in
Further extension of the model would be necessary to determine whether wider streets pose a greater barrier to insects than narrower ones. Interestingly, if, as we hypothesize, the barrier effect is mainly due to the asymmetry in housing materials in the front and back of houses, broader streets may not pose a greater barrier to insects. Finally, further work is needed to assess if the impact of streets is affected by the seasonality of
Our findings have implications for adapting control strategies to disease transmission dynamics. First, city blocks have been used as a practical unit of study previously
The difficulties presented in controlling Chagas vectors in cities are similar to those of other urban disease vectors and pests such as the mosquito vectors of Dengue (
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We thank Dr. Tony Smith, Dr. Sébastien Goubière, Dr. Vitaliano A. Cama, Ian Spalding, Dr. Chris Paciorek and Katelyn Levy for insightful comments; Katty BorriniMayori, Danitza Pamo, Giovanna Moscoso, Lina Mollesaca, Maria Luz Hancco, Manuel Burgos, Renzo Salazar, and the laboratory staff at UPCHLID. We gratefully acknowledge the work of the following organizations that have organized and conducted the Chagas disease control program in Arequipa: Ministerio de Salud del Perú (MINSA), the Dirección General de Salud de las Personas (DGSP), the Estrategia Sanitaria Nacional de Prevención y Control de Enfermedades Metaxénicas y Otras Transmitidas por Vectores (ESNPCEMOTVS), the Dirección General de Salud Ambiental (DIGESA), the Gobierno Regional de Arequipa, the Gerencia Regional de Salud de Arequipa (GRSA), the Pan American Health Organization (PAHO/OPS) and the Canadian International Development Agency (CIDA). We thank the district of Paucarpata for its participation in this study.