| 1. |
- Gyllenberg, M., et al.
(författare)
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Bayesian predictiveness, exchangeability and sufficientness in bacterial taxonomy
- 2002
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Ingår i: Mathematical Biosciences. - 0025-5564 .- 1879-3134. ; 177-178, s. 161-184
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- We present a theory of classification and predictive identification of bacteria. Bacterial strains are characterized by a binary vector and the taxonomy is specified by attaching a label to each vector. The theory is developed from only two basic assumptions, viz. that the sequence of pairs of feature vectors and the attached labels is judged (infinitely) exchangeable and predictively sufficient. We derive expressions for the training error and the probability of identification error and show that latter is an affine function of the former. We prove the law of large numbers for identification matrices, which contain the fundamental information of bacterial data. We prove the Bayesian risk consistency of the predictive identification rule given by the theory and show that the training error is a consistent estimate of the generalization error. © 2002 Published by Elsevier Science Inc.
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| 2. |
- Gyllenberg, Mats, et al.
(författare)
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Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model
- 1993
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 118:1, s. 25-49
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Tidskriftsartikel (refereegranskat)abstract
- A discrete model for a metapopulation consisting of two local populations connected by migration is described and analyzed. It is assumed that the local populations grow according to the logistic law, that both populations have the same emigration rate, and that migrants choose their new habitat patch at random. Mathematically this leads to a coupled system of two logistic equations. A complete characterization of fixed point and two-periodic orbits is given, and a bifurcation analysis is performed. The region in the parameter plane where the diagonal is a global attractor is determined. In the symmetric case, where both populations have the same growth rate, the analysis is rigorous with complete proofs. In the nonsymmetric case, where the populations grow at different rates, the results are obtained numerically. The results are interpreted biologically. Particular attention is given to the sense in which migration has a stabilizing and synchronizing effect on local dynamics.
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| 3. |
- Nåsell, Ingemar
(författare)
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Stochastic models of some endemic infections
- 2002
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Ingår i: Mathematical Biosciences. - 0025-5564 .- 1879-3134. ; 179:1, s. 1-19
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Tidskriftsartikel (refereegranskat)abstract
- Stochastic models are established and studied for several endemic infections with demography. Approximations of quasi-stationary distributions and of times to extinction are derived for stochastic versions of SI, SIS, SIR, and SIRS models. The approximations are valid for sufficiently large population sizes. Conditions for validity of the approximations are given for each of the models. These are also conditions for validity of the corresponding deterministic model. It is noted that some deterministic models are unacceptable approximations of the stochastic models for a large range of realistic parameter values.
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| 4. |
- Andersson, Claes, 1987, et al.
(författare)
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A Bayesian hierarchical point process model for epidermal nerve fiber patterns
- 2019
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 1879-3134 .- 0025-5564. ; 313, s. 48-60
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Tidskriftsartikel (refereegranskat)abstract
- We introduce the Thomas process in a Bayesian hierarchical setting as a model for point pattern data with a nested structure. This model is applied to a nerve fiber data set which consists of several point patterns of nerve entry points from 47 subjects divided into 3 groups, where the grouping is based on the diagnosed severity of a certain nerve disorder. The modeling assumption is that each point pattern is a realization of a Thomas process, with parameter values specific to the subject. These parameter values are in turn assumed to come from distributions that depend on which group the subject belongs to. To fit the model, we construct an MCMC algorithm, which is evaluated in a simulation study. The results of the simulation study indicate that the group level mean of each parameter is well estimated, but that the estimation of the between subject variance is more challenging. When fitting the model to the nerve fiber data, we find that the structure within clusters appears to be the same in all groups, but that the number of clusters decreases with the progression of the nerve disorder.
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| 5. |
- Andersson, Tom
(författare)
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Exploring voltage-dependent ion channels in silico by hysteretic conductance
- 2010
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 226:1, s. 16-27
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Tidskriftsartikel (refereegranskat)abstract
- Kinetic models of voltage-dependent ion channels are normally inferred from time records of macroscopic current relaxation or microscopic single channel data. A complementary explorative approach is outlined. Hysteretic conductance refers to conductance delays in response to voltage changes, delays at either macroscopic or microscopic levels of observation. It enables complementary assessments of model assumptions and gating schemes of voltage-dependent channels, e.g. independent versus cooperative gating, and multiple gating modes. Under the Hodgkin-Huxley condition of independent gating, and under ideal measurement conditions, hysteretic conductance makes it also possible to estimate voltage-dependent rate functions. The argument is mainly theoretical, based on experimental observations, and illustrated by simulations of Markov kinetic models.
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| 6. |
- Anguelova, Milena, 1978, et al.
(författare)
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Minimal output sets for identifiability
- 2012
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 1879-3134 .- 0025-5564.
