Malaria remains a formidable threat to public health in tropical regions. The parasite that causes the disease is transmitted to humans by bites from infected mosquitoes, and the complicated lifecycle of the parasite makes developing vaccines difficult. However, preventive strategies are effective at reducing the spread of malaria. The two most widely used and effective strategies are the use of pesticide-treated bed nets to create a barrier between sleeping families and biting mosquitoes, and indoor residual spraying to reduce the numbers of mosquitoes biting sleeping families in homesteads. Other potential preventive strategies include killing mosquito larvae in breeding sites and mass anti-malarial drug treatment for infected humans.

Targeting preventive efforts to malaria hotspots—the areas where the risk of malaria transmission is greatest—may help to eliminate malaria more efficiently. Unfortunately, identifying hotspots is complicated as there are many different factors that affect how malaria spreads. These factors range from ecological conditions such as rainfall and soil type, to human effects like population density and migration.

Bejon et al. have examined the patterns of malaria transmission in Kenya over 9 years. Over this period, 54% of children who went to health clinics with a fever tested positive for the parasite that causes malaria. Infected children from areas with the highest rate of malaria infection were, on average, younger than those from less infected regions. This makes sense as in highly affected areas children have a greater chance of encountering the parasite at an early age. They are therefore more likely to get malaria when younger and, as exposure to the parasite can provide some immunity to a child, they are also less likely to get infected again when older.

In addition, mapping the spread of malaria reveals hotspots at different geographical scales. Bejon et al. could see hotspots within hotspots, and in some cases could go as far as identifying the individual homesteads most at risk of malaria. Public health workers could potentially use these analyses to identify areas that are likely to be hotspots and then target preventive measures there for the next month. However, the constantly changing locations of the hotspots means workers would have to reanalyse the data and retarget their interventions at the end of each month.

The transmission of infectious disease often shows substantial heterogeneity (Woolhouse et al., 1997). Malaria transmission is determined by mosquito ecology and behavior, which is in turn determined by rainfall, hydrology, soils, human behavior and population distributions, and a range of other social, biotic and abiotic factors. Heterogeneity of malaria transmission is apparent at global scale (Gething et al., 2011), regional scale (Kleinschmidt et al., 2001a; Noor et al., 2009), and at fine scale in, for instance, Mali (Gaudart et al., 2006), Ghana (Kreuels et al., 2008), Ethiopia (Yeshiwondim et al., 2009) Kenya (Brooker et al., 2004; Ernst et al., 2006; Bejon et al., 2010), and Tanzania (Bousema et al., 2010). This spatial heterogeneity makes transmission relatively resilient to indiscriminate control efforts, but also provides an opportunity to engage in targeted malaria control on clusters of transmission (or ‘hotspots’), a strategy that is predicted to be highly effective (Dye and Hasibeder 1986; Woolhouse et al., 1997).

We have previously identified hotspots of malaria using active surveillance (Bejon et al., 2010). Others have identified hotspots using passive surveillance in health facilities linked to demographic surveillance systems (Ernst et al., 2006). Passive surveillance is more readily scaled up, but may be biased by variations in access to health care facilities and socially-determined health-seeking behavior (Sumba et al., 2008; Franckel and Lalou 2009). The incidence of febrile malaria presenting to health care is thus biased by access to care. This bias may be countered by using the malaria positive fraction (MPF) among children with fever (also termed ‘slide positivity rate’ in some publications [Jensen et al., 2009]). The MPF includes all febrile children presenting to the dispensary as the denominator, hence controlling for access to health care, in contrast to incidence for which all children in the community are included in the denominator. The MPF is less likely to show systematic spatial bias with distance from the health facility since parental accounts of illness have not been found to discriminate malaria from non-malarial fever (Luxemburger et al., 1998; Mwangi et al., 2005), and diagnostic testing is not available outside the dispensary.

We present data from demographic surveillance linked to passive case detection in Pingilikani dispensary in Kilifi District, coastal Kenya. Data are collected from 1500 homesteads within an 8 km radius followed for 9 years. We analyse the spatial heterogeneity of malaria cases in order to determine the temporal and spatial scales of case clustering so as to inform targeting in malaria control programmes. We also excluded visits with specific symptoms such as skin infections or cutaneous abscesses, otitis media, and gastroenteritis (>4 episodes diarrhoea per day) that might have been the primary motivation for seeking health care rather than fever per se.

