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1.
  • Ajazi, Fioralba, et al. (author)
  • Networks of random trees as a model of neuronal connectivity
  • 2019
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 79:5, s. 1639-1663
  • Journal article (peer-reviewed)abstract
    • We provide an analysis of a randomly grown 2-d network which models the morphological growth of dendritic and axonal arbors. From the stochastic geometry of this model we derive a dynamic graph of potential synaptic connections. We estimate standard network parameters such as degree distribution, average shortest path length and clustering coefficient, considering all these parameters as functions of time. Our results show that even a simple model with just a few parameters is capable of representing a wide spectra of architecture, capturing properties of well-known models, such as random graphs or small world networks, depending on the time of the network development. The introduced model allows not only rather straightforward simulations but it is also amenable to a rigorous analysis. This provides a base for further study of formation of synaptic connections on such networks and their dynamics due to plasticity.
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2.
  • Andersson, Patrik, et al. (author)
  • A stochastic SIS epidemic with demography : initial stages and time to extinction
  • 2011
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 62:3, s. 333-348
  • Journal article (peer-reviewed)abstract
    • We study an open population stochastic epidemic model from the time of introduction of the disease, through a possible outbreak and to extinction. The model describes an SIS (susceptible–infective–susceptible) epidemic where all individuals, including infectious ones, reproduce at a given rate. An approximate expression for the outbreak probability is derived using a coupling argument. Further, we analyse the behaviour of the model close to quasi-stationarity, and the time to disease extinction, with the aid of a diffusion approximation. In this situation the number of susceptibles and infectives behaves as an Ornstein–Uhlenbeck process, centred around the stationary point, for an exponentially distributed time before going extinct.
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3.
  • Baker, J., et al. (author)
  • On the establishment of a mutant
  • 2020
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 80, s. 1733-1757
  • Journal article (peer-reviewed)abstract
    • How long does it take for an initially advantageous mutant to establish itself in a resident population, and what does the population composition look like then? We approach these questions in the framework of the so called Bare Bones evolution model (Klebaner et al. in J Biol Dyn 5(2):147-162, 2011. https://doi.org/ 10.1080/ 17513758.2010.506041) that provides a simplified approach to the adaptive population dynamics of binary splitting cells. As the mutant population grows, cell division becomes less probable, and it may in fact turn less likely than that of residents. Our analysis rests on the assumption of the process starting from resident populations, with sizes proportional to a large carrying capacity K. Actually, we assume carrying capacities to be a(1)K and a(2)K for the resident and the mutant populations, respectively, and study the dynamics for K -> infinity. We find conditions for the mutant to be successful in establishing itself alongside the resident. The time it takes turns out to be proportional to log K. We introduce the time of establishment through the asymptotic behaviour of the stochastic nonlinear dynamics describing the evolution, and show that it is indeed 1/rho log K, where rho is twice the probability of successful division of the mutant at its appearance. Looking at the composition of the population, at times 1/rho log K + n, n is an element of Z(+), we find that the densities (i.e. sizes relative to carrying capacities) of both populations follow closely the corresponding two dimensional nonlinear deterministic dynamics that starts at a random point. We characterise this random initial condition in terms of the scaling limit of the corresponding dynamics, and the limit of the properly scaled initial binary splitting process of the mutant. The deterministic approximation with random initial condition is in fact valid asymptotically at all times 1/rho log K + n with n is an element of Z.
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4.
  • Ball, Frank, et al. (author)
  • A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon
  • 2013
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 66:4-5, s. 979-1019
  • Journal article (peer-reviewed)abstract
    • A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form a network. Clustering is obtained by forming small completely connected subgroups, and positive (negative) degree correlation is obtained by connecting a fraction of the stubs with stubs of similar (dissimilar) degree. An SIR (Susceptible Infective Recovered) epidemic model is defined on this network. Asymptotic properties of both the network and the epidemic, as the population size tends to infinity, are derived: the degree distribution, degree correlation and clustering coefficient, as well as a reproduction number , the probability of a major outbreak and the relative size of such an outbreak. The theory is illustrated by Monte Carlo simulations and numerical examples. The main findings are that (1) clustering tends to decrease the spread of disease, (2) the effect of degree correlation is appreciably greater when the disease is close to threshold than when it is well above threshold and (3) disease spread broadly increases with degree correlation when is just above its threshold value of one and decreases with when is well above one.
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5.
  • Ball, Frank, et al. (author)
  • A stochastic SIR network epidemic model with preventive dropping of edges
  • 2019
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 78:6, s. 1875-1951
  • Journal article (peer-reviewed)abstract
    • A Markovian Susceptible Infectious Recovered (SIR) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size N, assuming that the degrees of individuals are bounded. A central limit theorem is conjectured for the final size of the epidemic. The results are obtained for both the Molloy-Reed (in which the degrees of individuals are deterministic) and Newman-Strogatz-Watts (in which the degrees of individuals are independent and identically distributed) versions of the configuration model. The two versions yield the same limiting deterministic model but the asymptotic variances in the central limit theorems are greater in the Newman-Strogatz-Watts version. The basic reproduction number R0 and the process of susceptible individuals in the limiting deterministic model, for the model with dropping of edges, are the same as for a corresponding SIR model without dropping of edges but an increased recovery rate, though, when R0>1, the probability of a major outbreak is greater in the model with dropping of edges. The results are specialised to the model without dropping of edges to yield conjectured central limit theorems for the final size of Markovian SIR epidemics on configuration-model networks, and for the size of the giant components of those networks. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations are good, even for moderate N.
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6.
  • Ball, Frank, et al. (author)
  • Household epidemic models with varying infection response
  • 2011
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 63:2, s. 309-337
  • Journal article (peer-reviewed)abstract
    • This paper is concerned with SIR (susceptible -> infected -> removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to partial immunity, and in the second, the infection status of an individual depends on the infection status of its infector and on whether the individual was infected by a within- or between-household contact. The first scenario may be modelled using a multitype household epidemic model, and the second scenario by a model we denote by the infector-dependent-severity household epidemic model. Large population results of the two models are derived, with the focus being on the distribution of the total numbers of mild and severe cases in a typical household, of any given size, in the event that the epidemic becomes established. The aim of the paper is to investigate whether it is possible to determine which of the two underlying explanations is causing the varying response when given final size household outbreak data containing mild and severe cases. We conduct numerical studies which show that, given data on sufficiently many households, it is generally possible to discriminate between the two models by comparing the Kullback-Leibler divergence for the two fitted models to these data.