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Tidskriftsartikel (refereegranskat)abstract
- Ordinary differential equation models in biology often contain a large number of parameters that must be determined from measurements by parameter estimation. For a parameter estimation procedure to be successful, there must be a unique set of parameters that can have produced the measured data. This is not the case if a model is not uniquely structurally identifiable with the given set of outputs selected as measurements. In designing an experiment for the purpose of parameter estimation, given a set of feasible but resource-consuming measurements, it is useful to know which ones must be included in order to obtain an identifiable system, or whether the system is unidentifiable from the feasible measurement set. We have developed an algorithm that, from a user-provided set of variables and parameters or functions of them assumed to be measurable or known, determines all subsets that when used as outputs give a locally structurally identifiable system and are such that any output set for which the system is structurally identifiable must contain at least one of the calculated subsets. The algorithm has been implemented in Mathematica and shown to be feasible and efficient. We have successfully applied it in the analysis of large signalling pathway models from the literat
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| 7. |
- Azevedo, Ricardo B.R., et al.
(författare)
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A branching process model of evolutionary rescue
- 2021
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Ingår i: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 341
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Tidskriftsartikel (refereegranskat)abstract
- Evolutionary rescue is the process whereby a declining population may start growing again, thus avoiding extinction, via an increase in the frequency of fitter genotypes. These genotypes may either already be present in the population in small numbers, or arise by mutation as the population declines. We present a simple two-type discrete-time branching process model and use it to obtain results such as the probability of rescue, the shape of the population growth curve of a rescued population, and the time until the first rescuing mutation occurs. Comparisons are made to existing results in the literature in cases where both the mutation rate and the selective advantage of the beneficial mutations are small.
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| 8. |
- Ball, Frank, et al.
(författare)
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Reproduction numbers for epidemic models with households and other social structures II : Comparisons and implications for vaccination
- 2016
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 274, s. 108-139
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider epidemic models of directly transmissible SIR (susceptible -> infective -> recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting either of households or of households and workplaces. We review most reproduction numbers defined in the literature for these models, including the basic reproduction number R-0 introduced in the companion paper of this, for which we provide a simpler, more elegant derivation. Extending previous work, we provide a complete overview of the inequalities among these reproduction numbers and resolve some open questions. Special focus is put on the exponential-growth-associated reproduction number R-r, which is loosely defined as the estimate of R-0 based on the observed exponential growth of an emerging epidemic obtained when the social structure is ignored. We show that for the vast majority of the models considered in the literature R-r >= R-0 when R-0 >= 1 and R-r <= R-0 when R-0 <= 1. We show that, in contrast to models without social structure, vaccination of a fraction 1 - 1/R-0 of the population, chosen uniformly at random, with a perfect vaccine is usually insufficient to prevent large epidemics. In addition, we provide significantly sharper bounds than the existing ones for bracketing the critical vaccination coverage between two analytically tractable quantities, which we illustrate by means of extensive numerical examples.
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| 9. |
- Banks-Sills, Leslie, et al.
(författare)
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Strain Driven Transport for Bone Modeling at the Periosteal Surface
- 2011
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Ingår i: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 230:1, s. 37-44
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Tidskriftsartikel (refereegranskat)abstract
- Bone modeling and remodeling has been the subject of extensive experimental studies. There have been several mathematical models proposed to explain the observed behavior, as well. A different approach is taken here in which the bone is treated from a macroscopic view point. In this investigation, a one-dimensional analytical model is used to shed light on the factors which play the greatest role in modeling or growth of cortical bone at the periosteal surface. It is presumed that bone growth is promoted when increased amounts of bone nutrients, such as nitric oxide synthase (NOS) or messenger molecules, such as prostaglandin E2 (PGE2), seep out to the periosteal surface of cortical bone and are absorbed by osteoblasts. The transport of the bone nutrients is assumed to be a strain controlled process. Equations for the flux of these nutrients are written for a one-dimensional model of a long bone. The obtained partial differential equation is linearized and solved analytically. Based upon the seepage of nutrients out of the bone, the effect of loading frequency, number of cycles and strain level is examined for several experiments that were found in the literature. It is seen that bone nutrient seepage is greatest on the tensile side of the bone; this location coincides with the greatest amount of bone modeling
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| 10. |
- Bartoszek, Krzysztof
(författare)
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Exact and approximate limit behaviour of the Yule trees cophenetic index
- 2018
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Ingår i: Mathematical Biosciences. - : ELSEVIER SCIENCE INC. - 0025-5564 .- 1879-3134. ; 303, s. 26-45
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Tidskriftsartikel (refereegranskat)abstract
- In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure-birth tree conditioned on n contemporary tips. We show that this normalized phylogenetic balance index is a sub-martingale that converges almost surely and in L-2. We link our work with studies on trees without branch lengths and show that in this case the limit distribution is a contraction-type distribution, similar to the Quicksort limit distribution. In the continuous branch case we suggest approximations to the limit distribution. We propose heuristic methods of simulating from these distributions and it may be observed that these algorithms result in reasonable tails. Therefore, we propose a way based on the quantiles of the derived distributions for hypothesis testing, whether an observed phylogenetic tree is consistent with the pure-birth process. Simulating a sample by the proposed heuristics is rapid, while exact simulation (simulating the tree and then calculating the index) is a time-consuming procedure. We conduct a power study to investigate how well the cophenetic indices detect deviations from the Yule tree and apply the methodology to empirical phylogenies.
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