Among ∼20,000 remaining febrile presentations from ∼1500 different residences, 54% were positive for Plasmodium falciparum on blood smear examination. Using homestead as our unit of analysis, we found that the incidence of dispensary attendance declined with distance from the dispensary (on average −0.040 (95%CI 0.036–0.044) and −0.041 (95%CI 0.037–0.046) episodes per child year for each km for malaria smear positive and negative attendees, respectively). MPF was not found to vary significantly by distance of residence from the dispensary (from MPF = 0.50, 95%CI 0.47 to 0.54 at <2 km distance to MPF = 0.52, 95%CI 0.47 to 0.57 at 6–7 km, p=0.7).

The spatio-temporal distribution of MPF by homestead is shown in Video 1 (slow speed) and Video 2 (fast speed). The visual impression from these clips suggests marked spatial variation, with some geographical areas showing persistently high MPFs, and other areas showing more marked temporal variation. Temporally stable spatial heterogeneity would be expected to lead to spatial heterogeneity in the acquisition of immunity, which may be evidenced by variation in the age profiles of children with febrile malaria. We therefore tested this hypothesis as below.

Video 1

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Video 2

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Spatial heterogeneity in malaria risk and acquisition of immunity

MPF was inversely correlated with the average age of children with malaria, Spearman's rank correlation (r_s) = −0.16, p<0.0001 (Figure 1A–C). This suggests that greater exposure to malaria (i.e., high MPF) leads to more rapid acquisition of immunity as children grow up, hence predominantly younger children visiting the dispensary with febrile malaria. There was no evidence that this relationship was confounded by spatial clustering of age: the average age of children with non-malarial fever did not show spatial clustering (Moran's I = 0.01, p=0.5 within 1 km and Moran's I = 0.02, p=0.5 within 5 km) and was not associated with MPF (r_s = −0.02, p=0.4). We examined the effect of spatial scale at which this correlation occurred by imposing grids of increasing cell size on the study area, calculating r_s within each cell of the grid, and then estimating the mean r_s at each scale of grid (Figure 1D, blue lines). The mean r_s trended gradually away from 0 as the grid divisions became larger in scale. This pattern suggests gradual differentiation in transmission characteristics as the distance between homesteads included within a cell of the grid increases. We then examined the patterns seen on applying this analysis to simulated data. In order to exclude that this trend was a result of cells at fine-scale containing fewer homesteads, we ran permutations of the data using after randomly re-assigning spatial coordinates to the homesteads. These permutations show that a consistent correlation at r_s = −0.16 throughout the range of grid sizes, albeit with greater uncertainty with smaller cell size (Figure 1D, red lines). Hence, the trend of a gradually increasing inverse correlation as the grid size increases does not appear to be explained simply by having fewer homesteads in each cell at fine scale. In order to determine the pattern that might be seen with specific spatial scales of clustering, we conducted further simulations by imposed patterns with specific scales on the spatial coordinates of the homesteads, in varying proportions with random noise using a gamma distribution. These simulations show that a specific scale of clustering produces ‘spikes’ in r_s as the cell size varies, with the position of the spike coinciding with scale of the clustering (Figure 1—figure supplement 1). Reducing the Signal:Noise ratio eventually obscured the ‘spikes’ due to a characteristic pattern, but only at the point where the overall correlation was no longer discernible (Figure 1—figure supplement 2). Adding a gradient to the simulated characteristic scale attenuated but did not obscure the ‘spikes’ (Figure 1—figure supplement 3).

Figure 1 with 3 supplements see all

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Hotspots within hotspots

Using the Bernoulli model in SaTScan (Kulldorff, 1997), we identified a hotspot with a radius of 5.8 km at p<0.00001 (Figure 2A) using the full data set (for which n = 20,702). However, on re-analysis of the children within this hotspot (in which n = 5300), we identified a further hotspot (with a radius of 0.76 km) within the 5.8 km hotspot (p<0.00001, Figure 2B). Then on further re-analysis of the homesteads within that 0.76 km hotspot (within which n = 1406), we identified a third significant hotspot (p=0.016) which comprised a single homestead, in which there were 36 episodes of malaria compared with 3 malaria negative fevers (Figure 2D). When we selected a random 5-km square area outside the original 5.8 km radius hotspot, we identified a hotspot within this area a fourth hotspot with a 1.32 km radius (p<0.00001, Figure 2C).

Figure 2 with 2 supplements see all

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To further explore the scale of spatial clustering, we plotted the semivariogram (Figure 2—figure supplement 1) and the log–log transformed semivariogram (Figure 2—figure supplement 2). These plots suggested linear fits for the semivariogram, suggesting that spatial clustering occurred over a range of spatial scales.

