25 research outputs found

    Assessing the effects of interventions on child and maternal health-related outcomes in Uganda

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    In this PhD, health-related outcomes studied include the under-five mortality rate (U5MR), the prevalence of fever, diarrhoea, symptoms of acute respiratory infections (ARI) as well as maternal mortality ratio (MMR. Every year in the world, millions of children die before their fifth birthday. In 2016, an estimated 5.6 million under-five deaths occurred with half of the burden concentrated in the sub-Saharan Africa (SSA) region. In these countries, the U5MR is unacceptably high yet progress is slowed down by the uneven distribution of key determinants of child mortality, for example, child interventions, childhood diseases and the socio-economic factors. Such imbalances lead to substantial variations in the U5MR within countries which may hinder the achievement of Sustainable Development Goal (SDG) target 3.2. In Uganda, the U5MR is much higher than the SDG target of 25 or less deaths per 1 000 live births. In addition, significant differences in the U5MR as well as determinants of U5MR are huge and disproportionately distributed within the country. A better understanding of the determinants of the existing inequalities in the under-five mortality would guide in the prioritization of effective and equitable strategies to realise mortality targets Another fundamental mortality indicator is the maternal mortality ratio (MMR). MMR measures the quality of the health system and also reflects inequality between sub-groups and, between and within countries. The indicator is also essential for tracking progress in development and for spurring action to improve maternal health. According to the World Health Organisation, the MMR is highest in SSA and accounts for approximately 66% of the global maternal deaths. In SSA, direct and indirect causes of maternal deaths are the most prevalent conditions yet prevention and treatment measures are hindered by dysfunctional national health systems and a low socio-economic status. This leads to poor maternal health outcomes in SSA, resulting into vulnerable families and increased chances of infant mortality before reaching their second birthday. Furthermore, maternal mortality deteriorates economic development since more women survive with chronic and incapacitating ill health for each maternal death. Uganda ranks number nine among the top ten high-burdened countries and experiences a MMR far higher than the SDG target 3.1. At the same time, large regional disparities in MMR and its determinants (e.g. maternal interventions) prevail within the country. Therefore, strategies to end maternal mortality need to be implemented, in particular, approaches to address the sources of inequities. This may reduce variations in MMR within Uganda, and thus, quicken the achievement of SDG target 3.1 in the country. The adoption of the United Nations (UN) Millennium Declaration in the late 2000, established a global partnership of countries and development partners committed to eight voluntary development goals, to be achieved by 2015. Two of the eight Millennium Development Goals (MDGs) focused on U5MR reduction and maternal health improvement. U5MR has fallen by 53% and maternal mortality by 43% since 1990 to 2015. Even though this is a cause for celebration, both declines fell short of the MDG targets of two thirds and three quarters reductions from the 1990 levels. With the end of the era of the MDGs in 2015, the international community agreed on a new framework – the SDGs. The SDG targets for under-five and maternal mortality represent a renewed commitment to the world’s children and mothers. By 2030, end preventable deaths of children under five years of age, with all countries aiming to reduce U5MR to at least 25 deaths per 1 000 live births while maternal mortality should not exceed 140 deaths per 100 000 live births. Tracking progress towards child and maternal mortality SDG targets requires significant investment in measuring nationally representative data relevant to the estimation of mortality indicators. The implementation of the National Population and Housing Census (NPHC), nationally representative household surveys, that is, Demographic and Health Surveys (DHS), Malaria Indicator Surveys (MIS) and the Uganda Service Delivery Indicator (SDI) Survey has resulted in rich sources of data in Uganda which has made it practical to monitor progress in mortality indicators and their determinants. Censuses collect data for each individual in the country and are therefore an important source of microdata, which enables the study of sub-national differences. The SDI survey data facilitates the assessment of health facility readiness in the country while DHS and MIS data are spatially structured and can be used to identify high risky areas as well as track progress in the distribution of the determinants of mortality such as health interventions and diseases. Despite the rich data sources, data utilisation remains poor and information extracted by researchers is restricted to national estimates that neither take into account sub-national discrepancies nor assess the effects of interventions and childhood diseases on mortality or morbidity differentials in space. National estimates mask geographical heterogeneities that may exist at a local scale. Therefore, most important interventions at a local scale, areas affected by the disease burden as well as high mortality clusters cannot be identified. This is because the standard frequentist methods commonly employed in the analysis assume independence of observations yet the DHS and census collect mortality and morbidity data at neighbouring locations, and therefore correlated in space. This is because observations at close geographical proximity are likely to share common exposures and thus affected in a similar way. In case of mortality, spatial correlation arises from its determinants such as infectious diseases. An example is malaria which is transmitted by mosquitoes as they fly long distances in surrounding areas. Ignoring spatial correlation in the data results into imprecise effects of covariates and incorrect estimates of mortality risk which are essential for determining most important interventions, areas affected mostly by diseases and high mortality clusters. Spatial statistical methods