Mutation, selection, and ancestry in branching models: a variational approach

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. Here, the variational principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure

Yellow Fever in Africa: Estimating the Burden of Disease and Impact of Mass Vaccination from Outbreak and Serological Data

Background:Yellow fever is a vector-borne disease affecting humans and non-human primates in tropical areas of Africa and South America. While eradication is not feasible due to the wildlife reservoir, large scale vaccination activities in Africa during the 1940s to 1960s reduced yellow fever incidence for several decades. However, after a period of low vaccination coverage, yellow fever has resurged in the continent. Since 2006 there has been substantial funding for large preventive mass vaccination campaigns in the most affected countries in Africa to curb the rising burden of disease and control future outbreaks. Contemporary estimates of the yellow fever disease burden are lacking, and the present study aimed to update the previous estimates on the basis of more recent yellow fever occurrence data and improved estimation methods.Methods and Findings:Generalised linear regression models were fitted to a dataset of the locations of yellow fever outbreaks within the last 25 years to estimate the probability of outbreak reports across the endemic zone. Environmental variables and indicators for the surveillance quality in the affected countries were used as covariates. By comparing probabilities of outbreak reports estimated in the regression with the force of infection estimated for a limited set of locations for which serological surveys were available, the detection probability per case and the force of infection were estimated across the endemic zone.The yellow fever burden in Africa was estimated for the year 2013 as 130,000 (95% CI 51,000-380,000) cases with fever and jaundice or haemorrhage including 78,000 (95% CI 19,000-180,000) deaths, taking into account the current level of vaccination coverage. The impact of the recent mass vaccination campaigns was assessed by evaluating the difference between the estimates obtained for the current vaccination coverage and for a hypothetical scenario excluding these vaccination campaigns. Vaccination campaigns were estimated to have reduced the number of cases and deaths by 27% (95% CI 22%-31%) across the region, achieving up to an 82% reduction in countries targeted by these campaigns. A limitation of our study is the high level of uncertainty in our estimates arising from the sparseness of data available from both surveillance and serological surveys.Conclusions:With the estimation method presented here, spatial estimates of transmission intensity can be combined with vaccination coverage levels to evaluate the impact of past or proposed vaccination campaigns, thereby helping to allocate resources efficiently for yellow fever control. This method has been used by the Global Alliance for Vaccines and Immunization (GAVI Alliance) to estimate the potential impact of future vaccination campaigns.Please see later in the article for the Editors' Summary

Meson Production in p+d Reactions

The production of neutral and charged pions as well as eta mesons is studied in the Delta and N* resonance region, respectively. Heavy A=3 recoils were measured with the GEM detector. The differential cross sections covering the full angular range are compared with model calculations.Comment: 4 pages, latex, 4 figures, talk presented at the XVIIth European Conference on Few-Body Problems in Physics, Evora, Portugal, September 2000; to be published in Nucl. Phys.

Measurement of p + d -> 3He + eta in S(11) Resonance

We have measured the reaction p + d -> 3He + eta at a proton beam energy of 980 MeV, which is 88.5 MeV above threshold using the new ``germanium wall'' detector system. A missing--mass resolution of the detector system of 2.6% was achieved. The angular distribution of the meson is forward peaked. We found a total cross section of (573 +- 83(stat.) +- 69(syst.))nb. The excitation function for the present reaction is described by a Breit Wigner form with parameters from photoproduction.Comment: 8 pages, 2 figures, corrected typos in heade

Prion infectivity in the spleen of a <em>PRNP</em> heterozygous individual with subclinical variant Creutzfeldt-Jakob disease