Temporal trends of spatial heterogeneity

We also examined temporal trends for individual homesteads (Figure 3). There was an inverse correlation between the mean MPF and the variance in MPF over the 10-year study period (r_s = −0.61, p<0.0001, Figure 3A). The temporal trends for two subsets of homestead can be seen in Figure 3B (stable high MPF) and Figure 3C (unstable low MPF), suggesting that homesteads can be characterized as stable high transmission homesteads or unstable low transmission homesteads. Infant parasite rates have been proposed as a measure of transmission intensity that minimizes the offsetting of acquired immunity in macro-epidemiological studies (Snow et al., 1996). We therefore hypothesized that the malaria positive fractions in children <1 year of age (hereafter ‘MPF_<1yr’) would measure transmission intensity without the offsetting of acquired immunity, and that unstable transmission would result in higher risk of malaria in older children. To test this hypothesis, we calculated the mean MPF_<1yr and the variance in MPF_<1yr for each homestead over the 9 years of follow up and tested the relationships between these metrics and risk of malaria in older children in multivariable linear regression models.

Figure 3

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In multivariable linear regression models, MPF_<1yr was strongly correlated with MPFs in children in the 1- to 2-year-old and 2- to 3-year-old age group, but progressively less strongly correlated with MPF in older children (Figure 3Di). The regression coefficient was ∼0.4 for 1–2 year olds, meaning that each unit increase in MPF_<1yr is associated with a 0.4 increase in the MPF for 1- to 2-year-old children. On the other hand, the variance in MPF_<1yr was not correlated with MPFs in 1- to 2- or 2- to 3-year-old children, but was progressively more strongly correlated with MPF in older children (Figure 3Dii). Hence there were high stable transmission homesteads, with predominantly younger children getting febrile malaria, and low unstable transmission homesteads, with increasing risk to older children. This pattern of high stable vs low unstable transmission also occurs between regions or countries, and demonstrates a similarity between the micro- and macro-epidemiology of malaria (Hay et al., 2008).

Theoretical accuracy of targeted control undertaken at varying temporal and spatial scales

We then used our data set to simulate the accuracy of targeting cases that a malaria control programme might achieve on conducting surveillance over a defined period of time followed by targeted control. We assumed that malaria control programmes would need to define a priori the period of time to use for surveillance, and also to select a spatial scale at which to define hotspots. For varying time periods and spatial scales, we determined the % of excess malaria cases within the targeted hotspots compared with the surrounding area in the period of time immediately following the simulated surveillance.

One week periods of surveillance (top left panel of Figure 4) did not identify hotspots that are still present the following week at fine spatial scales (i.e., the plotted line indicates that the accuracy of targeting is 0% at scales of less than 1 km). On the other hand, at larger spatial scales we found that 1 week periods of surveillance were more accurate, resulting in the targeting of areas with a 60% excess of new malaria cases compared with the surrounding area at a scale of an 8 km diameter. A similar pattern was seen for monthly periods of surveillance. Longer surveillance periods (e.g., 6 months) resulted in targeting areas with an excess of 20% malaria cases compared with the surrounding area over the range of spatial scales examined.

Figure 4

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We found that malaria cases were spatially heterogeneous in an 8-km radius area of coastal Kenya. The strongly significant inverse correlation between the malaria positive fraction (MPF) and average age of children presenting with malaria suggests variable acquisition of immunity between homesteads. Homesteads at high transmission intensity have a high MPF and a young average age of malaria (with older children becoming immune and therefore not presenting to the dispensary) whereas homesteads at low transmission intensity have a low MPF but an older average age of malaria since older children are not becoming immune as rapidly. In theory, this inverse correlation might have arisen because of heterogeneity at various spatial scales. For instance, there might have been a block of homesteads all at high transmission in one half of the study area (thus with high MPF and low average age) and a second block of homesteads at low transmission in the other half (with low MPF and high average age). On the other hand, the inverse correlation might have arisen because of a random distribution of ‘high’ and ‘low’ transmission intensity homesteads throughout the study area.

