Understanding population health care utilisation and defining the catchment sizes of health providers are important for efficient planning and resource allocation 12. Utilisation is a function of access to health services and is affected by geographical accessibility, alongside many other factors 3456789. In low income countries, such as those of the African continent where the burden of ill health is greatest 1011121314, adequate information on the location of populations, health services, facility workload, patient addresses and socio-demographic characteristics are rarely available to develop high resolution utilisation models nationally 1516. Available data on health care utilisation are mainly from routine national household surveys undertaken every 3 to 5 years 17, while few countries have a spatial database of health service providers 1819. Recent developments in high spatial resolution population mapping in Africa 20 provide opportunities for understanding the location of services in relation to populations. There are no previous attempts, however, that combine routine household survey data on treatment seeking, such as the MIS, with health facility and population maps to develop spatial utilisation models at the national level in Africa.

Previous approaches to quantifying geographical accessibility to healthcare have included straight-line (Euclidean) distances 19212223242526, drive times 82728 and network analyses 2629. Euclidean distances fail to account for different patterns of service use and topography and assume utilisation rates are uniform within facility catchments and that patients always use the nearest facility 62526. Drive times have been shown to be a preferable measure in developed countries 30 where vehicular transport is widespread, but are unlikely to be useful in a developing country context where a large proportion of the population walk to the nearest facility 26. An alternative, the cost surface based on travel times, showed closer agreement with the pattern of use in rural South Africa when modelled as a logistic function 31. These forms of distance measurement have been used to analyse utilisation by using metrics such as number of health facilities within a certain predefined distance of the facility, the average distance to n number of health facilities and the gravity model 632. The gravity model is a spatial interaction model analogous to Newton's law of gravity where the force of attraction between two bodies varies proportionally to the product of their masses and inversely to distance between them 3334. In this form, patient interaction with healthcare is denoted by flow from patient origin to the health service while the masses are represented by various utilization effects such as cost, size of health facility or propensity of patient groups to use healthcare 15. The other distance metrics either ignore the interaction with other possible providers within the considered region or may assume that patients always use the nearest facility 35.

In this study, utilisation of the public health sector in Namibia was modelled using information on source of treatment of fevers from a routine national household survey. First, theoretical surface of travel times to nearest health facility were developed and combined with reported treatment seeking patterns to predict probability of using a facility on a 1 km by 1 km grid. The theoretical surface of travel times was used to define spatial catchments around public health facilities while the predicted probability of use was used in combination with population distribution and fever burden to define cases unlikely to seek care from the public health sector.

Data from MIS showed a moderate self-reported use of public health sector (51.1%, 95%CI: 46.2-56.0) for treatment of fever among children under the age of five years northern Namibia. Using this data, utilisation of the public health sector in northern Namibia for the treatment of fevers among children under the age of five years was modelled as a function of travel time. This function was used to model the probability of attendance at a health facility and the number of children likely to attend the nearest facility. Not surprisingly, the probability of attending the nearest health facility for the treatment of fevers was greatest in areas where there was a high concentration of public health facilities and population. Of the estimated 162,286 children under the age of five years in the northern provinces, 160,294 (98.8%) were within a public health facility catchment with overall fever burden of 24,830 cases. The proportion of fevers within the catchment of the public health sector in northern Namibia was 90.8% (22,553) and 16,195 (65.3%) were likely to use the public health sector. This implied that overall, 8,616 (34.7%) febrile children were unlikely to use at a public health facility in northern Namibia including 4,030 (47%) fever cases that lived outside of a health facility catchment (Table 3, Figure 5).