fitted via Markov Chain Monte Carlo simulations, are the novel approach developed to incorporate spatial correlation in space. They can estimate high mortality clusters within the country and evaluate the effects of health interventions and childhood diseases on health-related outcomes at the national and sub-national scale for targeted intervention. The goal of this PhD thesis is to develop Bayesian spatial models to assess the ffects of interventions on child and maternal health-related outcomes at the national and sub-national scale in Uganda, through the following specific objectives; 1) to quantify the effects of childhood diseases on all-cause under-five mortality over space; 2) to estimate the effects of health interventions on all-cause under-five mortality over space; 3) to assess the contribution of childhood diseases on the geographical distribution of fever risk among children less than five years; 4) to quantify the effect of the presence of soap and water at handwashing places in households on the risk of diarrhoea and respiratory infections among children under-five years and 5) to assess the effects of maternal health interventions on all-cause maternal mortality. In Chapter 2, Bayesian geostatistical proportional hazards models with spatially varying coefficients were applied on the 2011 DHS and 2009 MIS data to estimate the effects of childhood diseases on all-cause under-five mortality at the national and sub-national levels. The models took into account geographical misalignment in the locations of the surveys. Childhood diseases had significant but varying effects on mortality across regions. At national level, the U5M was associated with prevalence of malaria (hazard ratio (HR) = 1.74; 95% BCI: 1.42, 2.16), severe or moderate anaemia (HR =1.37; 95% BCI: 1.20, 1.75), severe or moderate malnutrition (HR = 1.49; 95% BCI: 1.25, 1.66) and diarrhoea (HR = 1.61; 95% BCI: 1.31, 2.05). The relationship between malaria and U5M was important in the regions of Central 2, East-Central, Mid-North, North-East and West-Nile. Diarrhoea was associated with under-five deaths in Central 2, East-central, Mid-Eastern and Mid-Western. Moderate/severe malnutrition was associated with U5M in East-Central, Mid-Eastern and North-East. Moderate/severe anaemia was associated with deaths in Central 1, Kampala, Mid-North, Mid-Western, North-East, South-West and West-Nile. In Chapter 3, Bayesian geostatistical proportional hazards models with spatially varying coefficients were developed to determine interventions’ effects on under-five mortality at national and sub-national levels, and to predict mortality risk at unsampled locations. The data used in the analysis were obtained from the 2011 DHS. The most important interventions at the national level were artemisinin-combination therapy (HR = 0.60; 95% BCI: 0.11, 0.79), initiation of breast feeding within one hour of birth (HR = 0.70; 95% BCI: 0.51, 0.86), intermittent preventive treatment (IPT) (HR = 0.74; 95% BCI: 0.67, 0.97) and insecticide treated nets (ITN) access (HR = 0.75; 95% BCI: 0.63 0.84). Other important health interventions had more or less comparable effects on mortality. The effects of health interventions on under-five mortality varied by region. In Central 2, Mid-Western and South-West regions, the largest reduction in the under-five mortality burden was associated with ITN access. Improved source of drinking water explains most under-five mortality reduction in Mid-North and West-Nile. Improved sanitation facilities account for the highest decline in under-five mortality in the North-East. In Kampala and Mid-Eastern, IPT had the largest impact on mortality. In Central 1 and East-Central, ORS or RHF and postnatal care were respectively associated with the highest decreases in under-five mortality. High mortality clusters were found in the North-East, West-Nile, southern of Mid-North, East-Central along the Victoria Nile River, southern of Central 1 stretching to the South-West region and along the country border in Mid-Western between Lakes Albert and Edward. Lowest mortality hazard rates were predicted in Kampala, centre of Mid-North extending to West-Nile, North-East, Mid-Eastern and East-Central regions. Also, areas around Lake George in Mid-Western and a few spots in Central 2 were predicted with low mortality hazard rates. In Chapter 4, we applied Bayesian geostatistical logistic models on the 2016 DHS data and quantified the contribution of childhood diseases to the geographical distribution of fever risk among children less than five years. At the national level, the population attribution fraction of diarrhoea, ARI and malaria to the prevalence of fever in the under-five was 38.12 (95% BCI: 25.15, 41.59), 30.99 (95% BCI: 9.82, 34.26) and 9.50 (95% BCI: 2.34, 25.15), respectively. The attribution of diarrhoea was common in all regions except Bunyoro, while ARI was more common in Bugisu, Karamoja and West Nile, and malaria was commonest in Bunyoro. In Lango, the attribution of diarrhoea and ARI was similar In Chapter 5, we analysed the 2016 DHS data and quantified the effect of the presence of soap and water at handwashing places in households on the risk of diarrhoea and ARI among the under-five using Bayesian geostatistical logistic models. The odds of diarrhoea and ARI in children who lived in households having soap and water at handwashing places were 14% and 24% less than those living in households without the intervention (adjusted odds ratio, aOR = 0.86; 95% BCI: 0.77 – 0.96) and (aOR = 0.76; 95% BCI: 0.65 – 0.88) respectively. In Chapter 6, Bayesian negative binomial CAR models were employed to evaluate the effects of maternal health interventions on all-cause maternal mortality. Data were extracted from the 2016 DHS and 2014 NPHC. The risk of maternal mortality declined with increasing coverage of intermittent preventive treatment (Mortality rate ratio (MRR) = 88%; 95% BCI: 86%, 91%), iron supplements (MRR = 95%; 95% BCI: 93%, 98%), skilled birth attendance (MRR = 96%; 95% BCI: 94%, 98%) and family planning (MRR = 95%; 95% BCI: 92%, 98%). The results of this thesis will guide prioritization and targeted allocation of high impact and evidence-based interventions to maximize benefits of resources. This will alleviate within country morbidity and mortality discrepancies and consequently accelerate progress towards achieving SDG targets 3.1 and 3.2 in Uganda by 2030

