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1.	Bellman, R., et al. (author) On Structural Identifiability 1970 In: Mathematical Biosciences. - 0025-5564. ; 7, s. 329-339 Journal article (peer-reviewed)abstract In this article we introduce a new concept, structural identifiability, which plays a central role in identification problems. The concept is useful when answering questions such as: To what extent is it possible to get insight into the internal structure of a system from input-output measurements? What experiments are necessary in order to determine the internal couplings uniquely? The definition of the concept of an identifiable structure is given. Criteria as well as certain identifiable structures are discussed. Particular emphasis is given to compartmental models.
2.	Hagander, Per, et al. (author) Incompatibility Alleles; Characteristics of a 1-Locus System 1974 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564. ; 20, s. 145-154 Journal article (peer-reviewed)abstract The 1-locus incompatibility system that is usually assumed to be present in the red clover is investigated. The allele fluctuations from one generation to the other are demonstrated. A mathematical state model is deduced for arbitrary numbers of alleles in the population, and its steady-state behaviour and stability are discussed. The eigenvalues of the linearized models as well as simulations show that the large systems react slowly to disturbances while the three-allele system oscillates around its equilibrium.
3.	Hagander, Per, et al. (author) Models for the Insulin Response to Intravenous Glucose 1978 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564. ; 42, s. 15-29 Journal article (peer-reviewed)abstract The Grodsky packet storage model describes many features of insulin release, but at present more or less arbitrary simplifications are necessary. The consequences of various simplifications are discussed, especially with regard to identification of parameters thought to be of importance for glucose tolerance. In particular, the insulin release dynamics of the ordinary intravenous glucose tolerance test is examined. The proposed model contains the following features: It considers arterial rather than venous blood glucose concentration as the stimulus, it takes the glucose injection time into account, and it contains a positive derivative term during the rise of the glucose concentration. When the insulin elimination-rate time constant is fixed to an a priori value, model fitting gives a clear quantification of the sensitivity of early and late insulin release to glucose.
4.	Hagander, Per (author) Random Effects in Biomedical Flow Systems 1977 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564. ; 36:3-4, s. 243-255 Journal article (peer-reviewed)abstract The random effects in tracer kinetics and cell cycle kinetics are usually described by the particle residence time. An analytical framework is developed, and the importance of the statistical independence of the residence times is emphasized.
5.	Johansson, Rolf, et al. (author) Multi-Stimulus Multi-Response Posturography 2001 In: Mathematical Biosciences. - 0025-5564. ; 174:1, s. 41-59 Journal article (peer-reviewed)abstract In this study a method for the analysis of simultaneous multiple measurements of kinematics and stabilizing forces related to human postural dynamics is proposed. Each subject in a group of normal subjects (n=10) was tested with eyes-open and eyes-closed with simultaneous but uncorrelated vestibular and proprioceptive stimuli in order to investigate the contributions of individual sensory feedback loops. Statistical analysis was made by means of multi-input multi-output identification of a transfer function from stimuli to stabilizing forces of the feet and the resulting body position, the transfer function being compatible with a biomechanical model formulated as a stabilized segmented inverted pendulum subject to feedback of body sway and position. Each individual model estimated is effective in predicting a subject's response to new stimuli and in describing the interacting effects of stimuli on body kinetics. The proposed methodology responds to the current needs of data analysis of multi-stimulus multi-response experiments.
6.	Johansson, Rolf, et al. (author) Optimal Coordination and Control of Posture and Locomotion 1991 In: Artificial Neural Networks: Proceedings of the 1991 International Conference on Artificial Neural Networks (ICANN-91). - 0444891781 - 9780444891785 ; 103, s. 203-244 Conference paper (peer-reviewed)abstract
7.	Fitzsimons, CJ, et al. (author) A novel algorithm for tracing the interaction of a track with molecular targets--use of Delaunay triangulation 1998 In: Mathematical biosciences. - 0025-5564. ; 154:2, s. 103-115 Journal article (peer-reviewed)
8.	Gyllenberg, M., et al. (author) Bayesian predictiveness, exchangeability and sufficientness in bacterial taxonomy 2002 In: Mathematical Biosciences. - 0025-5564 .- 1879-3134. ; 177-178, s. 161-184 Conference paper (other academic/artistic)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.
9.	Gyllenberg, Mats, et al. (author) Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model 1993 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 118:1, s. 25-49 Journal article (peer-reviewed)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.