This analysis builds on previous work to define facility catchments with information on utilisation patterns. Approaches similar to the one used in this study were presented in Tanser et al. 31 but using a two parameter logistic model and in Noor et al. 26 using a transect algorithm to characterize facility choice. These studies used local rather than national data sets with Tanser et al. 31 considering all forms of healthcare utilisation, not specifically fever. Whereas our fever-related attendance data suggest not all households used facilities at a travel time of zero, the Tanser et al. 31 study assumed that all households attended the healthcare facilities when the travel time was zero and the distance decay was more rapid than that observed here. This assumption is unlikely because regardless of proximity of households to a given health facility, treatment seeking behavior varies and are driven by other individual, household and community level choices 62. The model presented here also differs from the two parameter logistic model in that a third parameter was included to represent the phenomenon discussed by Pinheiro and Bates 60 which can be thought of as a generalization of the two parameter model where facility attendance is less than 100% at a travel time of zero. Previously, such models have been common in resource growth applications 63, but not in public health applications such as modeling facility utilisation. The third parameter C in the model significantly modifies the behavior of the logistic function. It represents a horizontal asymptote at a limiting value C which can be less than 1 (whereas the two parameter model eventually levels off at an asymptote of 1 as it approaches -∞) 64. This value does not relate directly to the proportion that sought treatment, but represents the maximum probability. Therefore, the logistic function never exceeds this value. The rate of decay of the logistic function is determined by the exponential function, e^(A-x)/B, in the denominator. An additional difference from the approach used here and those of previous studies is the application of a travel time threshold (3 hours) based on the distance decay curve, outside of which individuals were regarded to fall outside the catchment of any public health facility. Finally, to compute the number of fevers that will use a public health facility the continuous probability surface was multiplied with the fever case burden maps with assumption that, at every distance, the probability of using the public health sector will be < 1, thus, some will not seek treatment at a public health facility regardless of proximity or will seek treatment at facilities that is not the nearest. This approach, we believe, models a scenario closer to real-life utilization of health services in many African countries.

The methods used here have some limitations. First, in modeling travel times it was assumed that patients travel to their nearest facility by either walking, using a bicycle or any form of public transport. In contrast, people might not use the closest clinic due to various factors such as choice of better quality provider or income, socio-economic status, individual and community preferences and severity of illness 42226356566. However, since the MIS does not identify the specific healthcare facility used by an individual, it is not possible to model such effects from the available data. The exclusion of these determinants into the model are likely to change the probability of attendance computed for each travel time band and may be a reason for higher utilization than that reported in the MIS (14.2% difference). In addition, for various land cover classes an assumption was made that a patient would either (a) walk to their nearest facility with a correction for particular land use or land cover class and slope, (b) use a car as a form of transport to the facility or would walk to the nearest road then use public means of transport for rest of the journey or (c) cycle to the health facility. In reality, the distribution and use of public transport may be more sporadic and less predictable at the national level. Such discrete assumptions, however, are a tradeoff between model complexity and precision and empirical data to test and improve these assumptions are rarely available in sub-Saharan Africa settings. In estimating the fever burden for each facility's catchment, aggregate fever prevalence rates within each region were used. In reality fever prevalence is likely to vary by facility catchment and rates at this level may be considerably different to the regional mean prevalence which masks fine scale heterogeneity. Finally, the analysis focuses only on the northern regions of Namibia where household treatment seeking data are available and where the concentration of health services and population are highest. It is likely that the geographically larger but very sparsely populated southern regions will have different service utilisation patterns. Additional data is needed to model a nationwide estimate of service utilisation, catchment areas and catchment populations.

The relationship between travel time, service utilisation and disease outcomes has been demonstrated in several studies. Moïsi et al. 67 showed increasing travel time (greater than 1 hour) from a hospital was associated with disease severity among children under the age of five years with pneumonia and suspected meningitis. Another hospital case-control study carried out in Yemen illustrated similar outcomes, with children (6 to 10 years) likely to develop severe malaria with increasing distance (greater than 2 km) from the hospital 68 while O'Meara et al. 69 showed that incidences of malaria hospitalisation doubled after 2 hours of travel time from health facility. In these studies, children living at a further distance were likely to wait longer before using a health facility, leading to severity of illness that required in-patient care. Recent findings from a study in Ethiopia 70 suggest a five-fold risk of death (all case mortality) amongst children in rural population at a greater travel time (2 hours) from a nearest health facility. While the effect of travel time or distance has been associated with poor health outcomes, few studies demonstrate treatment seeking patterns within a health facility catchment which in turn are potentially useful in forecasting commodity needs for case management 71, optimization of facility-based interventions 66677071 and estimating underlying populations to define disease incidence 72. Okiro et al. 72 defined facility catchments at several hospital sites in Kenya using enumeration areas where over 90% of malaria cases resided, while Gething et al. 6673 assumed that catchment populations could be linearly related to total case loads observed for a long period of time (over five-years) at a facility and used this to standardize out-patient clinically diagnosed malaria data.