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7.
  • Borgqvist, Johannes, 1990, et al. (author)
  • Turing pattern formation on the sphere is robust to the removal of a hole
  • 2024
  • In: JOURNAL OF MATHEMATICAL BIOLOGY. - : Springer Science+Business Media B.V.. - 0303-6812 .- 1432-1416. ; 88:2
  • Journal article (peer-reviewed)abstract
    • The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit diffusion-driven pattern formation, thus providing a mechanism for bud formation. However, it is not known how the accumulation of bud scars on the cell membrane affect the ability of the Schnakenberg system to form patterns. We have approached this problem by modelling a bud scar on the cell membrane with a hole on the sphere. We have studied how the spectrum of the Laplace-Beltrami operator, which determines the resulting pattern, is affected by the size of the hole, and by numerically solving the Schnakenberg system on a sphere with a hole using the finite element method. Both theoretical predictions and numerical solutions show that pattern formation is robust to the introduction of a bud scar of considerable size, which lends credence to the hypothesis that bud formation is driven by diffusion-driven instability.
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8.
  • Britton, Tom, et al. (author)
  • The time to extinction for an SIS-household-epidemic model
  • 2010
  • In: Journal of Mathematical Biology. - Berlin : Springer. - 0303-6812 .- 1432-1416. ; 61:6, s. 763-769
  • Journal article (peer-reviewed)abstract
    • We analyse a Markovian SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission.
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9.
  • Brännström, Åke, 1975-, et al. (author)
  • Consequences of fluctuating group size for the evolution of cooperation
  • 2011
  • In: Journal of Mathematical Biology. - : SpringerLink. - 0303-6812 .- 1432-1416. ; 63:2, s. 263-281
  • Journal article (peer-reviewed)abstract
    • Studies of cooperation have traditionally focused on discrete games such as the well-known prisoner’s dilemma, in which players choose between two pure strategies: cooperation and defection. Increasingly, however, cooperation is being studied in continuous games that feature a continuum of strategies determining the level of cooperative investment. For the continuous snowdrift game, it has been shown that a gradually evolving monomorphic population may undergo evolutionary branching, resulting in the emergence of a defector strategy that coexists with a cooperator strategy. This phenomenon has been dubbed the ‘tragedy of the commune’. Here we study the effects of fluctuating group size on the tragedy of the commune and derive analytical conditions for evolutionary branching. Our results show that the effects of fluctuating group size on evolutionary dynamics critically depend on the structure of payoff functions. For games with additively separable benefits and costs, fluctuations in group size make evolutionary branching less likely, and sufficiently large fluctuations in group size can always turn an evolutionary branching point into a locally evolutionarily stable strategy. For games with multiplicatively separable benefits and costs, fluctuations in group size can either prevent or induce the tragedy of the commune. For games with general interactions between benefits and costs, we derive a general classification scheme based on second derivatives of the payoff function, to elucidate when fluctuations in group size help or hinder cooperation.
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10.
  • Brännström, Åke, 1975-, et al. (author)
  • Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces
  • 2011
  • In: Journal of Mathematical Biology. - : Springerlink. - 0303-6812 .- 1432-1416. ; 63:3, s. 575-592
  • Journal article (peer-reviewed)abstract
    • Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.
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11.
  • Chigansky, P., et al. (author)
  • What can be observed in real time PCR and when does it show?
  • 2018
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 76:3, s. 679-695
  • Journal article (peer-reviewed)abstract
    • Real time, or quantitative, PCR typically starts from a very low concentration of initial DNA strands. During iterations the numbers increase, first essentially by doubling, later predominantly in a linear way. Observation of the number of DNA molecules in the experiment becomes possible only when it is substantially larger than initial numbers, and then possibly affected by the randomness in individual replication. Can the initial copy number still be determined? This is a classical problem and, indeed, a concrete special case of the general problem of determining the number of ancestors, mutants or invaders, of a population observed only later. We approach it through a generalised version of the branching process model introduced in Jagers and Klebaner (J Theor Biol 224(3):299-304, 2003. doi: 10.1016/S0022-5193(03) 001668), and based on Michaelis-Menten type enzyme kinetical considerations from Schnell and Mendoza (J Theor Biol 184(4):433-440, 1997). A crucial role is played by the Michaelis-Menten constant being large, as compared to initial copy numbers. In a strange way, determination of the initial number turns out to be completely possible if the initial rate v is one, i.e all DNA strands replicate, but only partly so when v < 1, and thus the initial rate or probability of succesful replication is lower than one. Then, the starting molecule number becomes hidden behind a "veil of uncertainty". This is a special case, of a hitherto unobserved general phenomenon in population growth processes, which will be adressed elsewhere.
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12.
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13.
  • De Roos, Andre M., et al. (author)
  • Ontogenetic symmetry and asymmetry in energetics
  • 2013
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 66:4-5, s. 889-914
  • Journal article (peer-reviewed)abstract
    • Body size ( biomass) is the dominant determinant of population dynamical processes such as giving birth or dying in almost all species, with often drastically different behaviour occurring in different parts of the growth trajectory, while the latter is largely determined by food availability at the different life stages. This leads to the question under what conditions unstructured population models, formulated in terms of total population biomass, still do a fair job. To contribute to answering this question we first analyze the conditions under which a size-structured model collapses to a dynamically equivalent unstructured one in terms of total biomass. The only biologically meaningful case where this occurs is when body size does not affect any of the population dynamic processes, this is the case if and only if the mass-specific ingestion rate, the mass-specific biomass production and the mortality rate of the individuals are independent of size, a condition to which we refer as "ontogenetic symmetry". Intriguingly, under ontogenetic symmetry the equilibrium biomass-body size spectrum is proportional to 1/size, a form that has been conjectured for marine size spectra and subsequently has been used as prior assumption in theoretical papers dealing with the latter. As a next step we consider an archetypical class of models in which reproduction takes over from growth upon reaching an adult body size, in order to determine how quickly discrepancies from ontogenetic symmetry lead to relevant novel population dynamical phenomena. The phenomena considered are biomass overcompensation, when additional imposed mortality leads, rather unexpectedly, to an increase in the equilibrium biomass of either the juveniles or the adults (a phenomenon with potentially big consequences for predators of the species), and the occurrence of two types of size-structure driven oscillations, juvenile-driven cycles with separated extended cohorts, and adult-driven cycles in which periodically a front of relatively steeply decreasing frequencies moves up the size distribution. A small discrepancy from symmetry can already lead to biomass overcompensation; size-structure driven cycles only occur for somewhat larger discrepancies.