To determine at which spatial scale transmission was heterogeneous, we conducted an analysis where correlation coefficient was recalculated within each cell of a grid superimposed on the study area. The mean correlation coefficient of all cells was then presented as the cell size of the grid used was increased (Figure 1D). This analysis was done to identify the most influential geographical scale at which the inverse correlation was observed. In simulated data, we noted ‘spikes’ where the inverse correlation was abruptly lost when the size of cells in the grid coincides with the size of the geographical ‘blocks’ of homesteads that drove the inverse correlation, as seen in Figure 1—figure supplement 1. Similar spikes were seen after adding simulated noise and gradients in space over which the correlation varied (Figure 1—figure supplements 1, 2 and 3). Real-world data would contain more complex sources of variation than we have simulated, and hence may not produce distinct spikes. Nevertheless, the analysis of these simulations suggests that discontinuities in the correlation between MPF and average age of malaria over cell size might be expected when clustering is at a specific spatial scale. In fact there was no such discontinuity in the function shown in Figure 1D, indicating that the inverse correlation was present at every geographical scale examined within our study. It is likely that this pattern would extend at greater geographical scales, since a similar inverse correlation between the age distributions of malaria cases and transmission intensity can be seen on comparing countries and regions (Okiro et al., 2009).

The pattern of spatial heterogeneity is relevant to malaria control, since targeted disease control is predicted to be highly effective (Woolhouse et al., 1997). Spatial targeting is particularly appropriate for malaria ‘hotspots’ (Coleman et al., 2009; Moonen et al., 2010; Bousema et al., 2012; Sturrock et al., 2013) and many malaria control programmes are already engaged in spatially-targeted intervention (Zhou et al., 2010; Loha et al., 2012). Our data showing clustering at varying spatial scales suggest that malaria control programs can expect to identify hotspots at many different geographical scales. We demonstrate that hotspots occur within hotspots, down to the level of a single homestead, and also that hotspots can be identified on ‘zooming in’ on random areas outside the main hotspot (Figure 2C). These hotspots were based on analysis of a large dataset with adequate power, and were strongly significant based on the multiple permutations run in SaTScan, suggesting that type I statistical error is an unlikely explanation for our findings. The complexity of presenting ‘hotspots within hotspots’ to a malaria control programme is further compounded by the temporal instability of the spatial pattern (Figure 3).

We therefore simulated the accuracy with which hotspots could be targeted using varying spatial scales and varying time periods of surveillance. We found that using data aggregated over 1 month of surveillance to define 4 to 8 km diameter hotspots would provide greatest accuracy, but this information is only relevant for 1 month before temporal instability necessitates further surveillance. One might therefore consider a continuous programme of parallel surveillance and targeting, where the surveillance data are examined at the end of each month to determine the location to be targeted for the following month. Continuous surveillance would allow adaptive targeting of hotspots for the following month. Such a strategy might be employed all year round, or for a limited period of the year depending on local seasonality. (Cairns et al., 2012) Targeting at this spatial scale has the added practical advantage that it could be done with village-level location data and would not require fine-scale geo-positional data.

There are some caveats to this recommendation. Our observations are from a single site. Other sites should examine their local data to determine whether a similar targeting strategy is appropriate. Furthermore, some hotspots did show temporal stability. For instance, we identified a 6 km diameter hotspot south east of the dispensary that maintained a 30–60% increase in MPF compared with the surrounding area throughout the 9-year surveillance.

Children with positive microscopy slides for malaria presenting at the dispensary may have genuine febrile malaria, or alternatively may have chronic asymptomatic parasitaemia with co-incident non-malarial fever. Previous studies estimating malaria attributable fractions in the locality suggest 61% of the children in our analysis would have malaria as the proximate cause of their illness, with the other 39% having chronic asymptomatic parasitaemia with co-incident fever from another cause (Olotu et al., 2011). We have previously demonstrated that spatial heterogeneity is more temporally stable when analysed for asymptomatic parasitaemia rather than febrile malaria (Bejon et al., 2010). Targeting hotspots of asymptomatic parasitaemia would require community surveys rather than dispensary monitoring, which may need to be done less frequently than monitoring of febrile malaria episodes.

Furthermore MPF is not a comprehensive indicator of transmission intensity. Homesteads with consistently low average ages of febrile malaria are likely to be stable high transmission homesteads (such as those in subset p of Figure 3A) which amplify transmission in the areas surrounding them. Targeting such high transmission homesteads to interrupt transmission may be highly effective (Woolhouse et al., 1997). The stronger inverse correlation between MPF and average age of febrile malaria as spatial scale increases (Figure 1) suggests that the spatial heterogeneity of transmission is progressively more stable at more coarse spatial scales.