    Geographical variations of the associations between health interventions and all-cause under-five mortality in Uganda

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    To reduce the under-five mortality (U5M), fine-gained spatial assessment of the effects of health interventions is critical because national averages can obscure important sub-national disparities. In turn, sub-national estimates can guide control programmes for spatial targeting. The purpose of our study is to quantify associations of interventions with U5M rate at national and sub-national scales in Uganda and to identify interventions associated with the largest reductions in U5M rate at the sub-national scale.; Spatially explicit data on U5M, interventions and sociodemographic indicators were obtained from the 2011 Uganda Demographic and Health Survey (DHS). Climatic data were extracted from remote sensing sources. Bayesian geostatistical Weibull proportional hazards models with spatially varying effects at sub-national scales were utilized to quantify associations between all-cause U5M and interventions at national and regional levels. Bayesian variable selection was employed to select the most important determinants of U5M.; At the national level, interventions associated with the highest reduction in U5M were artemisinin-based combination therapy (hazard rate ratio (HRR) = 0.60; 95% Bayesian credible interval (BCI): 0.11, 0.79), initiation of breastfeeding within 1 h of birth (HR = 0.70; 95% BCI: 0.51, 0.86), intermittent preventive treatment (IPTp) (HRR = 0.74; 95% BCI: 0.67, 0.97) and access to insecticide-treated nets (ITN) (HRR = 0.75; 95% BCI: 0.63, 0.84). In Central 2, Mid-Western and South-West, largest reduction in U5M was associated with access to ITNs. In Mid-North and West-Nile, improved source of drinking water explained most of the U5M reduction. In North-East, improved sanitation facilities were associated with the highest decline in U5M. In Kampala and Mid-Eastern, IPTp had the largest associated with U5M. In Central1 and East-Central, oral rehydration solution and postnatal care were associated with highest decreases in U5M respectively.; Sub-national estimates of the associations between U5M and interventions can guide control programmes for spatial targeting and accelerate progress towards mortality-related Sustainable Development Goals

    Measuring health facility readiness and its effects on severe malaria outcomes in Uganda