10.	Nåsell, Ingemar (author) Stochastic models of some endemic infections 2002 In: Mathematical Biosciences. - 0025-5564 .- 1879-3134. ; 179:1, s. 1-19 Journal article (peer-reviewed)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.
11.	Andersson, Claes, 1987, et al. (author) A Bayesian hierarchical point process model for epidermal nerve fiber patterns 2019 In: Mathematical Biosciences. - : Elsevier BV. - 1879-3134 .- 0025-5564. ; 313, s. 48-60 Journal article (peer-reviewed)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.
12.	Andersson, Tom (author) Exploring voltage-dependent ion channels in silico by hysteretic conductance 2010 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 226:1, s. 16-27 Journal article (peer-reviewed)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.
13.	Anguelova, Milena, 1978, et al. (author) Minimal output sets for identifiability 2012 In: Mathematical Biosciences. - : Elsevier BV. - 1879-3134 .- 0025-5564. Journal article (peer-reviewed)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
14.	Azevedo, Ricardo B.R., et al. (author) A branching process model of evolutionary rescue 2021 In: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 341 Journal article (peer-reviewed)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.
15.	Ball, Frank, et al. (author) Reproduction numbers for epidemic models with households and other social structures II : Comparisons and implications for vaccination 2016 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 274, s. 108-139 Journal article (peer-reviewed)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.
16.	Banks-Sills, Leslie, et al. (author) Strain Driven Transport for Bone Modeling at the Periosteal Surface 2011 In: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 230:1, s. 37-44 Journal article (peer-reviewed)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
17.	Bartoszek, Krzysztof (author) Exact and approximate limit behaviour of the Yule trees cophenetic index 2018 In: Mathematical Biosciences. - : ELSEVIER SCIENCE INC. - 0025-5564 .- 1879-3134. ; 303, s. 26-45 Journal article (peer-reviewed)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.
18.	Bartoszek, Krzysztof (author) Quantifying the effects of anagenetic and cladogenetic evolution 2014 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 254, s. 42-57 Journal article (peer-reviewed)abstract An ongoing debate in evolutionary biology is whether phenotypic change occurs predominantly around the time of speciation or whether it instead accumulates gradually over time. In this work I propose a general framework incorporating both types of change, quantify the effects of speciational change via the correlation between species and attribute the proportion of change to each type. I discuss results of parameter estimation of Hominoid body size in this light. I derive mathematical formulae related to this problem, the probability generating functions of the number of speciation events along a randomly drawn lineage and from the most recent common ancestor of two randomly chosen tip species for a conditioned Yule tree. Additionally I obtain in closed form the variance of the distance from the root to the most recent common ancestor of two randomly chosen tip species.
19.	Bartoszek, Krzysztof, et al. (author) Squaring within the Colless index yields a better balance index 2021 In: Mathematical Biosciences. - : ELSEVIER SCIENCE INC. - 0025-5564 .- 1879-3134. ; 331 Journal article (peer-reviewed)abstract The Colless index for bifurcating phylogenetic trees, introduced by Colless (1982), is defined as the sum, over all internal nodes v of the tree, of the absolute value of the difference of the sizes of the clades defined by the children of v. It is one of the most popular phylogenetic balance indices, because, in addition to measuring the balance of a tree in a very simple and intuitive way, it turns out to be one of the most powerful and discriminating phylogenetic shape indices. But it has some drawbacks. On the one hand, although its minimum value is reached at the so-called maximally balanced trees, it is almost always reached also at trees that are not maximally balanced. On the other hand, its definition as a sum of absolute values of differences makes it difficult to study analytically its distribution under probabilistic models of bifurcating phylogenetic trees. In this paper we show that if we replace in its definition the absolute values of the differences of Glade sizes by the squares of these differences, all these drawbacks are overcome and the resulting index is still more powerful and discriminating than the original Colless index.
20.	Bock, Wolfgang, et al. (author) Optimal control of a multi-patch dengue model under the influence of Wolbachia bacterium 2019 In: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 315 Journal article (peer-reviewed)abstract In this work, a multi-patch model for dengue transmission dynamics including the bacterium Wolbachia is studied and by that the control efforts to minimize the disease spread by host and vector control are investigated. The multi-patch system models the host movement within the patches which coupled via a residence-time budgeting matrix P. Numerical results confirm that the control mechanism embedded in incidence rates of the disease transmission, effectively reduce the spread of the disease.
