Journal of Mathematical Biology

Items from 1 to 20 out of 62 results

article

Critical delay for overshooting in planned arm movements with delayed feedback

Dan Beamish, Christopher Peskun, Jianhong Wu

Journal of Mathematical Biology > 2005 > 50 > 1 > 22-48

. The Vector Integration To Endpoint (VITE) circuit describes a real time neural network model which simulates behavioral and neurobiological properties of planned arm movements by the interaction of two populations of neurons. This model is generalized to include delay between the interacting populations, which is found to have a detrimental effect on movement accuracy. Conditions are given on the...

article

An interacting particle system modelling aggregation behavior: from individuals to populations

Daniela Morale, Vincenzo Capasso, Karl Oelschläger

Journal of Mathematical Biology > 2005 > 50 > 1 > 49-66

. In this paper we investigate the stochastic modelling of a spatially structured biological population subject to social interaction. The biological motivation comes from the analysis of field experiments on a species of ants which exhibits a clear tendency to aggregate, still avoiding overcrowding. The model we propose here provides an explanation of this experimental behavior in terms of “long-ranged”...

article

An asymptotic maximum principle for essentially linear evolution models

Ellen Baake, Michael Baake, Anton Bovier, Markus Klein

Journal of Mathematical Biology > 2005 > 50 > 1 > 83-114

. Recent work on mutation-selection models has revealed that, under specific assumptions on the fitness function and the mutation rates, asymptotic estimates for the leading eigenvalue of the mutation-reproduction matrix may be obtained through a low-dimensional maximum principle in the limit N→∞ (where N, or N ^d with d≥1, is proportional to the number of types). In order to extend this variational...

article

On synchronization in semelparous populations

E. Mjølhus, A. Wikan, T. Solberg

Journal of Mathematical Biology > 2005 > 50 > 1 > 1-21

. Synchronization, i.e., convergence towards a dynamical state where the whole population is in one age class, is a characteristic feature of some population models with semelparity. We prove some rigorous results on this, for a simple class of nonlinear one- population models with age structure and semelparity: (i) the survival probabilities are assumed constant, and (ii) only the last age class...

article

Resident-invader dynamics and the coexistence of similar strategies

Stefan A. H. Geritz

Journal of Mathematical Biology > 2005 > 50 > 1 > 67-82

. We study the resident-invader dynamics for a given class of models of unstructured populations of finite-dimensional strategies. We prove various results on the existence and uniqueness of ω-limit sets in the interior of the resident-invader population state space, and we classify the generically possible types of dynamics in terms of the invasion conditions when the resident and invader strategies...

article

On the impossibility of coexistence of infinitely many strategies

Mats Gyllenberg, Géza Meszéna

Journal of Mathematical Biology > 2005 > 50 > 2 > 133-160

. We investigate the possibility of coexistence of pure, inherited strategies belonging to a large set of potential strategies. We prove that under biologically relevant conditions every model allowing for coexistence of infinitely many strategies is structurally unstable. In particular, this is the case when the “interaction operator” which determines how the growth rate of a strategy depends on...

article

Information and effective number of meioses in linkage analysis

Ola Hössjer

Journal of Mathematical Biology > 2005 > 50 > 2 > 208-232

. In this paper we introduce two information criteria in linkage analysis. The setup is a sample of families with unusually high occurrence of a certain inheritable disease. Given phenotypes from all families, the two criteria measure the amount of information inherent in the sample for 1) testing existence of a disease locus harbouring a disease gene somewhere along a chromosome or 2) estimating...

article

Spatial effects in discrete generation population models

C. Carrillo, P. Fife

Journal of Mathematical Biology > 2005 > 50 > 2 > 161-188

. A framework is developed for constructing a large class of discrete generation, continuous space models of evolving single species populations and finding their bifurcating patterned spatial distributions. Our models involve, in separate stages, the spatial redistribution (through movement laws) and local regulation of the population; and the fundamental properties of these events in a homogeneous...

article

Derivation of hyperbolic models for chemosensitive movement

Francis Filbet, Philippe Laurençot, Benoît Perthame

Journal of Mathematical Biology > 2005 > 50 > 2 > 189-207

. A Chapman-Enskog expansion is used to derive hyperbolic models for chemosensitive movements as a hydrodynamic limit of a velocity-jump process. On the one hand, it connects parabolic and hyperbolic chemotaxis models since the former arise as diffusion limits of a similar velocity-jump process. On the other hand, this approach provides a unified framework which includes previous models obtained by...

article

Effects of periodic input on the quasi-steady state assumptions for enzyme-catalysed reactions

I. Stoleriu, F.A. Davidson, J.L. Liu

Journal of Mathematical Biology > 2005 > 50 > 2 > 115-132

. In this paper we investigate the validity of a quasi-steady state assumption in approximating Michaelis-Menten type kinetics for enzyme-catalysed biochemical reactions that are subject to periodic substrate input.