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14.
  • Doublet, Violette, et al. (author)
  • Seed predation-induced Allee effects, seed dispersal and masting jointly drive the diversity of seed sources during population expansion
  • 2023
  • In: Journal of Mathematical Biology. - : Springer Nature. - 0303-6812 .- 1432-1416. ; 87:3
  • Journal article (peer-reviewed)abstract
    • The environmental factors affecting plant reproduction and effective dispersal, in particular biotic interactions, have a strong influence on plant expansion dynamics, but their demographic and genetic consequences remain an understudied body of theory. Here, we use a mathematical model in a one-dimensional space and on a single reproductive period to describe the joint effects of predispersal seed insect predators foraging strategy and plant reproduction strategy (masting) on the spatio-temporal dynamics of seed sources diversity in the colonisation front of expanding plant populations. We show that certain foraging strategies can result in a higher seed predation rate at the colonisation front compared to the core of the population, leading to an Allee effect. This effect promotes the contribution of seed sources from the core to the colonisation front, with long-distance dispersal further increasing this contribution. As a consequence, our study reveals a novel impact of the predispersal seed predation-induced Allee effect, which mitigates the erosion of diversity in expanding populations. We use rearrangement inequalities to show that masting has a buffering role: it mitigates this seed predation-induced Allee effect. This study shows that predispersal seed predation, plant reproductive strategies and seed dispersal patterns can be intermingled drivers of the diversity of seed sources in expanding plant populations, and opens new perspectives concerning the analysis of more complex models such as integro-difference or reaction-diffusion equations.
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15.
  • Drosinou, Ourania, et al. (author)
  • A stochastic parabolic model of MEMS driven by fractional Brownian motion
  • 2023
  • In: Journal of Mathematical Biology. - : Springer. - 0303-6812 .- 1432-1416. ; 86
  • Journal article (peer-reviewed)abstract
    • In this paper, we study a stochastic parabolic problem that emerges in the modeling and control of an electrically actuated MEMS (micro-electro-mechanical system) device. The dynamics under consideration are driven by an one dimensional fractional Brownian motion with Hurst index [Formula: see text]. We derive conditions under which the resulting SPDE has a global in time solution, and we provide analytic estimates for certain statistics of interest, such as quenching times and the corresponding quenching probabilities. Our results demonstrate the non-trivial impact of the fractional noise on the dynamics of the system. Given the significance of MEMS devices in biomedical applications, such as drug delivery and diagnostics, our results provide valuable insights into the reliability of these devices in the presence of positively correlated noise.
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16.
  • Favero, Martina, et al. (author)
  • A dual process for the coupled Wright-Fisher diffusion
  • In: Journal of Mathematical Biology. - 0303-6812 .- 1432-1416.
  • Journal article (peer-reviewed)abstract
    • The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in the drift, where the pairwise interaction among loci is modelled by an inter-locus selection. In this paper, an ancestral process, which is dual to the coupled Wright-Fisher diffusion, is derived. The dual process corresponds to the block counting process of coupled ancestral selection graphs, one for each locus. Jumps of the dual process arise from coalescence, mutation, single-branching, which occur at one locus at the time, and double-branching, which occur simultaneously at two loci. The coalescence and mutation rates have the typical structure of the transition rates of the Kingman coalescent process. The single-branching rate not only contains the one-locus selection parameters in a form that generalises the rates of an ancestral selection graph, but it also contains the two-locus selection parameters to include the effect of the pairwise interaction on the single loci. The double-branching rate reflects the particular structure of pairwise selection interactions of the coupled Wright-Fisher diffusion. Moreover, in the special case of two loci, two alleles, with selection and parent independent mutation, the stationary density for the coupled Wright-Fisher diffusion and the transition rates of the dual process are obtained in an explicit form.
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17.
  • Favero, Martina, et al. (author)
  • A dual process for the coupled Wright-Fisher diffusion
  • 2021
  • In: Journal of Mathematical Biology. - : Springer Nature. - 0303-6812 .- 1432-1416. ; 82:1-2
  • Journal article (peer-reviewed)abstract
    • The coupled Wright-Fisher diffusion is a multi-dimensional Wright-Fisher diffusion for multi-locus and multi-allelic genetic frequencies, expressed as the strong solution to a system of stochastic differential equations that are coupled in the drift, where the pairwise interaction among loci is modelled by an inter-locus selection. In this paper, an ancestral process, which is dual to the coupled Wright-Fisher diffusion, is derived. The dual process corresponds to the block counting process of coupled ancestral selection graphs, one for each locus. Jumps of the dual process arise from coalescence, mutation, single-branching, which occur at one locus at the time, and double-branching, which occur simultaneously at two loci. The coalescence and mutation rates have the typical structure of the transition rates of the Kingman coalescent process. The single-branching rate not only contains the one-locus selection parameters in a form that generalises the rates of an ancestral selection graph, but it also contains the two-locus selection parameters to include the effect of the pairwise interaction on the single loci. The double-branching rate reflects the particular structure of pairwise selection interactions of the coupled Wright-Fisher diffusion. Moreover, in the special case of two loci, two alleles, with selection and parent independent mutation, the stationary density for the coupled Wright-Fisher diffusion and the transition rates of the dual process are obtained in an explicit form.
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18.
  • Fransson, Carolina, et al. (author)
  • SIR epidemics and vaccination on random graphs with clustering
  • 2019
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 78:7, s. 2369-2398
  • Journal article (peer-reviewed)abstract
    • In this paper we consider Susceptible Infectious Recovered (SIR) epidemics on random graphs with clustering. To incorporate group structure of the underlying social network, we use a generalized version of the configuration model in which each node is a member of a specified number of triangles. SIR epidemics on this type of graph have earlier been investigated under the assumption of homogeneous infectivity and also under the assumption of Poisson transmission and recovery rates. We extend known results from literature by relaxing the assumption of homogeneous infectivity both in individual infectivity and between different kinds of neighbours. An important special case of the epidemic model analysed in this paper is epidemics in continuous time with arbitrary infectious period distribution. We use branching process approximations of the spread of the disease to provide expressions for the basic reproduction number R0, the probability of a major outbreak and the expected final size. In addition, the impact of random vaccination with a perfect vaccine on the final outcome of the epidemic is investigated. We find that, for this particular model, R0 equals the perfect vaccine-associated reproduction number. Generalizations to groups larger than three are discussed briefly.