21.	Bouchnita, Anass, et al. (author) A multiscale model to design therapeutic strategies that overcome drug resistance to tyrosine kinase inhibitors in multiple myeloma 2020 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 319 Journal article (peer-reviewed)
22.	Britton, Tom, et al. (author) A stochastic vector-borne epidemic model : Quasi-stationarity and extinction 2017 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 289, s. 89-95 Journal article (peer-reviewed)abstract We consider a stochastic model describing the spread of a vector borne disease in a community where individuals (hosts and vectors) die and new individuals (hosts and vectors) are born. The time to extinction of the disease, T-Q, starting in quasi-stationary (conditional on non extinction) is studied. Properties of the limiting distribution are used to obtain an approximate expression for E(T-Q), the mean-parameter in the exponential distribution of the time to extinction, for a finite population. It is then investigated numerically and by means of simulations how E(T-Q) and its approximations depend on the different model parameters.
23.	Britton, Tom, 1965-, et al. (author) An epidemic model with infector and exposure dependent severity 2009 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 218:2, s. 105-120 Journal article (peer-reviewed)abstract A stochastic epidemic model allowing for both mildly and severely infectious individuals is defined, where an individual can become severely infectious directly upon infection or if additionally exposed to infection. It is shown that, assuming a large community, the initial phase of the epidemic may be approximated by a suitable branching process and that the main part of an epidemic that becomes established admits a law of large numbers and a central limit theorem, leading to a normal approximation for the final outcome of such an epidemic. Effects of vaccination prior to an outbreak are studied and the critical vaccination coverage, above which only small outbreaks can occur, is derived. The results are illustrated by simulations that demonstrate that the branching process and normal approximations work well for finite communities, and by numerical examples showing that the final outcome may be close to discontinuous in certain model parameters and that the fraction mildly infected may actually increase as an effect of vaccination.
24.	Britton, Tom, et al. (author) Epidemic modelling : aspects where stochasticity matters 2009 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 22:2, s. 109-116 Journal article (peer-reviewed)abstract Epidemic models are always simplifications of real world epidemics. Which real world features to include, and which simplifications to make, depend both on the disease of interest and on the purpose of the modelling. In the present paper we discuss some such purposes for which a stochastic model is preferable to a deterministic counterpart. The two main examples illustrate the importance of allowing the infectious and latent periods to be random when focus lies on the probability of a large epidemic outbreak and/or on the initial speed, or growth rate, of the epidemic. A consequence of the latter is that estimation of the basic reproduction number R0 is sensitive to assumptions about the distributions of the infectious and latent periods when using data from the early stages of an outbreak, which we illustrate with data from the H1N1 influenza A pandemic. Some further examples are also discussed as are some practical consequences related to these stochastic aspects.
25.	Britton, Tom, et al. (author) Inhomogeneous epidemics on weighted networks 2012 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 240:2, s. 124-131 Journal article (peer-reviewed)abstract A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g., reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such that individuals are heterogeneous in terms of how susceptible and infectious they are. The basic reproduction number R-0 is derived and studied for various examples, but also the size and probability of a major outbreak. The qualitative conclusion is that R-0 gets larger as the community becomes more heterogeneous but that different heterogeneities (degree distribution, weight, susceptibility and infectivity) can sometimes have the cumulative effect of homogenizing the community, thus making R-0 smaller. The effect on the probability and final size of an outbreak is more complicated.
26.	Britton, Tom, et al. (author) SEIRS epidemics with disease fatalities in growing populations 2018 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 296, s. 45-59 Research review (peer-reviewed)abstract An SEIRS epidemic with disease fatalities is introduced in a growing population (modelled as a super-critical linear birth and death process). The study of the initial phase of the epidemic is stochastic, while the analysis of the major outbreaks is deterministic. Depending on the values of the parameters, the following scenarios are possible. i) The disease dies out quickly, only infecting few; ii) the epidemic takes off, the number of infected individuals grows exponentially, but the fraction of infected individuals remains negligible; iii) the epidemic takes off, the number of infected grows initially quicker than the population, the disease fatalities diminish the growth rate of the population, but it remains super critical, and the fraction of infected go to an endemic equilibrium; iv) the epidemic takes off, the number of infected individuals grows initially quicker than the population, the diseases fatalities turn the exponential growth of the population to an exponential decay.