article

State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences

Sanyi Tang, Robert A. Cheke

Journal of Mathematical Biology > 2005 > 50 > 3 > 257-292

. A state-dependent impulsive model is proposed for integrated pest management (IPM). IPM involves combining biological, mechanical, and chemical tactics to reduce pest numbers to tolerable levels after a pest population has reached its economic threshold (ET). The complete expression of an orbitally asymptotically stable periodic solution to the model with a maximum value no larger than the given...

article

An algorithm for molecular dissection of tumor progression

Tian Liu, Wei Zhao, Lili Tian, Rongling Wu

Journal of Mathematical Biology > 2005 > 50 > 3 > 336-354

. The volumetric growth of tumor cells as a function of time is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, i.e., quantitative trait loci (QTL), based on polymorphic markers. In this article, we present...

article

A cardiovascular-respiratory control system model including state delay with application to congestive heart failure in humans

Jerry J. Batzel, Franz Kappel, Susanne Timischl-Teschl

Journal of Mathematical Biology > 2005 > 50 > 3 > 293-335

. This paper considers a model of the human cardiovascular-respiratory control system with one and two transport delays in the state equations describing the respiratory system. The effectiveness of the control of the ventilation rate is influenced by such transport delays because blood gases must be transported a physical distance from the lungs to the sensory sites where these gases are measured...

article

Model selection and parameter estimation for ion channel recordings with an application to the K ⁺ outward-rectifier in barley leaf

M.C.M. de Gunst, J.G. Schouten

Journal of Mathematical Biology > 2005 > 50 > 3 > 233-256

. We present a statistical method, and its accompanying algorithms, for the selection of a mathematical model of the gating mechanism of an ion channel and for the estimation of the parameters of this model. The method assumes a hidden Markov model that incorporates filtering, colored noise and state-dependent white excess noise for the recorded data. The model selection and parameter estimation are...

article

A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait

Reinhard Bürger

Journal of Mathematical Biology > 2005 > 50 > 4 > 355-396

. The equilibrium structure of an additive, diallelic multilocus model of a quantitative trait under frequency- and density-dependent selection is derived. The trait is under stabilizing selection and mediates intraspecific competition as induced, for instance, by differential resource utilization. It is assumed that stabilizing selection is weak, but the strength of competition may be arbitrary relative...

article

Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: “quorum” sensing by a single bacterium

A.J. Koerber, J.R. King, P. Williams

Journal of Mathematical Biology > 2005 > 50 > 4 > 440-488

. Deterministic and stochastic models describing quorum sensing by Staphylococcus aureus within an endosome, and the subsequent escape via the production of virulence factors, are developed and analysed. Particular attention is given to a biologically-relevant asymptotic limit of the problem, for which the solutions, including the endosome escape time, can be explicitly characterised in terms of the...

article

Modelling Human Granulopoiesis under Poly-chemotherapy with G-CSF Support

M. Scholz, C. Engel, M. Loeffler

Journal of Mathematical Biology > 2005 > 50 > 4 > 397-439

. Cytotoxic drugs administered in polychemotherapy cause a characteristic neutropenic period depending on the schedule of the drugs, which can partly be prevented by G-CSF growth factor support. To quantify these effects and to gain a deeper insight into the dynamics of bone marrow recovery after such suppressing and stimulating disturbances, we construct a biomathematical compartment model of human...

article

Characterizing the symmetric equilibrium of multi-strain host-pathogen systems in the presence of cross immunity

L.J. Abu-Raddad, N.M. Ferguson

Journal of Mathematical Biology > 2005 > 50 > 5 > 531-558

. We investigate the population dynamics of host-pathogen systems in which the pathogen has a potentially arbitrary number of antigenically distinct strains interacting via cross-immunity. The interior equilibrium configuration of the symmetric multiple strain SIR model with cross-immunity is characterized. We develop an efficient iterative method for numerically solving the equilibrium equation together...

article

Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations

Peter G. Schofield, Mark A.J. Chaplain, Stephen F. Hubbard

Journal of Mathematical Biology > 2005 > 50 > 5 > 559-583

. In this paper we develop a general mathematical model describing the spatio-temporal dynamics of host-parasitoid systems with forced generational synchronisation, for example seasonally induced diapause. The model itself may be described as an individual-based stochastic model with the individual movement rules derived from an underlying continuum PDE model. This approach permits direct comparison...

article

Mathematical analysis of Mayer waves

B. Vielle

Journal of Mathematical Biology > 2005 > 50 > 5 > 595-606

. The goal of this paper is to explore the low-frequency oscillations of arterial pressure in humans, also called Mayer waves. We carefully describe the cardiovascular control system in order to analyse how its different components may be involved in the occurrence of sustained oscillations. We carry out an analysis of stability leading to the definition of a stability index, which we use to study...

