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Biomedical subjects

A D Barbour

Publications and source records attributed to A D Barbour.

12 recordsLinked to original sources
PubMed2004

Convergence of a structured metapopulation model to Levins's model.

We consider a structured metapopulation model describing the dynamics of a single species, whose members are located in separate patches that are linked through migration according to a mean field rule. Our main aim is to find conditions under which its equilibrium distribution is reasonably approximated by that of the unstructured model of Levins (1969). We do this by showing that the (positive) equilibrium distribution converges, as the carrying capacity of each population goes to infinity together with appropriate scalings on the other parameters, to a bimodal distribution, consisting of a point mass at 0, together with a positive part which is closely approximated by a shifted Poisson centred near the carrying capacity. Under this limiting regime, we also give simpler approximate formulae for the equilibrium distribution. We conclude by showing how to compute persistence regions in parameter space for the exact model, and then illustrate all our results with numerical examples. Our proofs are based on Stein's method.

Animals↗
PubMed2003

The duration of a sequence of epidemics.

The typical duration of an epidemic in a sequence of linearly ordered populations shows a surprising nonmonotonic behaviour with respect to population size, which was noted by Swinton (1998) [Bull. Math. Biol., 60, 215-230]. This paper gives the sketch of a proof of the phenomenon.

Animals↗
PubMed1999

Recognizing very distant sequence relationships among proteins by family profile analysis.

Family profile analysis (FPA), described in this paper, compares all available homologous amino acid sequences of a target family with the profile of a probe family while conventional sequence profile analysis (Gribskov M, Lüthy R, Eisenberg D. Meth Enzymol 1990;183:146-159) considers only a single target sequence in comparison with the probe family. The increased input of sequence information in FPA expands the range for sequence-based recognition of structural relationships. In the FPA algorithm, Zscores of each of the target sequences, obtained from a probe profile search over all known amino acid sequences, are averaged and then compared with the scores for sequences of 100 reference families in the same probe family search. The resulting F-Zscore of the target family, expressed in "effective standard deviations" of the mean Zscores of the reference families, with value above a threshold of 3.5 indicates a statistically significant evolutionary relationship between the target and probe families. The sensitivity of FPA to sequence information was tested with several protein families where distant relationships have been verified from known tertiary protein architectures, which included vitamin B6-dependent enzymes, (beta/alpha)8-barrel proteins, beta-trefoil proteins, and globins. In comparison to other methods, FPA proved to be significantly more sensitive, finding numerous new homologies. The FPA technique is not only useful to test a suspected relationship between probe and target families but also identifies possible target families in profile searches over all known primary structures.

Algorithms↗
PubMed1998

Mathematical model of a virus-neutralizing immunglobulin response.

We present a mathematical model to simulate the kinetics of B-cell activation and the virus-neutralizing immunoglobulin response in the spleen of mice after infection with vesicular stomatitis virus (VSV). Our model combines data from in vitro experiments and in vivo kinetic observations. A system of eight nonlinear differential equations was used in the computer experiments and numerically solved. The isotype switch from IgM to IgG in the presence of T-cell help was modelled by a time variable function, used as a parameter. The model solutions indicate fast kinetics of the generation of VSV-neutralizing IgM antibodies within 2-3 days post immunization peaking on day 5 at a serum concentration of approximately 80 microgram ml-1 IgM, which is the equivalent to about 10% of the total IgM serum concentration. The frequency of virus-specific B cells increases about 1000-fold within the first 4 days after immunization. Protective levels of VSV-neutralizing IgG antibodies (>/=10 microgram ml-1) are reached within 5 to 6 days post immunization. Fitting the model solution to the experimentally observed neutralizing serum titers suggests an increase in the neutralizing activity of IgGs occurring between days 5 and 8 post-infection. The model indicates that less than 10 VSV-specific B cells have to be triggered daily to maintain protective IgG serum titers during the memory phase.

Animals↗
PubMed1996

Modeling the transmission of schistosomiasis: an introductory view.