27.	Britton, Tom (author) Stochastic epidemic models : A survey 2010 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 225:1, s. 24-35 Journal article (peer-reviewed)abstract This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.
28.	Cai, Liming, et al. (author) Optimal control of a malaria model with asymptomatic class and superinfection 2017 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 288, s. 94-108 Journal article (peer-reviewed)abstract In this paper, we introduce a malaria model with an asymptomatic class in human population and exposed classes in both human and vector populations. The model assumes that asymptomatic individuals can get re-infected and move to the symptomatic class. In the case of an incomplete treatment, symptomatic individuals move to the asymptomatic class. If successfully treated, the symptomatic individuals recover and move to the susceptible class. The basic reproduction number, R0,R0, is computed using the next generation approach. The system has a disease-free equilibrium (DFE) which is locally asymptomatically stable when R0<1,R0<1, and may have up to four endemic equilibria. The model exhibits backward bifurcation generated by two mechanisms; standard incidence and superinfection. If the model does not allow for superinfection or deaths due to the disease, then DFE is globally stable which suggests that backward bifurcation is no longer possible. Simulations suggest that total prevalence of malaria is the highest if all individuals show symptoms upon infection, but then undergoes an incomplete treatment and the lowest when all the individuals first move to the symptomatic class then treated successfully. Total prevalence is average if more individuals upon infection move to the asymptomatic class. We study optimal control strategies applied to bed-net use and treatment as main tools for reducing the total number of symptomatic and asymptomatic individuals. Simulations suggest that the optimal control strategies are very dynamic. Although they always lead to decrease in the symptomatic infectious individuals, they may lead to increase in the number of asymptomatic infectious individuals. This last scenario occurs if a large portion of newly infected individuals move to the symptomatic class but many of them do not complete treatment or if they all complete treatment but the superinfection rate of asymptomatic individuals is average.
29.	Cardilin, Tim, 1989, et al. (author) Optimization of additive chemotherapy combinations for an in vitro cell cycle model with constant drug exposures 2021 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 338 Journal article (peer-reviewed)abstract Proliferation of an in vitro population of cancer cells is described by a linear cell cycle model with n states, subject to provocation with m chemotherapeutic compounds. Minimization of a linear combination of constant drug exposures is considered, with stability of the system used as a constraint to ensure a stable or shrinking cell population. The main result concerns the identification of redundant compounds, and an explicit solution formula for the case where all exposures are nonzero. The orthogonal case, where each drug acts on a single and different stage of the cell cycle, leads to a version of the classic inequality between the arithmetic and geometric means. Moreover, it is shown how the general case can be solved by converting it to the orthogonal case using a linear invertible transformation. The results are illustrated with two examples corresponding to combination treatment with two and three compounds, respectively.
30.	Deijfen, Maria (author) Epidemics and vaccination on weighted graphs 2011 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 232:1, s. 57-65 Journal article (peer-reviewed)abstract A Reed-Frost epidemic with inhomogeneous infection probabilities on a graph with prescribed degree distribution is studied. Each edge (u, v) in the graph is equipped with two weights W((u,v)) and W((v,u)) that represent the (subjective) strength of the connection and determine the probability that u infects v in case u is infected and vice versa. Expressions for the epidemic threshold are derived for i.i.d. weights and for weights that are functions of the degrees. For i.i.d. weights, a variation of the so called acquaintance vaccination strategy is analyzed where vertices are chosen randomly and neighbors of these vertices with large edge weights are vaccinated. This strategy is shown to outperform the strategy where the neighbors are chosen randomly in the sense that the basic reproduction number is smaller for a given vaccination coverage.
31.	Diehl, Stefan, et al. (author) Analysis of photobioreactors in series 2018 In: Mathematical Biosciences. - : ELSEVIER SCIENCE INC. - 0025-5564 .- 1879-3134. ; 306, s. 107-118 Journal article (peer-reviewed)abstract A photobioreactor (PBR) contains microalgae which under illumination consume carbon dioxide and substrate dissolved in water, and produce oxygen. The process is used in water recovery resource facilities with a continuous flow of wastewaster through the PBR. With several PBRs in series the reduction of substrate can be improved. This paper contains a thorough analysis of a model of PBRs in series, where each PBR is modelled with a system of three ordinary differential equations for the concentrations of dissolved substrate and biomass (algae), and the internal cell quota of substrate to biomass. Each PBR has a certain volume and irradiation. The absorption rate of substrate into the cells is modelled with Monod kinetics, whereas the biomass growth rate is modelled with Droop kinetics, in which both a minimum and a maximum internal cell quota are assumed. The main result is that the model has a unique stable steady-state solution with algae in all PBRs. Another stable steady-state solution is the wash-out solution with no algae in the system. Other steady-state solutions are combinations of these two with no algae in some of the first PBRs and algae in the rest of the PBRs in the series. Conditions on the illumination, volumetric flow and volumes of the PBRs are given for the respective solution. Numerical solutions illustrate the theoretical results and indicate further properties.