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19.
  • Geli, Patricia (author)
  • Modeling the Mechanism of Postantibiotic Effect and Determining Implications for Dosing Regimens
  • 2009
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 59:5, s. 1416-1432
  • Journal article (peer-reviewed)abstract
    • A stochastic model is proposed to explain one possible underlying mechanism of the postantibiotic effect (PAE). This phenomenon, of continued inhibition of bacterial growth after removal of the antibiotic drug, is of high relevance in the context of optimizing dosing regimens. One clinical implication of long PAE lies in the possibility of increasing intervals between drug administrations. The model describes the dynamics of synthesis, saturation and removal of penicillin binding proteins (PBPs). High fractions of saturated PBPs are in the model associated with a lower growth capacity of bacteria. An analytical solution for the bivariate probability of saturated and unsaturated PBPs is used as a basis to explore optimal antibiotic dosing regimens. Our finding that longer PAEs do not necessarily promote for increased intervals between doses, might help for our understanding of data provided from earlier PAE studies and for the determination of the clinical relevance of PAE in future studies.
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20.
  • Geritz, Stefan A. H., et al. (author)
  • Mutual invadability near evolutionarily singular strategies for multivariate traits, with special reference to the strongly convergence stable case
  • 2016
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 72:4, s. 1081-1099
  • Journal article (peer-reviewed)abstract
    • Over the last two decades evolutionary branching has emerged as a possible mathematical paradigm for explaining the origination of phenotypic diversity. Although branching is well understood for one-dimensional trait spaces, a similarly detailed understanding for higher dimensional trait spaces is sadly lacking. This note aims at getting a research program of the ground leading to such an understanding. In particular, we show that, as long as the evolutionary trajectory stays within the reign of the local quadratic approximation of the fitness function, any initial small scale polymorphism around an attracting invadable evolutionarily singular strategy (ess) will evolve towards a dimorphism. That is, provided the trajectory does not pass the boundary of the domain of dimorphic coexistence and falls back to monomorphism (after which it moves again towards the singular strategy and from there on to a small scale polymorphism, etc.). To reach these results we analyze in some detail the behavior of the solutions of the coupled Lande-equations purportedly satisfied by the phenotypic clusters of a quasi-n-morphism, and give a precise characterisation of the local geometry of the set in trait space squared harbouring protected dimorphisms. Intriguingly, in higher dimensional trait spaces an attracting invadable ess needs not connect to . However, for the practically important subset of strongly attracting ess-es (i.e., ess-es that robustly locally attract the monomorphic evolutionary dynamics for all possible non-degenerate mutational or genetic covariance matrices) invadability implies that the ess does connect to , just as in 1-dimensional trait spaces. Another matter is that in principle there exists the possibility that the dimorphic evolutionary trajectory reverts to monomorphism still within the reign of the local quadratic approximation for the invasion fitnesses. Such locally unsustainable branching cannot occur in 1- and 2-dimensional trait spaces, but can do so in higher dimensional ones. For the latter trait spaces we give a condition excluding locally unsustainable branching which is far stricter than the one of strong convergence, yet holds good for a relevant collection of published models. It remains an open problem whether locally unsustainable branching can occur around general strongly attracting invadable ess-es.
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21.
  • Groh, A., et al. (author)
  • Numerical rate function determination in partial differential equations modeling cell population dynamics
  • 2016
  • In: Journal of Mathematical Biology. - : Springer. - 0303-6812 .- 1432-1416. ; , s. 1-33
  • Journal article (peer-reviewed)abstract
    • This paper introduces a method to solve the inverse problem of determining an unknown rate function in a partial differential equation (PDE) based on discrete measurements of the modeled quantity. The focus is put on a size-structured population balance equation (PBE) predicting the evolution of the number distribution of a single cell population as a function of the size variable. Since the inverse problem at hand is ill-posed, an adequate regularization scheme is required to avoid amplification of measurement errors in the solution method. The technique developed in this work to determine a rate function in a PBE is based on the approximate inverse method, a pointwise regularization scheme, which employs two key ideas. Firstly, the mollification in the directions of time and size variables are separated. Secondly, instable numerical data derivatives are circumvented by shifting the differentiation to an analytically given function. To examine the performance of the introduced scheme, adapted test scenarios have been designed with different levels of data disturbance simulating the model and measurement errors in practice. The success of the method is substantiated by visualizing the results of these numerical experiments.
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22.
  • Gyllenberg, Mats, et al. (author)
  • A nonlinear structured population model of tumor growth with quiescence
  • 1990
  • In: Journal of Mathematical Biology. - 0303-6812 .- 1432-1416. ; 28:6, s. 671-694
  • Journal article (peer-reviewed)abstract
    • A nonlinear structured cell population model of tumor growth is considered. The model distinguishes between two types of cells within the tumor: proliferating and quiescent. Within each class the behavior of individual cells depends on cell size, whereas the probabilities of becoming quiescent and returning to the proliferative cycle are in addition controlled by total tumor size. The asymptotic behavior of solutions of the full nonlinear model, as well as some linear special cases, is investigated using spectral theory of a positive semigroup of operators
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23.
  • Gyllenberg, Mats, et al. (author)
  • Population models with environmental stochasticity
  • 1994
  • In: Journal of Mathematical Biology. - 0303-6812 .- 1432-1416. ; 32:2, s. 93-108
  • Journal article (peer-reviewed)abstract
    • Two discrete population models, one with stochasticity in the carrying capacity and one with stochasticity in the per capita growth rate, are investigated. Conditions under which the corresponding Markov processes are null recurrent and positively recurrent are derived
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24.
  • Gyllenberg, Mats, et al. (author)
  • Quasi-stationary distributions of a stochastic metapopulation model
  • 1994
  • In: Journal of Mathematical Biology. - 0303-6812 .- 1432-1416. ; 33:1, s. 35-70
  • Journal article (peer-reviewed)abstract
    • A stochastic metapopulation model which explicitly considers first order interactions between local populations is constructed. The model takes the spatial arrangement of patches into account and keeps track of which patches are occupied and which are empty. The time-evolution of the meta-population is governed by a Markov chain with finite state space. We give a detailed description of the long term behaviour of the Markov chain. Many interesting biological issues can be addressed using the model. As an especially important example we discuss the so-called core and satellite species hypothesis in the light of the model.