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    There is paucity of evidence for the role of health service delivery to the malaria decline in Uganda We developed a methodology to quantify health facility readiness and assessed its role on severe malaria outcomes among lower-level facilities (HCIIIs and HCIIs) in the country. Malaria data was extracted from the Health Management Information System (HMIS). General service and malaria-specific readiness indicators were obtained from the 2013 Uganda service delivery indicator survey. Multiple correspondence analysis (MCA) was used to construct a composite facility readiness score based on multiple factorial axes. Geostatistical models assessed the effect of facility readiness on malaria deaths and severe cases. Malaria readiness was achieved in one-quarter of the facilities. The composite readiness score explained 48% and 46% of the variation in the original indicators compared to 23% and 27%, explained by the first axis alone for HCIIIs and HCIIs, respectively. Mortality rate was 64% (IRR = 0.36, 95% BCI: 0.14-0.61) and 68% (IRR = 0.32, 95% BCI: 0.12-0.54) lower in the medium and high compared to low readiness groups, respectively. A composite readiness index is more informative and consistent than the one based on the first MCA factorial axis. In Uganda, higher facility readiness is associated with a reduced risk of severe malaria outcomes

    The effect of case management and vector-control interventions on space-time patterns of malaria incidence in Uganda

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    Electronic reporting of routine health facility data in Uganda began with the adoption of the District Health Information Software System version 2 (DHIS2) in 2011. This has improved health facility reporting and overall data quality. In this study, the effects of case management with artemisinin-based combination therapy (ACT) and vector control interventions on space-time patterns of disease incidence were determined using DHIS2 data reported during 2013-2016.; Bayesian spatio-temporal negative binomial models were fitted on district-aggregated monthly malaria cases, reported by two age groups, defined by a cut-off age of 5 years. The effects of interventions were adjusted for socio-economic and climatic factors. Spatial and temporal correlations were taken into account by assuming a conditional autoregressive and a first-order autoregressive AR(1) process on district and monthly specific random effects, respectively. Fourier trigonometric functions were incorporated in the models to take into account seasonal fluctuations in malaria transmission.; The temporal variation in incidence was similar in both age groups and depicted a steady decline up to February 2014, followed by an increase from March 2015 onwards. The trends were characterized by a strong bi-annual seasonal pattern with two peaks during May-July and September-December. Average monthly incidence in children < 5 years declined from 74.7 cases (95% CI 72.4-77.1) in 2013 to 49.4 (95% CI 42.9-55.8) per 1000 in 2015 and followed by an increase in 2016 of up to 51.3 (95% CI 42.9-55.8). In individuals ≥ 5 years, a decline in incidence from 2013 to 2015 was followed by an increase in 2016. A 100% increase in insecticide-treated nets (ITN) coverage was associated with a decline in incidence by 44% (95% BCI 28-59%). Similarly, a 100% increase in ACT coverage reduces incidence by 28% (95% BCI 11-45%) and 25% (95% BCI 20-28%) in children < 5 years and individuals ≥ 5 years, respectively. The ITN effect was not statistically important in older individuals. The space-time patterns of malaria incidence in children < 5 are similar to those of parasitaemia risk predicted from the malaria indicator survey of 2014-15.; The decline in malaria incidence highlights the effectiveness of vector-control interventions and case management with ACT in Uganda. This calls for optimizing and sustaining interventions to achieve universal coverage and curb reverses in malaria decline

    The effects and contribution of childhood diseases on the geographical distribution of all-cause under-five mortality in Uganda