Malaria transmission is determined by mosquito ecology and behavior. Mosquito ecology may be determined by obvious geographical features such as altitude (Reyburn et al., 2005), cultivation practices (Lindsay et al., 1991), streams and dams (Ghebreyesus et al., 1999), wind direction (Midega et al., 2012) and mosquito searching behaviour for hosts (Smith et al., 2004). Ecological models based on such features have been developed using frequentist techniques (Omumbo et al., 2005), Bayesian approaches (Craig et al., 2007), and fuzzy logic (Snow et al., 1998). However, the same ecological factor may act inconsistently in different geographical areas (Kleinschmidt et al., 2001b; Gemperli et al., 2006; Noor et al., 2008), and the effect of ecological factors is modified by fine-scale vector and host movement (Perkins et al., 2013). Our data suggests that the environmental factors determining malaria transmission operate at a range of spatial scales. We might speculate that mosquito breeding site density could be equally influenced by proximity to a large geographical feature such as a river, or to a micro-geographical feature such as a cow hoof-print (Sattler et al., 2005). Hence ecological models of malaria transmission will need to include data at a range of spatial scales in order to accurately predict malaria risk.

Approval for human participation in these cohorts was given by Kenya Medical Research Institute Ethics Research Committee, and research was conducted according to the principles of the declaration of Helsinki.

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Author details

1. Philip Bejon

   1. KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya
   2. Centre for Clinical Vaccinology and Tropical Medicine, University of Oxford, Oxford, United Kingdom

   Contribution

   PB, Conception and design, Analysis and interpretation of data, Drafting or revising the article

   For correspondence

   pbejon@kemri-wellcome.org

   Competing interests

   The authors declare that no competing interests exist.

2. Thomas N Williams

   1. KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya
   2. Imperial College London, London, United Kingdom

   Contribution

   TNW, Acquisition of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

3. Christopher Nyundo

   KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya

   Contribution

   CN, Acquisition of data, Analysis and interpretation of data

   Competing interests

   The authors declare that no competing interests exist.

4. Simon I Hay

   Spatial Ecology and Epidemiology Group, Department of Zoology, University of Oxford, Oxford, United Kingdom

   Contribution

   SIH, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

5. David Benz

   Spatial Ecology and Epidemiology Group, Department of Zoology, University of Oxford, Oxford, United Kingdom

   Contribution

   DB, Acquisition of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

6. Peter W Gething

   Spatial Ecology and Epidemiology Group, Department of Zoology, University of Oxford, Oxford, United Kingdom

   Contribution

   PWG, Conception and design, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

7. Mark Otiende

   KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya

   Contribution

   MO, Acquisition of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

8. Judy Peshu

   KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya

   Contribution

   JP, Acquisition of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

9. Mahfudh Bashraheil

   KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya

   Contribution

   MB, Acquisition of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

10. Bryan Greenhouse

    Department of Medicine, University of California, San Francisco, San Francisco, United States

    Contribution

    BG, Conception and design, Analysis and interpretation of data, Drafting or revising the article

    Competing interests

    The authors declare that no competing interests exist.

11. Teun Bousema

    1. Department of Medical Microbiology, Radboud University Nijmegen Medical Centre, Nijmegen, Netherlands
    2. London School of Hygiene and Tropical Medicine, London, United Kingdom

    Contribution

    TB, Conception and design, Acquisition of data, Drafting or revising the article

    Competing interests

    The authors declare that no competing interests exist.

12. Evasius Bauni

    KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya

    Contribution

    EB, Conception and design, Acquisition of data, Drafting or revising the article

    Competing interests

    The authors declare that no competing interests exist.

13. Kevin Marsh

    1. KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya
    2. Centre for Clinical Vaccinology and Tropical Medicine, University of Oxford, Oxford, United Kingdom

    Contribution

    KM, Conception and design, Drafting or revising the article

    Competing interests

    The authors declare that no competing interests exist.

14. David L Smith

    John Hopkins Malaria Research Institute, Baltimore, United States

    Contribution

    DLS, Analysis and interpretation of data, Drafting or revising the article

    Competing interests

    The authors declare that no competing interests exist.

15. Steffen Borrmann

    1. KEMRI-Wellcome Trust Research Programme, Kilifi, Kenya
    2. Institute for Tropical Medicine, University of Tübingen, Germany
    3. German Centre for Infection Research, Tübingen, Germany

    Contribution

    SB, Conception and design, Acquisition of data, Drafting or revising the article

    Competing interests

    The authors declare that no competing interests exist.

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