The transmission of schistosomiasis can be modeled at various levels of complexity in terms of systems of mathematical equations. This paper shows how such models can be set up, and stresses the importance of incorporating the right basic assumptions from the outset. The use of models for evaluating possible control strategies is illustrated in the context of a simple prevalence model of transmission. Some limitations and uncertainties involved in modeling schistosomiasis are also indicated.

Animals↗
PubMed1993

A host-parasite model yielding heterogeneous parasite loads.

Many models of parasitic infections lead to an approximately Poisson distribution of parasites among hosts, in stark contrast to the highly over-dispersed distributions that are usually encountered in practice. In this paper, a model is analyzed which, while assuming all individuals to be alike, can still lead to a very heterogeneous distribution of parasites among the host population. The model can be viewed as a very simple mean field interacting particle system, with the particles corresponding to the individual hosts, which behaves like an associated deterministic system when the number of hosts is large. The deterministic system describes the evolution over time of the proportions of the population with different parasite loads and its equilibria are interpreted as typical distributions of parasites among hosts. Despite its simplicity, the model is complicated enough mathematically to leave a number of open problems.

Animals↗
PubMed1991

Modeling the overdispersion of parasite loads.

Many epidemic models lead to an approximately Poisson distribution of parasites among hosts. This is at variance with observation, where heavy overdispersion is the rule. A simple model is proposed that, while treating individuals alike, nonetheless gives rise to highly variable parasite loads.

Animals↗
PubMed1989

Aspects of line-fitting in bivariate allometric analyses.

One of the fundamental problems involved in analyses of the scaling effects of body size (allometric analysis is the choice of an appropriate best-fit line in bivariate logarithmic plots. Following a discussion of some basic aspects of allometric analysis, the tow mai procedures for the determination of a best-fit line - the least-squares regression and the major axis - are examined with respect to their different properties and underlying models. It is important to distinguish intraspecific from interspecific scaling and to recognize the distinction between use of a best-fit line to define a relationship and use of the line for prediction. An alternative model to the bivariate normal distribution, referred to as the 'extruded normal distribution', is presented and its implications are examined with respect to two test cases (scaling of basal metabolic rate in human males; scaling of population density in mammals).

Animals↗
PubMed1985

The importance of age and water contact patterns in relation to Schistosoma haematobium infection.

Data obtained by Dalton & Pole in 1978 were analysed in order to assess the relative importance of age and water contact patterns in explaining the variations in level of infection with Schistosoma haematobium observed among their study population. It was found that age and sex were the only two significant factors, and that the information about an individual's water contact pattern contained in the data was of no further help in predicting his level of infection. This conclusion is in marked opposition to that reached by Dalton & Pole.

Adolescent↗
PubMed1978

Macdonald's model and the transmission of bilharzia.

The paper considers a model for the transmission of bilharzia based on Macdonald's assumptions, in the light of data observed in the field. It is shown, in particular, that the threshold parameter governing whether or not an endemic cycle can be established is closely related to the proportion of infected snails in a community, and that this proportion is normally observed to be rather smaller than is compatible with the model. By considering more sophisticated models, allowing for the latent period of infection in the snails, and also for spatial and seasonal heterogeneity, the effective proportion of infected snails, from the point of view of Macdonald's model, is shown to be rather larger, and expressions are given whereby it can be evaluated from observable quantities. However, for the data from Malirong which are taken as illustration, it is also demonstrated that an even more plausible threshold value is obtained from a simple model incorporating human immunity in addition to the assumptions of Macdonald's model, and that, if this model were reasonable, human immunity would appear to be the most important factor in controlling the level of the disease in Malirong.

Animals↗
PubMedDate not supplied

GC/MS analysis of propylated barbiturates.

A simple and reproducible method for the analysis of barbiturates by GC/MS after derivatization with dimethylformamide dipropyl acetal is reported. The method is readily adapted to screening, confirmation, and quantitation.

Barbiturates↗