32.	Gerlee, Philip, 1980, et al. (author) Travelling wave analysis of a mathematical model of glioblastoma growth 2016 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 276, s. 75-81 Journal article (peer-reviewed)abstract In this paper we analyse a previously proposed cell-based model of glioblastoma (brain tumour) growth, which is based on the assumption that the cancer cells switch phenotypes between a proliferative and motile state (Gerlee and Nelander, PLoS Comp. Bio., 8(6) 2012). The dynamics of this model can be described by a system of partial differential equations, which exhibits travelling wave solutions whose wave speed depends crucially on the rates of phenotypic switching. We show that under certain conditions on the model parameters, a closed form expression of the wave speed can be obtained, and using singular perturbation methods we also derive an approximate expression of the wave front shape. These new analytical results agree with simulations of the cell-based model, and importantly show that the inverse relationship between wave front steepness and speed observed for the Fisher equation no longer holds when phenotypic switching is considered.
33.	Guillot, Gilles, et al. (author) Discrimination and scoring using small sets of genes for two-sample microarray data 2007 In: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 205:2, s. 195-203 Journal article (peer-reviewed)abstract Comparison of gene expression for two groups of individuals form an important subclass of microarray experiments. We study multivariate procedures, in particular use of Hotelling's T2 for discrimination between the groups with a special emphasis on methods based on few genes only. We apply the methods to data from an experiment with a group of atopic dermatitis patients compared with a control group. We also compare our methodology to other recently proposed methods on publicly available datasets. It is found that (i) use of several genes gives a much improved discrimination of the groups as compared to one gene only, (ii) the genes that play the most important role in the multivariate analysis are not necessarily those that rank first in univariate comparisons of the groups, (iii) Linear Discriminant Analysis carried out with sets of 2-5 genes selected according to their Hotelling T2 give results comparable to state-of-the-art methods using many more genes, a feature of our method which might be crucial in clinical applications. Finding groups of genes that together give optimal multivariate discrimination (given the size of the group) can identify crucial pathways and networks of genes responsible for a disease. The computer code that we developed to make computations is available as an R package.
34.	Gustafsson, Leif, et al. (author) Bringing consistency to simulation of population models - Poisson simulation as a bridge between micro and macro simulation 2007 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 209:2, s. 361-385 Journal article (peer-reviewed)abstract Population models concern collections of discrete entities such as atoms, cells, humans, animals, etc., where the focus is on the number of entities in a population. Because of the complexity of such models, simulation is usually needed to reproduce their complete dynamic and stochastic behaviour. Two main types of simulation models are used for different purposes, namely micro-simulation models, where each individual is described with its particular attributes and behaviour, and macro-simulation models based on stochastic differential equations, where the population is described in aggregated terms by the number of individuals in different states. Consistency between micro- and macro-models is a crucial but often neglected aspect. This paper demonstrates how the Poisson Simulation technique can be used to produce a population macro-model consistent with the corresponding micro-model. This is accomplished by defining Poisson Simulation in strictly mathematical terms as a series of Poisson processes that generate sequences of Poisson distributions with dynamically varying parameters. The method can be applied to any population model. It provides the unique stochastic and dynamic macro-model consistent with a correct micro-model. The paper also presents a general macro form for stochastic and dynamic population models. In an appendix Poisson Simulation is compared with Markov Simulation showing a number of advantages. Especially aggregation into state variables and aggregation of many events per time-step makes Poisson Simulation orders of magnitude faster than Markov Simulation. Furthermore, you can build and execute much larger and more complicated models with Poisson Simulation than is possible with the Markov approach.