Blood transfusion has been identified as a source of human-to-human transmission of variant Creutzfeldt–Jakob disease. Three cases of variant Creutzfeldt–Jakob disease have been identified following red cell transfusions from donors who subsequently developed variant Creutzfeldt–Jakob disease and an asymptomatic red cell transfusion recipient, who did not die of variant Creutzfeldt–Jakob disease, has been identified with prion protein deposition in the spleen and a lymph node, but not the brain. This individual was heterozygous (MV) at codon 129 of the prion protein gene (PRNP), whereas all previous definite and probable cases of variant Creutzfeldt–Jakob disease have been methionine homozygotes (MM). A critical question for public health is whether the prion protein deposition reported in peripheral tissues from this MV individual correlates with infectivity. Additionally it is important to establish whether the PRNP codon 129 genotype has influenced the transmission characteristics of the infectious agent. Brain and spleen from the MV blood recipient were inoculated into murine strains that have consistently demonstrated transmission of the variant Creutzfeldt–Jakob disease agent. Mice were assessed for clinical and pathological signs of disease and transmission data were compared with other transmission studies in variant Creutzfeldt–Jakob disease, including those on the spleen and brain of the donor to the index case. Transmission of variant Creutzfeldt–Jakob disease was observed from the MV blood recipient spleen, but not from the brain, whereas there was transmission from both spleen and brain tissues from the red blood cell donor. Longer incubation times were observed for the blood donor spleen inoculum compared with the blood donor brain inoculum, suggesting lower titres of infectivity in the spleen. The distribution of vacuolar pathology and abnormal prion protein in infected mice were similar following inoculation with both donor and recipient spleen homogenates, providing initial evidence of similar transmission properties after propagation in PRNP codon 129 MV and MM individuals. These studies demonstrate that spleen tissue from a PRNP MV genotype individual can propagate the variant Creutzfeldt–Jakob disease agent and that the infectious agent can be present in the spleen without CNS involvement

Nowcasting pandemic influenza A/H1N1 2009 hospitalizations in the Netherlands

During emerging epidemics of infectious diseases, it is vital to have up-to-date information on epidemic trends, such as incidence or health care demand, because hospitals and intensive care units have limited excess capacity. However, real-time tracking of epidemics is difficult, because of the inherent delay between onset of symptoms or hospitalizations, and reporting. We propose a robust algorithm to correct for reporting delays, using the observed distribution of reporting delays. We apply the algorithm to pandemic influenza A/H1N1 2009 hospitalizations as reported in the Netherlands. We show that the proposed algorithm is able to provide unbiased predictions of the actual number of hospitalizations in real-time during the ascent and descent of the epidemic. The real-time predictions of admissions are useful to adjust planning in hospitals to avoid exceeding their capacity

Solution of the Crow-Kimura and Eigen models for alphabets of arbitrary size by Schwinger spin coherent states

To represent the evolution of nucleic acid and protein sequence, we express the parallel and Eigen models for molecular evolution in terms of a functional integral representation with an $h$-letter alphabet, lifting the two-state, purine/pyrimidine assumption often made in quasi-species theory. For arbitrary $h$ and a general mutation scheme, we obtain the solution of this model in terms of a maximum principle. Euler's theorem for homogeneous functions is used to derive this `thermodynamic' formulation of evolution. The general result for the parallel model reduces to known results for the purine/pyrimidine $h=2$ alphabet and the nucleic acid $h=4$ alphabet for the Kimura 3 ST mutation scheme. Examples are presented for the $h=4$ and $h=20$ cases. We derive the maximum principle for the Eigen model for general $h$. The general result for the Eigen model reduces to a known result for $h=2$. Examples are presented for the nucleic acid $h=4$ and the amino acid $h=20$ alphabet. An error catastrophe phase transition occurs in these models, and the order of the phase transition changes from second to first order for smooth fitness functions when the alphabet size is increased beyond two letters to the generic case. As examples, we analyze the general analytic solution for sharp peak, linear, quadratic, and quartic fitness functions.Comment: 50 pages, 8 figures, to appear in J. Stat. Phys; some typos fixe

Also at National Accelerator Centre, Faure, South Africa On leave from ICUF

Abstract A stack of annular detectors made of high-purity germanium was developed. The detectors are position sensitive with radial structures. The first one (&quot;Quirl&quot;) is double-sided position sensitive defining 40 000 pixels, the following three (E1, E2 and E3) have 32 wedges each. The Quirl acts as tracker while the other three act as calorimeter. The stack was successfully operated in meson production reactions close to threshold