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25.
  • Hamis, S., et al. (author)
  • Spatial cumulant models enable spatially informed treatment strategies and analysis of local interactions in cancer systems
  • 2023
  • In: Journal of Mathematical Biology. - : Springer Nature. - 0303-6812 .- 1432-1416. ; 86:5
  • Journal article (peer-reviewed)abstract
    • Theoretical and applied cancer studies that use individual-based models (IBMs) have been limited by the lack of a mathematical formulation that enables rigorous analysis of these models. However, spatial cumulant models (SCMs), which have arisen from theoretical ecology, describe population dynamics generated by a specific family of IBMs, namely spatio-temporal point processes (STPPs). SCMs are spatially resolved population models formulated by a system of differential equations that approximate the dynamics of two STPP-generated summary statistics: first-order spatial cumulants (densities), and second-order spatial cumulants (spatial covariances). We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells. To formulate model equations, we use computational tools that enable the generation of STPPs, SCMs and mean-field population models (MFPMs) from user-defined model descriptions (Cornell et al. Nat Commun 10:4716, 2019). To calculate and compare STPP, SCM and MFPM-generated summary statistics, we develop an application-agnostic computational pipeline. Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when MFPMs fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics. We, therefore, argue that SCMs can be used to increase IBMs' applicability in cancer research.
  •  
26.
  • Hamza, K., et al. (author)
  • On the establishment, persistence, and inevitable extinction of populations
  • 2016
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 72:4, s. 797-820
  • Journal article (peer-reviewed)abstract
    • Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations are assumed to start small, by mutation or immigration, reproduce supercritically while smaller than the habitat carrying capacity but subcritically above it. Such populations establish themselves with a probability wellknown from branching process theory. Once established, they grow up to a band around the carrying capacity in a time that is logarithmic in the latter, assumed large. There they prevail during a time period whose duration is exponential in the carrying capacity. Even populations whose life style is sustainble in the sense that the habitat carrying capacity is not eroded but remains the same, ultimately enter an extinction phase, which again lasts for a time logarithmic in the carrying capacity. However, if the habitat can carry a population which is large, say millions of individuals, and it manages to avoid early extinction, time in generations to extinction will be exorbitantly long, and during it, population composition over ages, types, lineage etc. will have time to stabilise. This paper aims at an exhaustive description of the life cycle of such populations, from inception to extinction, extending and overviewing earlier results. We shall also say some words on persistence times of populations with smaller carrying capacities and short life cycles, where the population may indeed be in danger in spite of not eroding its environment.
  •  
27.
  • Hössjer, Ola (author)
  • On the eigenvalue effective size of structured populations
  • 2015
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 71:3, s. 595-646
  • Journal article (peer-reviewed)abstract
    • A general theory is developed for the eigenvalue effective size () of structured populations in which a gene with two alleles segregates in discrete time. Generalizing results of Ewens (Theor Popul Biol 21:373-378, 1982), we characterize in terms of the largest non-unit eigenvalue of the transition matrix of a Markov chain of allele frequencies. We use Perron-Frobenius Theorem to prove that the same eigenvalue appears in a linear recursion of predicted gene diversities between all pairs of subpopulations. Coalescence theory is employed in order to characterize this recursion, so that explicit novel expressions for can be derived. We then study asymptotically, when either the inverse size and/or the overall migration rate between subpopulations tend to zero. It is demonstrated that several previously known results can be deduced as special cases. In particular when the coalescence effective size exists, it is an asymptotic version of in the limit of large populations.
  •  
28.
  • Hössjer, Ola, et al. (author)
  • Quasi equilibrium, variance effective size and fixation index for populations with substructure
  • 2014
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 69:5, s. 1057-1128
  • Journal article (peer-reviewed)abstract
    • In this paper, we develop a method for computing the variance effective size , the fixation index and the coefficient of gene differentiation of a structured population under equilibrium conditions. The subpopulation sizes are constant in time, with migration and reproduction schemes that can be chosen with great flexibility. Our quasi equilibrium approach is conditional on non-fixation of alleles. This is of relevance when migration rates are of a larger order of magnitude than the mutation rates, so that new mutations can be ignored before equilibrium balance between genetic drift and migration is obtained. The vector valued time series of subpopulation allele frequencies is divided into two parts; one corresponding to genetic drift of the whole population and one corresponding to differences in allele frequencies among subpopulations. We give conditions under which the first two moments of the latter, after a simple standardization, are well approximated by quantities that can be explicitly calculated. This enables us to compute approximations of the quasi equilibrium values of , and . Our findings are illustrated for several reproduction and migration scenarios, including the island model, stepping stone models and a model where one subpopulation acts as a demographic reservoir. We also make detailed comparisons with a backward approach based on coalescence probabilities.
  •  
29.
  •  
30.
  • Jagers, Peter, 1941, et al. (author)
  • Amendment to: populations in environments with a soft carrying capacity are eventually extinct
  • 2021
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 1432-1416 .- 0303-6812. ; 83:1
  • Journal article (peer-reviewed)abstract
    • This sharpens the result in the paperJagers and Zuyev (J Math Biol 81:845-851, 2020): consider a population changing at discrete (but arbitrary and possibly random) time points, the conditional expected change, given the complete past population history being negative, whenever population size exceeds a carrying capacity. Further assume that there is an epsilon > 0 such that the conditional probability of a population decrease at the next step, given the past, always exceeds epsilon if the population is not extinct but smaller than the carrying capacity. Then the population must die out.
  •  
31.
  • Jagers, Peter, 1941, et al. (author)
  • Amendment to: populations in environments with a soft carrying capacity are eventually extinct
  • 2021
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 83:1
  • Journal article (peer-reviewed)abstract
    • This sharpens the result in the paperJagers and Zuyev (J Math Biol 81:845-851, 2020): consider a population changing at discrete (but arbitrary and possibly random) time points, the conditional expected change, given the complete past population history being negative, whenever population size exceeds a carrying capacity. Further assume that there is an epsilon > 0 such that the conditional probability of a population decrease at the next step, given the past, always exceeds epsilon if the population is not extinct but smaller than the carrying capacity. Then the population must die out.
  •  
32.