35.	Gustafsson, Leif, et al. (author) Consistent micro, macro and state-based population modelling 2010 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 225:2, s. 94-107 Journal article (peer-reviewed)abstract A population system can be modelled using a micro model focusing on the individual entities, a macro model where the entities are aggregated into compartments, or a state-based model where each possible discrete state in which the system can exist is represented. However, the concepts, building blocks, procedural mechanisms and the time handling for these approaches are very different. For the results and conclusions from studies based on micro, macro and state-based models to be consistent (contradiction-free), a number of modelling issues must be understood and appropriate modelling procedures be applied. This paper presents a uniform approach to micro, macro and state-based population modelling so that these different types of models produce consistent results and conclusions. In particular, we demonstrate the procedures (distribution, attribute and combinatorial expansions) necessary to keep these three types of models consistent. We also show that the different time handling methods usually used in micro, macro and state-based models can be regarded as different integration methods that can be applied to any of these modelling categories. The result is free choice in selecting the modelling approach and the time handling method most appropriate for the study without distorting the results and conclusions.
36.	Gustafsson, Leif, et al. (author) When can a deterministic model of a population system reveal what will happen on average? 2013 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 243:1, s. 28-45 Journal article (peer-reviewed)abstract A dynamic population system is often modelled by a deterministic difference equation model to obtain average estimates. However, there is a risk of the results being distorted because unexplained (random) variations are left out and because entities in the population are described by continuous quantities of an infinitely divisible population so that irregularly occurring events are described by smooth flows. These distortions have many aspects that cannot be understood by only regarding a deterministic approach. However, the reasons why a deterministic model may behave differently and produce biased results become visible when the deterministic model is compared with a stochastic model of the same structure. This paper focuses first on demographic stochasticity, i.e. stochasticity that refers to random variations in the occurrence of events affecting the state of an individual, and investigates the consequences of omitting this by deterministic modelling. These investigations reveal that bias may be strongly influenced by the type of question to be answered and by the stopping criterion ending the analysis or simulation run. Two cases are identified where deterministic models produce unbiased state variables: (1) Dynamic systems with stable local linear dynamics produce unbiased state variables asymptotically, in the limit of large flows; and (2) linear dynamic systems produce unbiased state variables as long as all state variables remain non-negative in both the deterministic and the stochastic models. Both cases also require the question under study to be compatible with a solution over a fixed time interval. Stochastic variability of initial values between simulation runs because of uncertainty or lack of information about the initial situation is denoted initial value stochasticity. Elimination of initial value stochasticity causes bias unless the model is linear. It may also considerably enlarge bias from other sources. Unknown or unexplained variations from the environment (i.e. from outside the borders of the studied system) enter the model in the form of stochastic parameters. The omission of this environmental stochasticity almost always creates biased state variables. Finally, even when a deterministic model produces unbiased state variables, the results will be biased if the output functions are not linear functions of the state variables.
37.	Gyllingberg, Linnéa, et al. (author) Finding analytical approximations for discrete, stochastic, individual-based models of ecology 2023 In: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 365 Journal article (peer-reviewed)abstract Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how ’bottom up’, individual-based models can be approximated by ’top down’ models of dynamics. Here, we study a class of spatially explicit individual-based models with contest competition: where species compete for space in local cells and then disperse to nearby cells. We start by describing simulations of the model, which exhibit large-scale discrete oscillations and characterize these oscillations by measuring spatial correlations. We then develop two new approximate descriptions of the resulting spatial population dynamics. The first is based on local interactions of the individuals and allows us to give a difference equation approximation of the system over small dispersal distances. The second approximates the long-range interactions of the individual-based model. These approximations capture demographic stochasticity from the individual-based model and show that dispersal stabilizes population dynamics. We calculate extinction probability for the individual-based model and show convergence between the local approximation and the non-spatial global approximation of the individual-based model as dispersal distance and population size simultaneously tend to infinity. Our results provide new approximate analytical descriptions of a complex bottom-up model and deepen understanding of spatial population dynamics.
38.	Gyllingberg, Linnéa, et al. (author) The lost art of mathematical modelling 2023 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 362 Journal article (peer-reviewed)abstract We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities - (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data - inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of a pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls - universalism, creating models of models, etc. - that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.
