Spatial clustering in the spatio-temporal dynamics of endemic cholera

Abstract

Background: The spatio-temporal patterns of infectious diseases that are environmentally driven reflect the combined effects of transmission dynamics and environmental heterogeneity. They contain important information on different routes of transmission, including the role of environmental reservoirs. Consideration of the spatial component in infectious disease dynamics has led to insights on the propagation of fronts at the level of counties in rabies in the US, and the metapopulation behavior at the level of cities in childhood diseases such as measles in the UK, both at relatively coarse scales. As epidemiological data on individual infections become available, spatio-temporal patterns can be examined at higher resolutions.

Methods: The extensive spatio-temporal data set for cholera in Matlab, Bangladesh, maps the individual location of cases from 1983 to 2003. This unique record allows us to examine the spatial structure of cholera outbreaks, to address the role of primary transmission, occurring from an aquatic reservoir to the human host, and that of secondary transmission, involving a feedback between current and past levels of infection. We use Ripley's K and L indices and bootstrapping methods to evaluate the occurrence of spatial clustering in the cases during outbreaks using different temporal windows. The spatial location of cases was also confronted against the spatial location of water sources.

Results: Spatial clustering of cholera cases was detected at different temporal and spatial scales. Cases relative to water sources also exhibit spatial clustering.

Conclusions: The clustering of cases supports an important role of secondary transmission in the dynamics of cholera epidemics in Matlab, Bangladesh. The spatial clustering of cases relative to water sources, and its timing, suggests an effective role of water reservoirs during the onset of cholera outbreaks. Once primary transmission has initiated an outbreak, secondary transmission takes over and plays a fundamental role in shaping the epidemics in this endemic area.

Figure 1

Study Area. The Matlab rural area. Light gray points are mapped water sources (ponds), dark gray points are baris and, as example, black points map cases from one epidemic of cholera classical Ogawa. Black lines represent the limits of the study area and light gray lines are rivers.

Figure 2

Temporal Dynamics of Cholera epidemics. The different lines represent annual cholera epidemics, solid black lines correspond to epidemics of classical (Inaba and Ogawa) strain, dashed dark gray lines show El Tor epidemics (Inaba and Ogawa). Variability is strongly marked, not only inter-annual or seasonality, but also intra-annual variability in both the timing of the outbursts and magnitude of the epidemics.

Figure 3

Ripley's L function for an particular epidemic. These three examples show variability and characteristics of the spatial clustering. Plotted in dark gray, the Ripley's L function for the observed data against distance. The Ripley's L function for observed data (dark gray) is plotted bold when statistically significant (i.e., outside the bootstrapping envelop), but otherwise is dashed. The light gray area was defined by the 10000 bootstrapping replications, these replications were constructed using all the cases for a particular epidemic. The most significant cluster size, or simply cluster size, is defined as the distance at which the difference between the bootstrapping envelope and the observation is maximum (black bold vertical segment), this is indicated by the vertical dashed line in the figure. The top panel shows a case where the cluster size is relatively large (2340 meters) but small scale significant clusters are also present. The bottom-left shows a cluster size with small scale (50 meters) without the occurrence of clusters at large scales. The bottom-right displays a large cluster size (5010 meters) without clusters at small scales.

Figure 4

Cholera seasonality. Seasonal variation is shown on the mean number of cholera cases (El Tor Inaba) during the epidemics. In this plot the time has been rescaled and hence outbreaks from several years were aggregated. The vertical lines show beginning, first peak, the inter epidemic trough, second peak and end of the average occurrence of cases.

Figure 5

Cluster size for the different epidemics. Time has been rescaled and π represents the Fall peak and 3π the Spring peak. Cluster Size for cases is shown in (a) and cluster size for cases-water in (b) Different symbols represent different epidemics a temporal window of 5 days for the disease data was used for this figure, but see additional figures for a disaggregation for the different epidemics and temporal windows. In (a) the occurrence of small clusters is clearly abundant, moreover medium size clusters (less than 6 Km) are less abundant and bigger clusters are rare, this pattern is not clear for (b). In addition, clusters clearly occur more often in the Fall peak and in the Spring.

Figure 6

Temporal dynamics of clustering and epidemic size. Temporal dynamics of clustering and epidemic size averaged for all epidemics. Top row shows cluster size for cases in gray and epidemic size in black. Bottom row shows cluster size for cases-water in gray over epidemic size in black. Left column displays classical Ogawa data, center is classical Inaba and right column shows El Tor Inaba data.

Figure 7

Distribution of cluster sizes for different strains. Top row shows cluster size for cases. Bottom row shows cluster size for cases-water. Left column displays classical Ogawa data, center is classical Inaba and right column shows El Tor Inaba data. Different lines represent different temporal aggregation of the data.