  • Jagers, Peter, 1941, et al. (author)
  • Populations in environments with a soft carrying capacity are eventually extinct
  • 2020
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 81:3, s. 845-851
  • Journal article (peer-reviewed)abstract
    • Consider a population whose size changes stepwise by its members reproducing or dying (disappearing), but is otherwise quite general. Denote the initial (non-random) size by Z(0) and the size of the nth change by C-n, n = 1, 2, .... Population sizes hence develop successively as Z(1) = Z(0) + C-1, Z(2) = Z(1)+ C-2 and so on, indefinitely or until there are no further size changes, due to extinction. Extinction is thus assumed final, so that Z(n) = 0 implies that Z(n+1) = 0, without there being any other finite absorbing class of population sizes. We make no assumptions about the time durations between the successive changes. In the real world, or more specific models, those may be of varying length, depending upon individual life span distributions and their interdependencies, the age-distribution at hand and intervening circumstances. We could consider toy models of Galton-Watson type generation counting or of the birth-and-death type, with one individual acting per change, until extinction, or the most general multitype CMJ branching processes with, say, population size dependence of reproduction. Changes may have quite varying distributions. The basic assumption is that there is a carrying capacity, i.e. a non-negative number K such that the conditional expectation of the change, given the complete past history, is non-positive whenever the population exceeds the carrying capacity. Further, to avoid unnecessary technicalities, we assume that the change C-n equals -1 (one individual dying) with a conditional (given the past) probability uniformly bounded away from 0. It is a simple and not very restrictive way to avoid parity phenomena, it is related to irreducibility in Markov settings. The straightforward, but in contents and implications far-reaching, consequence is that all such populations must die out. Mathematically, it follows by a supermartingale convergence property and positive probability of reaching the absorbing extinction state.
  •  
33.
  • Janson, Svante, 1955-, et al. (author)
  • Near-critical SIR epidemic on a random graph with given degrees
  • 2017
  • In: Journal of Mathematical Biology. - : SPRINGER HEIDELBERG. - 0303-6812 .- 1432-1416. ; 74:4, s. 843-886
  • Journal article (peer-reviewed)abstract
    • Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, such phenomena involve the process of infections and recoveries passing through a critical threshold where the basic reproductive ratio is 1. In this paper, we study near-critical behaviour in the context of a susceptible-infective-recovered epidemic on a random (multi)graph on n vertices with a given degree sequence. We concentrate on the regime just above the threshold for the emergence of a large epidemic, where the basic reproductive ratio is , with tending to infinity slowly as the population size, n, tends to infinity. We determine the probability that a large epidemic occurs, and the size of a large epidemic. Our results require basic regularity conditions on the degree sequences, and the assumption that the third moment of the degree of a random susceptible vertex stays uniformly bounded as . As a corollary, we determine the probability and size of a large near-critical epidemic on a standard binomial random graph in the 'sparse' regime, where the average degree is constant. As a further consequence of our method, we obtain an improved result on the size of the giant component in a random graph with given degrees just above the critical window, proving a conjecture by Janson and Luczak.
  •  
34.
  • Jones, Graham (author)
  • Algorithmic improvements to species delimitation and phylogeny estimation under the multispecies coalescent
  • 2017
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 74:1, s. 447-467
  • Journal article (peer-reviewed)abstract
    • The focus of this article is a Bayesian method for inferring both species delimitations and species trees under the multispecies coalescent model using molecular sequences from multiple loci. The species delimitation requires no a priori assignment of individuals to species, and no guide tree. The method is implemented in a package called STACEY for BEAST2, and is a extension of the author's DISSECT package. Here we demonstrate considerable efficiency improvements by using three new operators for sampling from the posterior using the Markov chain Monte Carlo algorithm, and by using a model for the population size parameters along the branches of the species tree which allows these parameters to be integrated out. The correctness of the moves is demonstrated by tests of the implementation. The practice of using a pipeline approach to species delimitation under the multispecies coalescent, has been shown to have major problems on simulated data (Olave et al. in Syst Biol 63:263-271. doi:10.1093/sysbio/syt106, 2014). The same simulated data set is used to demonstrate the accuracy and improved convergence of the present method. We also compare performance with *BEAST for a fixed delimitation analysis on a large data set, and again show improved convergence.
  •  
35.
  • Kaj, Ingemar, 1957-, et al. (author)
  • Analysis of diversity-dependent species evolution using concepts in population genetics
  • 2021
  • In: Journal of Mathematical Biology. - : Springer Nature. - 0303-6812 .- 1432-1416. ; 82:4
  • Journal article (peer-reviewed)abstract
    • In this work, we consider a two-type species model with trait-dependent speciation, extinction and transition rates under an evolutionary time scale. The scaling approach and the diffusion approximation techniques which are widely used in mathematical population genetics provide modeling tools and conceptual background to assist in the study of species dynamics, and help exploring the analogy between trait-dependent species diversification and the evolution of allele frequencies in the population genetics setting. The analytical framework specified is then applied to models incorporating diversity-dependence, in order to infer effective results from processes in which the net diversification of species depends on the total number of species. In particular, the long term fate of a rare trait may be analyzed under a partly symmetric scenario, using a time-change transform technique.
  •  
36.
  • Kozlov, Vladimir, 1954-, et al. (author)
  • Global stability of an age-structured population model on several temporally variable patches
  • 2021
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 83:6-7
  • Journal article (peer-reviewed)abstract
    • We consider an age-structured density-dependent population model on several temporally variable patches. There are two key assumptions on which we base model setup and analysis. First, intraspecific competition is limited to competition between individuals of the same age (pure intra-cohort competition) and it affects density-dependent mortality. Second, dispersal between patches ensures that each patch can be reached from every other patch, directly or through several intermediary patches, within individual reproductive age. Using strong monotonicity we prove existence and uniqueness of solution and analyze its large-time behavior in cases of constant, periodically variable and irregularly variable environment. In analogy to the next generation operator, we introduce the net reproductive operator and the basic reproduction number R0R0 for time-independent and periodical models and establish the permanence dichotomy: if R0≤1R0≤1, extinction on all patches is imminent, and if R0>1R0>1, permanence on all patches is guaranteed. We show that a solution for the general time-dependent problem can be bounded by above and below by solutions to the associated periodic problems. Using two-side estimates, we establish uniform boundedness and uniform persistence of a solution for the general time-dependent problem and describe its asymptotic behaviour.
  •  
37.