39.	Hagander, Per (author) Simulation and Flow-System Analysis of the Cell Cycle 1980 In: Mathematical Biosciences. - 0025-5564. ; 48, s. 241-265 Journal article (peer-reviewed)
40.	Hug, S., et al. (author) High-dimensional Bayesian parameter estimation: Case study for a model of JAK2/STAT5 signaling 2013 In: Mathematical Biosciences. - : Elsevier. - 0025-5564 .- 1879-3134. ; 246:2, s. 293-304 Journal article (peer-reviewed)abstract In this work we present results of a detailed Bayesian parameter estimation for an analysis of ordinary differential equation models. These depend on many unknown parameters that have to be inferred from experimental data. The statistical inference in a high-dimensional parameter space is however conceptually and computationally challenging. To ensure rigorous assessment of model and prediction uncertainties we take advantage of both a profile posterior approach and Markov chain Monte Carlo sampling. We analyzed a dynamical model of the JAK2/STAT5 signal transduction pathway that contains more than one hundred parameters. Using the profile posterior we found that the corresponding posterior distribution is bimodal. To guarantee efficient mixing in the presence of multimodal posterior distributions we applied a multi-chain sampling approach. The Bayesian parameter estimation enables the assessment of prediction uncertainties and the design of additional experiments that enhance the explanatory power of the model. This study represents a proof of principle that detailed statistical analysis for quantitative dynamical modeling used in systems biology is feasible also in high-dimensional parameter spaces.
41.	Hössjer, Ola, et al. (author) A new general analytical approach for modeling patterns of genetic differentiation and effective size of subdivided populations over time 2014 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 258, s. 113-133 Journal article (peer-reviewed)abstract The main purpose of this paper is to develop a theoretical framework for assessing effective population size and genetic divergence in situations with structured populations that consist of various numbers of more or less interconnected subpopulations. We introduce a general infinite allele model for a diploid, monoecious and subdivided population, with subpopulation sizes varying overtime, including local subpopulation extinction and recolonization, bottlenecks, cyclic census size changes or exponential growth. Exact matrix analytic formulas are derived for recursions of predicted (expected) gene identities and gene diversities, identity by descent and coalescence probabilities, and standardized variances of allele frequency change. This enables us to compute and put into a general framework a number of different types of genetically effective population sizes (N-e) including variance, inbreeding, nucleotide diversity, and eigenvalue effective size. General expressions for predictions (g(ST)) of the coefficient of gene differentiation G(ST) are also derived. We suggest that in order to adequately describe important properties of a subdivided population with respect to allele frequency change and maintenance of genetic variation over time, single values of g(ST) and N-e are not enough. Rather, the temporal dynamic patterns of these properties are important to consider. We introduce several schemes for weighting subpopulations that enable effective size and expected genetic divergence to be calculated and described as functions of time, globally for the whole population and locally for any group of subpopulations. The traditional concept of effective size is generalized to situations where genetic drift is confounded by external sources, such as immigration and mutation. Finally, we introduce a general methodology for state space reduction, which greatly decreases the computational complexity of the matrix analytic formulas.
42.	Hössjer, Ola, et al. (author) Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation 2016 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 272, s. 100-112 Journal article (peer-reviewed)abstract The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a. Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates.
43.	Isheden, G, et al. (author) A unifying framework for continuous tumour growth modelling of breast cancer screening data 2022 In: Mathematical biosciences. - : Elsevier BV. - 1879-3134 .- 0025-5564. ; 353, s. 108897- Journal article (peer-reviewed)
44.	Janzén, David, et al. (author) Extending existing structural identifiability analysis methods to mixed-effects models 2018 In: Mathematical Biosciences. - : Elsevier BV. - 1879-3134 .- 0025-5564. ; 295, s. 1-10 Journal article (peer-reviewed)abstract The concept of structural identifiability for state-space models is expanded to cover mixed-effects state-space models. Two methods applicable for the analytical study of the structural identifiability of mixed-effects models are presented. The two methods are based on previously established techniques for non-mixed-effects models; namely the Taylor series expansion and the input-output form approach. By generating an exhaustive summary, and by assuming an infinite number of subjects, functions of random variables can be derived which in turn determine the distribution of the system’s observation function(s). By considering the uniqueness of the analytical statistical moments of the derived functions of the random variables, the structural identifiability of the corresponding mixed-effects model can be determined. The two methods are applied to a set of examples of mixed-effects models to illustrate how they work in practice.
45.	Järemo, Johannes (author) Evaluating spread of invaders from gravity scores - A way of using gravity models in ecology. 2009 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564. ; 222, s. 53-58 Journal article (peer-reviewed)abstract This study is a theoretical excursion into gravity models and their usability in evaluating importance of spatial structure and population development for the spread of colonizing organisms. A so called "gravity score" for sites is deduced, and such a score could be used for predicting risk of colonization once one site in an area has been subject to introduction of a new species. The analysis further suggests that factors deciding spread between sites differs from those that govern expected population sizes. Gravity models of the kind presented here includes both population dynamics and spatial structure and could be a complement to other models describing organism spread.