National representative health sample surveys such as the MIS, DHS, Multiple Indicator Cluster Surveys (MICS) and the AIDS Indicator Survey (AIS), usually constitute a representative sample of the national population and are being used to study health outcomes and impact of interventions in Africa 747576. Although the Namibia MIS of 2009 was only undertaken in the northern regions, this study nonetheless demonstrates the potential of routine household survey data on treatment seeking for fevers to model public health care utilisation, catchment areas and populations in Africa. This provides the opportunity to model facility catchment population, compute disease incidence and determine risk and resource needs. This approach could be extended to the large accumulation of DHS, MIS and the MICS surveys conducted by the United Nations Children's Fund in several countries Africa. This possibility is further improved by the availability of high spatial resolution population maps of Africa under the Afripop project 20 and the increasing spatial resolution of ancillary spatial data such as roads, elevation, drainage, land cover and land used data. The input data, however, require improvements in two important ways. First, countries must have maps of all their health facilities or at least of those that are in the public sector. Secondly, even though utilisation patterns appear stable regardless of time of survey, treatment seeking data are available only for children under the age of five for almost all the national household surveys. In a recent MIS undertaken in the 15 northern states of the Sudan, a country with similar ecology and utilisation patterns as Namibia, fever treatment seeking among all ages was recorded showing minimal change in treatment seeking with age 77. While it is not clear if this holds true for all other African countries, focusing on a narrow age group in areas where fever prevalence is low may result in unstable sample sizes and low model precision. Future surveys should, therefore, explore the possibility of capturing information on a wider age range, preferably for all ages.

ASTER: Advanced spaceborne thermal emission and reflection radiometer; AIS: AIDS indicator survey; AIDS: Acquired immune deficiency syndrome; DHS: Demographic health survey; ESRI: Environmental system research institute; GDEM: Global digital elevation model; GIS: Geographic information system; GlobCover: Global cover; GPS: Global positioning system; ITN: Insecticide treated net; LCCS: Land cover classification system; MDG: Millennium development goals; MERG: Monitoring and evaluation reference group; MERIS: MEdium resolution imaging spectrometer; METI: Ministry of economy trade and industry; MIS: Malaria Indicator Survey; MoHSS: Ministry of health and social services; NASA: National aeronautics and space administration; RBM: Roll back malaria; UN: United nations; WHO: World health organization.

The authors declare that they have no competing interests.

VAA was responsible for study design, data cleaning, analysis, interpretation, drafting and production of the final manuscript. PU contributed to the data assembly, cleaning and contributed to final manuscript. JW was responsible for study design, analysis, interpretation and production of the final manuscript. AMN, PMA and RWS were responsible for overall scientific management, analysis, interpretation and preparation of the final manuscript. All authors read and approved the final manuscript.

VAA is supported by the Wellcome Trust Fellowship (#090633). AMN is supported by the Wellcome Trust as an Intermediate Research Fellow (#095127). RWS is supported by the Wellcome Trust as Principal Research Fellow (#079080). This work was partly funded a grant from the Namibia Ministry of Health and Social Services-Global Fund Programme and a Wellcome Trust Major Overseas Programme grant to the KEMRI/Wellcome Trust Research Programme (#092654). This work forms part of the output of the Malaria Atlas Project (MAP, http://www.map.ox.ac.uk), principally funded by the Wellcome Trust, UK. VAA, AMN and RWS also acknowledge support from the Kenya Medical Research Institute. The funders played no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.