  • Kurasov, Pavel, et al. (author)
  • Analytic solutions for stochastic hybrid models of gene regulatory networks
  • 2021
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 82:1-2
  • Journal article (peer-reviewed)abstract
    • Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely large. Therefore hybrid models, in which protein counts are replaced by average protein concentrations, have become a popular alternative. The evolution of the corresponding probability density functions is given by a coupled system of hyperbolic PDEs. This system has Markovian nature but its hyperbolic structure makes it difficult to apply standard functional analytical methods. We are able to prove convergence towards the stationary solution and determine such equilibrium explicitly by combining abstract methods from the theory of positive operators and elementary ideas from potential analysis.
  •  
38.
  • Lalam, Nadia, 1976 (author)
  • A quantitative approach for polymerase chain reactions based on a hidden Markov model
  • 2009
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 59:4, s. 517-533
  • Journal article (peer-reviewed)abstract
    • Polymerase chain reaction (PCR) is a major DNA amplification technology from molecular biology. The quantitative analysis of PCR aims at determining the initial amount of the DNA molecules from the observation of typically several PCR amplifications curves. The mainstream observation scheme of the DNA amplification during PCR involves fluorescence intensity measurements. Under the classical assumption that the measured fluorescence intensity is proportional to the amount of present DNA molecules, and under the assumption that these measurements are corrupted by an additive Gaussian noise, we analyze a single amplification curve using a hidden Markov model(HMM). The unknown parameters of the HMM may be separated into two parts. On the one hand, the parameters from the amplification process are the initial number of the DNA molecules and the replication efficiency, which is the probability of one molecule to be duplicated. On the other hand, the parameters from the observational scheme are the scale parameter allowing to convert the fluorescence intensity into the number of DNA molecules and the mean and variance characterizing the Gaussian noise. We use the maximum likelihood estimation procedure to infer the unknown parameters of the model from the exponential phase of a single amplification curve, the main parameter of interest for quantitative PCR being the initial amount of the DNA molecules. An illustrative example is provided.
  •  
39.
  • Lashari, Abid Ali, et al. (author)
  • Branching process approach for epidemics in dynamic partnership network
  • 2018
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 76:1-2, s. 265-294
  • Journal article (peer-reviewed)abstract
    • We study the spread of sexually transmitted infections (STIs) and other infectious diseases on a dynamic network by using a branching process approach. The nodes in the network represent the sexually active individuals, while connections represent sexual partnerships. This network is dynamic as partnerships are formed and broken over time and individuals enter and leave the sexually active population due to demography. We assume that individuals enter the sexually active network with a random number of partners, chosen according to a suitable distribution and that the maximal number of partners that an individual can have at a time is finite. We discuss two different branching process approximations for the initial stages of an outbreak of the STI. In the first approximation we ignore some dependencies between infected individuals. We compute the offspring mean of this approximating branching process and discuss its relation to the basic reproduction number R0. The second branching process approximation is asymptotically exact, but only defined if individuals can have at most one partner at a time. For this model we compute the probability of a minor outbreak of the epidemic starting with one or few initial cases. We illustrate complications caused by dependencies in the epidemic model by showing that if individuals have at most one partner at a time, the probabilities of extinction of the two approximating branching processes are different. This implies that ignoring dependencies in the epidemic model leads to a wrong prediction of the probability of a large outbreak. Finally, we analyse the first branching process approximation if the number of partners an individual can have at a given time is unbounded. In this model we show that the branching process approximation is asymptomatically exact as the population size goes to infinity.
  •  
40.
  •  
41.
  • Lindström, Torsten (author)
  • Qualitative analysis of a predator-prey system with limit cycles
  • 1993
  • In: Journal of Mathematical Biology. - 0303-6812 .- 1432-1416. ; 31:6, s. 541-546
  • Journal article (peer-reviewed)abstract
    • Fairly regular multiannual microtine rodent cycles are observed in boreal Fennoscandia. In the southern parts of Fennoscandia these multiannual cycles are not observed. It has been proposed that these cycles may be stabilized by generalist predation in the south. We show that if the half-saturation of the generalist predators is high compared to the number of small rodents the cycles are likely to be stabilized by generalist predation as observed. We give examples showing that if the half-saturation of the generalist predators is low compared to the number of small rodents, then multiple equilibria and multiple limit cycles may occur as the generalist predator density increases
  •  
42.
  • Lindwall, Gustav, 1992, et al. (author)
  • Fast and precise inference on diffusivity in interacting particle systems
  • 2023
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 1432-1416 .- 0303-6812. ; 86:5
  • Journal article (peer-reviewed)abstract
    • Particle systems made up of interacting agents is a popular model used in a vast array of applications, not the least in biology where the agents can represent everything from single cells to animals in a herd. Usually, the particles are assumed to undergo some type of random movements, and a popular way to model this is by using Brownian motion. The magnitude of random motion is often quantified using mean squared displacement, which provides a simple estimate of the diffusion coefficient. However, this method often fails when data is sparse or interactions between agents frequent. In order to address this, we derive a conjugate relationship in the diffusion term for large interacting particle systems undergoing isotropic diffusion, giving us an efficient inference method. The method accurately accounts for emerging effects such as anomalous diffusion stemming from mechanical interactions. We apply our method to an agent-based model with a large number of interacting particles, and the results are contrasted with a naive mean square displacement-based approach. We find a significant improvement in performance when using the higher-order method over the naive approach. This method can be applied to any system where agents undergo Brownian motion and will lead to improved estimates of diffusion coefficients compared to existing methods.
  •  
43.
  • Lötstedt, Per (author)
  • Derivation of continuum models from discrete models of mechanical forces in cell populations
  • 2021
  • In: Journal of Mathematical Biology. - : Springer Nature. - 0303-6812 .- 1432-1416. ; 83:6-7
  • Journal article (peer-reviewed)abstract
    • In certain discrete models of populations of biological cells, the mechanical forces between the cells are center based or vertex based on the microscopic level where each cell is individually represented. The cells are circular or spherical in a center based model and polygonal or polyhedral in a vertex based model. On a higher, macroscopic level, the time evolution of the density of the cells is described by partial differential equations (PDEs). We derive relations between the modelling on the micro and macro levels in one, two, and three dimensions by regarding the micro model as a discretization of a PDE for conservation of mass on the macro level. The forces in the micro model correspond on the macro level to a gradient of the pressure scaled by quantities depending on the cell geometry. The two levels of modelling are compared in numerical experiments in one and two dimensions.