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    Introduction: Information on the causes of death among under-five children is key in designing and implementation of appropriate interventions. In Uganda, civil death registration is incomplete which limits the estimation of disease-related mortality burden especially at a local scale. In the absence of routine cause-specific data, we used household surveys to quantify the effects and contribution of main childhood diseases such as malaria, severe or moderate anaemia, severe or moderate malnutrition, diarrhoea and acute respiratory infections (ARIs) on all-cause under-five mortality (U5M) at national and sub-national levels. We related all-cause U5M with risks of childhood diseases after adjusting for geographical disparities in coverages of health interventions, socio-economic, environmental factors and disease co-endemicities. Methods: Data on U5M, disease prevalence, socio-economic and intervention coverage indicators were obtained from the 2011 Demographic and Health Survey, while data on malaria prevalence were extracted from the 2009 Malaria Indicator Survey. Bayesian geostatistical Weibull proportional hazards models with spatially varying disease effects at sub-national scales were fitted to quantify the associations between childhood diseases and the U5M. Spatial correlation between clusters was incorporated via locational random effects while region-specific random effects with conditional autoregressive prior distributions modeled the geographical variation in the effects of childhood diseases. The models addressed geographical misalignment in the locations of the two surveys. The contribution of childhood diseases to under-five mortality was estimated using population attributable fractions. Results: The overall U5M rate was 90 deaths per 1000 live births. Large regional variations in U5M rates were observed, lowest in Kampala at 56 and highest in the North-East at 152 per 1000 live births. National malaria parasitemia prevalence was 42%, with Kampala experiencing the lowest of 5% and the Mid-North the highest of 62%. About 27% of Ugandan children aged 6–59 months were severely or moderately anaemic; lowest in South-West (8%) and highest in East-Central (46%). Overall, 17% of children were either severely or moderately malnourished. The percentage of moderately/severely malnourished children varied by region with Kampala having the lowest (8%) and North-East the highest (45%). Nearly a quarter of the children under-five years were reported to have diarrhoea at national level, and this proportion was highest in East-Central (32%) and Mid-Eastern (33%) and lowest in South-West (14%). Overall, ARIs in the two weeks before the survey was 15%; highest in Mid-North (22%) and lowest in Central 1 (9%). At national level, the U5M was associated with prevalence of malaria (hazard ratio (HR) = 1.74; 95% BCI: 1.42, 2.16), severe or moderate anaemia (HR =1.37; 95% BCI: 1.20, 1.75), severe or moderate malnutrition (HR = 1.49; 95% BCI: 1.25, 1.66) and diarrhoea (HR = 1.61; 95% BCI: 1.31, 2.05). The relationship between malaria and U5M was important in the regions of Central 2, East-Central, Mid-North, North-East and West-Nile. Diarrhoea was associated with under-five deaths in Central 2, East-central, Mid-Eastern and Mid-Western. Moderate/severe malnutrition was associated with U5M in East-Central, Mid-Eastern and North-East. Moderate/severe anaemia was associated with deaths in Central 1, Kampala, Mid-North, Mid-Western, North-East, South-West and West-Nile.At the national level, 97% (PAF = 96.9; 95%BCI: 94.4, 98.0), 91% (PAF = 90.9; 95%BCI: 84.4, 95.3), 89% (PAF = 89.3; 95%BCI: 76.0,93.8) and 93% (PAF = 93.3 95%BCI: 87.7,96.0) of the deaths among children less than five years in Uganda were attributable to malaria, severe/moderate anaemia, severe/moderate malnutrition and diarrhoea respectively. The attribution of malaria was comparable in Central 2, East-Central, Mid-North, North-East and West-Nile while severe/moderate anaemia was more common in all regions except Central 2, East-Central and Mid-Eastern. The attribution of diarrhoea in Central 2, East-Central, Mid-Eastern and Mid-Western was similar. The attribution of severe/moderate malnutrition was common in East-Central, Mid-Eastern and North-East. Conclusion: In Uganda, the contribution and effects of childhood diseases on U5M vary by region. Majority of the under-five deaths are due to malaria, followed by diarrhoea, severe/moderate anaemia and severe/moderate malnutrition. Thus, strengthening disease-specific interventions especially in the affected regions may be an important strategy to accelerate progress towards the reduction of the U5M as per the SDG target by 2030. In particular, Indoor Residual Spraying, iron supplementation, deworming, exclusive breastfeeding, investment in nutrition and education in nutrition practices, oral rehydration therapy or recommended home fluid, improved sanitation facilities should be improved. Keywords: DHS, Under-five mortality, Malaria, Anaemia, Malnutrition, Diarrhoea, Respiratory infections, Population attributable fractions, Bayesian geostatistical inference, Ugand

    Geostatistical modelling of malaria indicator survey data to assess the effects of interventions on the geographical distribution of malaria prevalence in children less than 5 years in Uganda