46.	Kannan, V, et al. (author) A minimal unified model of disease trajectories captures hallmarks of multiple sclerosis 2017 In: Mathematical biosciences. - : Elsevier BV. - 1879-3134 .- 0025-5564. ; 289, s. 1-8 Journal article (peer-reviewed)
47.	Kowalewski, Jacob M, et al. (author) Modeling the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations 2006 In: Mathematical biosciences. - : Elsevier BV. - 0025-5564. ; 204:2, s. 232-249 Journal article (peer-reviewed)abstract Calcium (Ca2+) oscillations play fundamental roles in various cell signaling processes and have been the subject of numerous modeling studies. Here we have implemented a general mathematical model to simulate the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations. In addition, we have compared two different models of the inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) and their influences on intracellular Ca2+ oscillations. Store-operated Ca2+ entry following Ca2+ depletion of endoplasmic reticulum (ER) is an important component of Ca2+ signaling. We have developed a phenomenological model of store-operated Ca2+ entry via store-operated Ca2+ (SOC) channels, which are activated upon ER Ca2+ depletion. The depletion evokes a bi-phasic Ca2+ signal, which is also produced in our mathematical model. The IP3R is an important regulator of intracellular Ca2+ signals. This IP3 sensitive Ca2+ channel is also regulated by Ca2+. We apply two IP3R models, the Mak-McBride-Foskett model and the De Young and Keizer model, with significantly different channel characteristics. Our results show that the two separate IP3R models evoke intracellular Ca2+ oscillations with different frequencies and amplitudes. Store-operated Ca2+ entry affects the oscillatory behavior of these intracellular Ca2+ oscillations. The IP3 threshold is altered when store-operated Ca2+ entry is excluded from the model. Frequencies and amplitudes of intracellular Ca2+ oscillations are also altered without store-operated Ca2+ entry. Under certain conditions, when intracellular Ca2+ oscillations are absent, excluding store-operated Ca2+ entry induces an oscillatory response. These findings increase knowledge concerning store-operated Ca2+ entry and its impact on intracellular Ca2+ oscillations.
48.	Kurasov, Pavel, et al. (author) Stochastic hybrid models of gene regulatory networks - A PDE approach 2018 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 305, s. 170-177 Journal article (peer-reviewed)abstract A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models is extremely challenging due to their large discrete state space. We therefore propose a hybrid approximation approach based on a system of partial differential equations, where we assume a continuous-deterministic evolution for the protein counts. We discuss efficient analysis methods for both modeling approaches and compare their performance. We show that the hybrid approach yields accurate results for sufficiently large molecule counts, while reducing the computational effort from one ordinary differential equation for each state to one partial differential equation for each mode of the system. Furthermore, we give an analytical steady-state solution of the hybrid model for the case of a self-regulatory gene.
49.	Larsson, Sara, et al. (author) Estimating the distribution of the G2 phase duration from flow cytometric histograms 2008 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 211:1, s. 1-17 Journal article (peer-reviewed)abstract A mathematical model, based on branching processes, is proposed to interpret BrdUrd DNA FCM-derived data. Our main interest is in determining the distribution of the G(2) phase duration. Two different model classes involving different assumptions on the distribution of the G(2) phase duration are considered. Different assumptions of the G(2) phase duration result in very similar distributions of the S phase duration and the estimated means and standard deviations of the G(2) phase duration are all in the same range.
50.	Larsson, Sara, et al. (author) Estimating the variation in S phase duration from flow cytometric histograms 2008 In: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 213:1, s. 40-49 Journal article (peer-reviewed)abstract A stochastic model for interpreting BrdUrd DNA FCM-derived data is proposed. The model is based on branching processes and describes the progression of the DNA distribution of BrdUrd-labelled cells through the cell cycle. With the main focus on estimating the S phase duration and its variation, the DNA replication rate is modelled by a piecewise linear function, while assuming a gamma distribution for the S phase duration. Estimation of model parameters was carried out using maximum likelihood for data from two different cell lines. The results provided quite a good fit to the data, suggesting that stochastic models may be a valuable tool for analysing this kind of data.

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