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2005

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51 (33)
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Keywords

MATHEMATICAL MODEL (5)
POPULATION DYNAMICS (3)
ADAPTIVE DYNAMICS (2)
BIFURCATION (2)
HOPF BIFURCATION (2)
MAYER WAVES (2)
RECOMBINATION (2)
SIZE STRUCTURE (2)
STABILITY (2)
AGE-STRUCTURED POPULATION MODELS (1)
AGEING (1)
AGENT BASED MODELS (1)
AGGREGATION (1)
ALLOMETRIC RELATIONSHIPS (1)
ANCESTRAL DISTRIBUTION (1)
ANTIGENIC VARIATION (1)
ARM MOVEMENT (1)
ASYMPTOTICS OF LEADING EIGENVALUE (1)
BALANCING SELECTION (1)
BAROREFLEX CONTROL (1)
BASAL STEM DIAMETER (1)
BAYESIAN ESTIMATION (1)
BAYESIAN MODEL (1)
BIASED RANDOM WALK (1)
BIOMEMBRANES (1)
BOTTLENECK (1)
CANNIBALISM (1)
CARDIOVASCULAR (1)
CARDIOVASCULAR CONTROL (1)
CARDIOVASCULAR SYSTEM (1)
CEREBRAL AUTOREGULATION (1)
CEREBRAL CIRCULATION (1)
CEREBRAL OXYGEN SUPPLY (1)
CHEMOSTAT (1)
CHEMOSTAT DYNAMICS (1)
CHEMOTAXIS (1)
CHEMOTHERAPEUTIC DRUGS (1)
COEXISTENCE (1)
COLOUR SPACE (1)
COLOUR-MATCHING FUNCTION (1)
COMPARTMENT MODEL (1)
COMPETITION (1)
COMPOUND MATRICES (1)
COUPLED Β-CELLS (1)
CRANIOFACIAL GROWTH (1)
CROSS-IMMUNITY (1)
DEGENERATE EQUILIBRIUM (1)
DELAY (1)
DELAY DIFFERENTIAL EQUATION (1)
DELAY DIFFERENTIAL EQUATIONS (1)
DELAYED NONMONOTONE GROWTH (1)
DENSITY DEPENDENT DIFFUSION (1)
DENSITY-DEPENDENT SELECTION (1)
DIFFERENCE EQUATIONS (1)
DIFFERENTIAL EQUATION (1)
DIFFERENTIAL EQUATIONS (1)
DIFFERENTIAL SUSCEPTIBILITY (1)
DIFFUSION (1)
DIRECTED MOTION (1)
DISRUPTIVE SELECTION (1)
DIVERSITY (1)
DYNAMICAL MODELS (1)
DYNAMICAL SYSTEMS (1)
ECOLOGICAL NICHE (1)
ECONOMIC THRESHOLD (1)
EFFECTIVE NUMBER OF MEIOSES (1)
EMPIRICAL MEASURES (1)
ENDEMIC EQUILIBRIUM (1)
ENTANGLEMENT (1)
ENVIRONMENTAL SEASONALITY (1)
ENVIRONMENTAL TRANSMISSION (1)
ENZYME-KINETICS (1)
EPIDEMIC DISEASE (1)
EPIDEMIOLOGY (1)
EQUILIBRIUM (1)
EULERIAN NUMBERS (1)
EVOLUTION (1)
EVOLUTION OF SEED-SIZE (1)
EXCITATION WAVE (1)
EXTINCTION (1)
FRACTAL MIMICRY (1)
FRACTALITY IN EVOLUTION (1)
FREE BOUNDARY PROBLEMS (1)
FREE LIVING PARASITE (1)
FREQUENCY-DEPENDENT SELECTION (1)
GAMUT SIZE (1)
GAP JUNCTIONS (1)
GENE ALGEBRA (1)
GENERAL RATIO-DEPENDENT RESPONSE (1)
GENETIC CODE ALGEBRA (1)
GENETIC VARIATION (1)
GEOMETRICALLY CONSTRAINT EQUATION (1)
GLOBAL STABILITY (1)
GOMPERTZIAN CURVE (1)
GRADIENT SYSTEM (1)
GRANULOCYTE-COLONY STIMULATING FACTOR (G-CSF) (1)
GRASSMAN’S LAWS (1)
GROWTH TRAJECTORY (1)
HAEMATOTOXICITY (1)
HAMILTONIAN SYSTEM (1)
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Journal of Mathematical Biology

Critical delay for overshooting in planned arm movements with delayed feedback

An interacting particle system modelling aggregation behavior: from individuals to populations

An asymptotic maximum principle for essentially linear evolution models

On synchronization in semelparous populations

Resident-invader dynamics and the coexistence of similar strategies

On the impossibility of coexistence of infinitely many strategies

Information and effective number of meioses in linkage analysis

Spatial effects in discrete generation population models

Derivation of hyperbolic models for chemosensitive movement

Effects of periodic input on the quasi-steady state assumptions for enzyme-catalysed reactions

State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences

An algorithm for molecular dissection of tumor progression

A cardiovascular-respiratory control system model including state delay with application to congestive heart failure in humans

Model selection and parameter estimation for ion channel recordings with an application to the K ⁺ outward-rectifier in barley leaf

A multilocus analysis of intraspecific competition and stabilizing selection on a quantitative trait

Deterministic and stochastic modelling of endosome escape by Staphylococcus aureus: “quorum” sensing by a single bacterium

Modelling Human Granulopoiesis under Poly-chemotherapy with G-CSF Support

Characterizing the symmetric equilibrium of multi-strain host-pathogen systems in the presence of cross immunity

Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations

Mathematical analysis of Mayer waves

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