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    Malaria burden in Uganda has declined disproportionately among regions despite overall high intervention coverage across all regions. The Uganda Malaria Indicator Survey (MIS) 2014-15 was the second nationally representative survey conducted to provide estimates of malaria prevalence among children less than 5 years, and to track the progress of control interventions in the country. In this present study, 2014-15 MIS data were analysed to assess intervention effects on malaria prevalence in Uganda among children less than 5 years, assess intervention effects at regional level, and estimate geographical distribution of malaria prevalence in the country.; Bayesian geostatistical models with spatially varying coefficients were used to determine the effect of interventions on malaria prevalence at national and regional levels. Spike-and-slab variable selection was used to identify the most important predictors and forms. Bayesian kriging was used to predict malaria prevalence at unsampled locations.; Indoor Residual Spraying (IRS) and Insecticide Treated Nets (ITN) ownership had a significant but varying protective effect on malaria prevalence. However, no effect was observed for Artemisinin Combination-based Therapies (ACTs). Environmental factors, namely, land cover, rainfall, day and night land surface temperature, and area type were significantly associated with malaria prevalence. Malaria prevalence was higher in rural areas, increased with the child's age, and decreased with higher household socioeconomic status and higher level of mother's education. The highest prevalence of malaria in children less than 5 years was predicted for regions of East Central, North East and West Nile, whereas the lowest was predicted in Kampala and South Western regions, and in the mountainous areas in Mid-Western and Mid-Eastern regions.; IRS and ITN ownership are important interventions against malaria prevalence in children less than 5 years in Uganda. The varying effects of the interventions calls for selective implementation of control tools suitable to regional ecological settings. To further reduce malaria burden and sustain malaria control in Uganda, current tools should be supplemented by health system strengthening, and socio-economic development

    Interactions between climatic changes and intervention effects on malaria spatio-temporal dynamics in Uganda

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    Although malaria burden in Uganda has declined since 2009 following the scale-up of interventions, the disease is still the leading cause of hospitalization and death. Transmission remains high and is driven by suitable weather conditions. There is a real concern that intervention gains may be reversed by climatic changes in the country. In this study, we investigate the effects of climate on the spatio-temporal trends of malaria incidence in Uganda during 2013-2017.; Bayesian spatio-temporal negative binomial models were fitted on district-aggregated monthly malaria cases, reported by two age groups, defined by a cut-off age of 5 years. Weather data was obtained from remote sensing sources including rainfall, day land surface temperature (LSTD) and night land surface temperature (LSTN), Normalized Difference Vegetation Index (NDVI), altitude, land cover, and distance to water bodies. Spatial and temporal correlations were taken into account by assuming a conditional autoregressive and a first-order autoregressive process on district and monthly specific random effects, respectively. Fourier trigonometric functions modeled seasonal fluctuations in malaria transmission. The effects of climatic changes on the malaria incidence changes between 2013 and 2017 were estimated by modeling the difference in time varying climatic conditions at the two time points and adjusting for the effects of intervention coverage, socio-economic status and health seeking behavior.; Malaria incidence declined steadily from 2013 to 2015 and then increased in 2016. The decrease was by over 38% and 20% in children <5 years and individuals ≥5 years, respectively. Temporal trends depict a strong bi-annual seasonal pattern with two peaks during April-June and October-December. The annual average of rainfall, LSTD and LSTN increased by 3.7 mm, 2.2 °C and 1.0 °C, respectively, between 2013 and 2017, whereas NDVI decreased by 6.8%. On the one hand, the increase in LSTD and decrease in NDVI were associated with a reduction in the incidence decline. On the other hand, malaria interventions and treatment seeking behavior had reverse effects, that were stronger compared to the effects of climatic changes. Important interactions between interventions with NDVI and LSTD suggest a varying impact of interventions on malaria burden in different climatic conditions.; Climatic changes in Uganda during the last five years contributed to a favorable environment for malaria transmission, and had a detrimental effect on malaria reduction gains achieved through interventions scale-up efforts. The NMCP should create synergies with the National Meteorological Authority with an ultimate goal of developing a Malaria Early Warning System to mitigate adverse climatic change effects on malaria risk in the country

    Predicted malaria prevalence in children less than 5 years; median (top), 2.5<sup>th</sup> percentile (bottom left) and 97.5<sup>th</sup> percentile posterior predictive distribution (bottom right).

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    <p>Predicted malaria prevalence in children less than 5 years; median (top), 2.5<sup>th</sup> percentile (bottom left) and 97.5<sup>th</sup> percentile posterior predictive distribution (bottom right).</p
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