  •  
44.
  • Malik, Adam, 1991, et al. (author)
  • Mathematical modelling of cell migration: stiffness dependent jump rates result in durotaxis
  • 2019
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 78:7, s. 2289-2315
  • Journal article (peer-reviewed)abstract
    • Durotaxis, the phenomena where cells migrate up a gradient in substrate stiffness, remains poorly understood. It has been proposed that durotaxis results from the reinforcement of focal adhesions on stiff substrates. In this paper we formulate a mathematical model of single cell migration on elastic substrates with spatially varying stiffness. We develop a stochastic model where the cell moves by updating the position of its adhesion sites at random times, and the rate of updates is determined by the local stiffness of the substrate. We investigate two physiologically motivated mechanisms of stiffness sensing. From the stochastic model of single cell migration we derive a population level description in the form of a partial differential equation for the time evolution of the density of cells. The equation is an advection-diffusion equation, where the advective velocity is proportional to the stiffness gradient. The model shows quantitative agreement with experimental results in which cells tend to cluster when seeded on a matrix with periodically varying stiffness.
  •  
45.
  • Metz, Johan A Jacob, et al. (author)
  • The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle.
  • 2015
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 1432-1416 .- 0303-6812. ; 74:4, s. 1125-1152
  • Journal article (peer-reviewed)abstract
    • This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value principle from evolutionary ecology, (4) show that the latter in turn is equivalent to Pontryagin's maximum principle, a well known equivalence that however in the literature is given either ex cathedra or is proven with more advanced tools, (5) connect the classical optimisation arguments of life history theory a little better to real biology (Mendelian populations with separate sexes subject to an environmental feedback loop), (6) make a minor improvement to the form of the CE for the examples in Dieckmann et al. and Parvinen et al.
  •  
46.
  • Obatake, Nida, et al. (author)
  • Oscillations and bistability in a model of ERK regulation
  • 2019
  • In: Journal of Mathematical Biology. - : Springer Nature. - 0303-6812 .- 1432-1416. ; 79:4, s. 1515-1549
  • Journal article (peer-reviewed)abstract
    • This work concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consider a model for dual-site phosphorylation and dephosphorylation of extracellular signal-regulated kinase (ERK). We prove that oscillations persist even as the model is greatly simplified (reactions are made irreversible and intermediates are removed). Bistability, however, is much less robust—this property is lost when intermediates are removed or even when all reactions are made irreversible. Moreover, bistability is characterized by the presence of two reversible, catalytic reactions: as other reactions are made irreversible, bistability persists as long as one or both of the specified reactions is preserved. Finally, we investigate the maximum number of steady states, aided by a network’s “mixed volume” (a concept from convex geometry). Taken together, our results shed light on the question of how oscillations and bistability emerge from a limiting network of the ERK network—namely, the fully processive dual-site network—which is known to be globally stable and therefore lack both oscillations and bistability. Our proofs are enabled by a Hopf bifurcation criterion due to Yang, analyses of Newton polytopes arising from Hurwitz determinants, and recent characterizations of multistationarity for networks having a steady-state parametrization
  •  
47.
  • Oddsdóttir, Hildur Æsa, et al. (author)
  • On dynamically generating relevant elementary flux modes in a metabolic network using optimization
  • 2014
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416.
  • Journal article (peer-reviewed)abstract
    • Elementary flux modes (EFMs) are pathways through a metabolic reaction network that connect external substrates to products. Using EFMs, a metabolic network can be transformed into its macroscopic counterpart, in which the internal metabolites have been eliminated and only external metabolites remain. In EFMs-based metabolic flux analysis (MFA) experimentally determined external fluxes are used to estimate the flux of each EFM. It is in general prohibitive to enumerate all EFMs for complex networks, since the number of EFMs increases rapidly with network complexity. In this work we present an optimization-based method that dynamically generates a subset of EFMs and solves the EFMs-based MFA problem simultaneously. The obtained subset contains EFMs that contribute to the optimal solution of the EFMs-based MFA problem. The usefulness of our method was examined in a case-study using data from a Chinese hamster ovary cell culture and two networks of varied complexity. It was demonstrated that the EFMs-based MFA problem could be solved at a low computational cost, even for the more complex network. Additionally, only a fraction of the total number of EFMs was needed to compute the optimal solution.
  •  
48.
  • Olofsson, Peter, et al. (author)
  • Mutational meltdown in asexual populations doomed to extinction
  • 2023
  • In: Journal of Mathematical Biology. - : Springer. - 0303-6812 .- 1432-1416. ; 87:6
  • Journal article (peer-reviewed)abstract
    • Asexual populations are expected to accumulate deleterious mutations through a process known as Muller’s ratchet. Lynch and colleagues proposed that the ratchet eventually results in a vicious cycle of mutation accumulation and population decline that drives populations to extinction. They called this phenomenon mutational meltdown. Here, we analyze mutational meltdown using a multi-type branching process model where, in the presence of mutation, populations are doomed to extinction. We analyse the change in size and composition of the population and the time of extinction under this model.
  •  
49.
  • Ouboter, Tanneke, et al. (author)
  • Stochastic SIR epidemics in a population with households and schools
  • 2016
  • In: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 72:5, s. 1177-1193
  • Journal article (peer-reviewed)abstract
    • We study the spread of stochastic SIR (Susceptible Infectious Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school and one household. In the independent partition model, the partitions of the population into schools and households are independent of each other. This model corresponds to the well-studied household-workplace model. In the hierarchical model which we introduce here, members of the same household are also members of the same school. We introduce computable branching process approximations for both types of populations and use these to compare the probabilities of a large outbreak. The branching process approximation in the hierarchical model is novel and of independent interest. We prove by a coupling argument that if all households and schools have the same size, an epidemic spreads easier (in the sense that the number of individuals infected is stochastically larger) in the independent partition model. We also show by example that this result does not necessarily hold if households and/or schools do not all have the same size.
  •  
50.
  • Pasquini, Mirko, 1991-, et al. (author)
  • On convergence for hybrid models of gene regulatory networks under polytopic uncertainties : a Lyapunov approach
  • 2021
  • In: Journal of Mathematical Biology. - : Springer Nature. - 0303-6812 .- 1432-1416. ; 83:6-7
  • Journal article (peer-reviewed)abstract
    • Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results.
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