The response of a floating ice sheet to an accelerating line load

The two-dimensional response of a thin, floating sheet of ice to a line load that accelerates from rest at $t = 0$ to a uniform velocity V for $t \geq T$ is determined through an integral-transform solution of the linearized equations of motion. If $T = 0$ – i.e. if the load is impulsively started with velocity V – the solution exhibits singularities at $V = c_0$, the shallow-water-gravity-wave speed, and $V = c_{\min}$, the minimum speed for transverse motion of the ice, but these singularities are avoided by the acceleration of the load through the critical speeds

The distribution of haemoglobin C and its prevalence in newborns in Africa

Haemoglobin C (HbC) is one of the commonest structural haemoglobin variants in human populations. Although HbC causes mild clinical complications, its diagnosis and genetic counselling are important to prevent inheritance with other haemoglobinopathies. Little is known about its contemporary distribution and the number of newborns affected. We assembled a global database of population surveys. We then used a Bayesian geostatistical model to create maps of HbC frequency across Africa and paired our predictions with high-resolution demographics to calculate heterozygous (AC) and homozygous (CC) newborn estimates and their associated uncertainty. Data were too sparse outside Africa for this methodology to be applied. The highest frequencies were found in West Africa but HbC was commonly found in other parts of the continent. The expected annual numbers of AC and CC newborns in Africa were 672,117 (interquartile range (IQR): 642,116-705,163) and 28,703 (IQR: 26,027-31,958), respectively. These numbers are about two times previous estimates

Global epidemiology of sickle haemoglobin in neonates: a contemporary geostatistical model-based map and population estimates.

BACKGROUND: Reliable estimates of populations affected by diseases are necessary to guide efficient allocation of public health resources. Sickle haemoglobin (HbS) is the most common and clinically significant haemoglobin structural variant, but no contemporary estimates exist of the global populations affected. Moreover, the precision of available national estimates of heterozygous (AS) and homozygous (SS) neonates is unknown. We aimed to provide evidence-based estimates at various scales, with uncertainty measures. METHODS: Using a database of sickle haemoglobin surveys, we created a contemporary global map of HbS allele frequency distribution within a Bayesian geostatistical model. The pairing of this map with demographic data enabled calculation of global, regional, and national estimates of the annual number of AS and SS neonates. Subnational estimates were also calculated in data-rich areas. FINDINGS: Our map shows subnational spatial heterogeneities and high allele frequencies across most of sub-Saharan Africa, the Middle East, and India, as well as gene flow following migrations to western Europe and the eastern coast of the Americas. Accounting for local heterogeneities and demographic factors, we estimated that the global number of neonates affected by HbS in 2010 included 5,476,000 (IQR 5,291,000-5,679,000) AS neonates and 312,000 (294,000-330,000) SS neonates. These global estimates are higher than previous conservative estimates. Important differences predicted at the national level are discussed. INTERPRETATION: HbS will have an increasing effect on public health systems. Our estimates can help countries and the international community gauge the need for appropriate diagnoses and genetic counselling to reduce the number of neonates affected. Similar mapping and modelling methods could be used for other inherited disorders. FUNDING: The Wellcome Trust

G6PD deficiency prevalence and estimates of affected populations in malaria endemic countries: a geostatistical model-based map.

BACKGROUND: Primaquine is a key drug for malaria elimination. In addition to being the only drug active against the dormant relapsing forms of Plasmodium vivax, primaquine is the sole effective treatment of infectious P. falciparum gametocytes, and may interrupt transmission and help contain the spread of artemisinin resistance. However, primaquine can trigger haemolysis in patients with a deficiency in glucose-6-phosphate dehydrogenase (G6PDd). Poor information is available about the distribution of individuals at risk of primaquine-induced haemolysis. We present a continuous evidence-based prevalence map of G6PDd and estimates of affected populations, together with a national index of relative haemolytic risk. METHODS AND FINDINGS: Representative community surveys of phenotypic G6PDd prevalence were identified for 1,734 spatially unique sites. These surveys formed the evidence-base for a Bayesian geostatistical model adapted to the gene's X-linked inheritance, which predicted a G6PDd allele frequency map across malaria endemic countries (MECs) and generated population-weighted estimates of affected populations. Highest median prevalence (peaking at 32.5%) was predicted across sub-Saharan Africa and the Arabian Peninsula. Although G6PDd prevalence was generally lower across central and southeast Asia, rarely exceeding 20%, the majority of G6PDd individuals (67.5% median estimate) were from Asian countries. We estimated a G6PDd allele frequency of 8.0% (interquartile range: 7.4-8.8) across MECs, and 5.3% (4.4-6.7) within malaria-eliminating countries. The reliability of the map is contingent on the underlying data informing the model; population heterogeneity can only be represented by the available surveys, and important weaknesses exist in the map across data-sparse regions. Uncertainty metrics are used to quantify some aspects of these limitations in the map. Finally, we assembled a database of G6PDd variant occurrences to inform a national-level index of relative G6PDd haemolytic risk. Asian countries, where variants were most severe, had the highest relative risks from G6PDd. CONCLUSIONS: G6PDd is widespread and spatially heterogeneous across most MECs where primaquine would be valuable for malaria control and elimination. The maps and population estimates presented here reflect potential risk of primaquine-associated harm. In the absence of non-toxic alternatives to primaquine, these results represent additional evidence to help inform safe use of this valuable, yet dangerous, component of the malaria-elimination toolkit. Please see later in the article for the Editors' Summary