Journal of Mathematical Biology, ISSN 0303-6812, 2016, Volume 72, pp. 877 - 908

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 01/2015, Volume 70, Issue 1-2, pp. 367 - 397

A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires...

Coalescent point process | Multitype branching process | 60J85 | 60G55 | Secondary 92D15 | Mathematical and Computational Biology | LÃ©vy process | 60G51 | Mathematics | Phylogeny | Birthâ€“death process | Protracted speciation | 92D25 | Reconstructed tree | Applications of Mathematics | Scale function | Primary 60J80 | 92D40 | Splitting tree | SPLITTING TREES | DIVERSIFICATION | Birth-death process | CONNECTIONS | RATES | SHAPE | BIRTH-DEATH-MODELS | Levy process | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | MOLECULAR PHYLOGENIES | Biological Evolution | Likelihood Functions | Markov Chains | Time Factors | Models, Biological | Genetic Speciation | Mathematical Concepts | Extinction, Biological | Biodiversity | Usage | Origin of species | Evolutionary biology | Analysis | Research | Likelihood functions | Life Sciences

Coalescent point process | Multitype branching process | 60J85 | 60G55 | Secondary 92D15 | Mathematical and Computational Biology | LÃ©vy process | 60G51 | Mathematics | Phylogeny | Birthâ€“death process | Protracted speciation | 92D25 | Reconstructed tree | Applications of Mathematics | Scale function | Primary 60J80 | 92D40 | Splitting tree | SPLITTING TREES | DIVERSIFICATION | Birth-death process | CONNECTIONS | RATES | SHAPE | BIRTH-DEATH-MODELS | Levy process | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | MOLECULAR PHYLOGENIES | Biological Evolution | Likelihood Functions | Markov Chains | Time Factors | Models, Biological | Genetic Speciation | Mathematical Concepts | Extinction, Biological | Biodiversity | Usage | Origin of species | Evolutionary biology | Analysis | Research | Likelihood functions | Life Sciences

Journal Article

Bulletin of Mathematical Biology, ISSN 0092-8240, 3/2019, Volume 81, Issue 3, pp. 639 - 675

Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an...

60J10 | Life Sciences, general | 92D25 | Mathematical and Computational Biology | Approximate Bayesian computation | Mathematics | Stochastic modelling | Phase variable genes | Population genetics | 62F15 | Cell Biology | SURVIVAL | ANTIGENIC VARIATION | RATES | PHASE | IMPACT | EVOLUTION | GROWTH | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | Bacteria | Models | Genetic aspects | Algorithms | Analysis | Parameter estimation | Mutation | Calibration | Bayesian analysis | Campylobacter | Fitness

60J10 | Life Sciences, general | 92D25 | Mathematical and Computational Biology | Approximate Bayesian computation | Mathematics | Stochastic modelling | Phase variable genes | Population genetics | 62F15 | Cell Biology | SURVIVAL | ANTIGENIC VARIATION | RATES | PHASE | IMPACT | EVOLUTION | GROWTH | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | Bacteria | Models | Genetic aspects | Algorithms | Analysis | Parameter estimation | Mutation | Calibration | Bayesian analysis | Campylobacter | Fitness

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 9/2016, Volume 73, Issue 3, pp. 597 - 625

We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each...

60H10 | 60H30 | 92D25 | Mathematical and Computational Biology | Stochastic control | Mathematics | Applications of Mathematics | Management of natural resources | Optimization under uncertainties | SYSTEM | FLUCTUATING ENVIRONMENTS | PERSISTENCE | EQUATIONS | RANDOM PERTURBATION | PREDATOR | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | LOGISTIC POPULATION | EXTINCTION | RANDOM-ENVIRONMENTS | Food Chain | Environment | Stochastic Processes | Models, Biological | Learning models (Stochastic processes) | Usage | Food chains (Ecology) | Models

60H10 | 60H30 | 92D25 | Mathematical and Computational Biology | Stochastic control | Mathematics | Applications of Mathematics | Management of natural resources | Optimization under uncertainties | SYSTEM | FLUCTUATING ENVIRONMENTS | PERSISTENCE | EQUATIONS | RANDOM PERTURBATION | PREDATOR | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | LOGISTIC POPULATION | EXTINCTION | RANDOM-ENVIRONMENTS | Food Chain | Environment | Stochastic Processes | Models, Biological | Learning models (Stochastic processes) | Usage | Food chains (Ecology) | Models

Journal Article

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Optimal contraception control for a size-structured population model with extra mortality

Applicable Analysis, ISSN 0003-6811, 2018, pp. 1 - 14

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 09/2017, Volume 23, Issue 9, pp. 1529 - 1541

We consider a discrete time competition model. Populations compete for common limited resources but they have different fertilities and mortalities rates. We...

periodic cycle | competitive exclusion | Secondary: 37N25 | Primary: 92D25 | Nonlinear Leslie model | 92D40 | population dynamics | MATHEMATICS, APPLIED | MODELS | NEST-SITE LOTTERY | Competition | Applied mathematics | Mathematical models | Mathematics - Dynamical Systems

periodic cycle | competitive exclusion | Secondary: 37N25 | Primary: 92D25 | Nonlinear Leslie model | 92D40 | population dynamics | MATHEMATICS, APPLIED | MODELS | NEST-SITE LOTTERY | Competition | Applied mathematics | Mathematical models | Mathematics - Dynamical Systems

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 7/2018, Volume 77, Issue 1, pp. 107 - 134

We develop a multi-patch and multi-group model that captures the dynamics of an infectious disease when the host is structured into an arbitrary number of...

Multi-group | Heterogeneity | 92D30 | 92D25 | Mathematical and Computational Biology | Global stability | Multi-patch | Mobility | Mathematics | Applications of Mathematics | Residence times | STABILITY | POPULATIONS | TRANSMISSION | INFECTIOUS-DISEASES | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | VECTOR-BORNE DISEASES | MOVEMENT | DYNAMICS | SPREAD | Epidemics | Usage | Models | Mathematical models | Economic models | Reproduction | Infectious diseases | Computer simulation | Patches (structures) | Stochasticity | Group dynamics | Epidemiology | Quantitative Biology - Populations and Evolution | Life Sciences | Human health and pathology | SantÃ© publique et Ã©pidÃ©miologie | Dynamical Systems

Multi-group | Heterogeneity | 92D30 | 92D25 | Mathematical and Computational Biology | Global stability | Multi-patch | Mobility | Mathematics | Applications of Mathematics | Residence times | STABILITY | POPULATIONS | TRANSMISSION | INFECTIOUS-DISEASES | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | VECTOR-BORNE DISEASES | MOVEMENT | DYNAMICS | SPREAD | Epidemics | Usage | Models | Mathematical models | Economic models | Reproduction | Infectious diseases | Computer simulation | Patches (structures) | Stochasticity | Group dynamics | Epidemiology | Quantitative Biology - Populations and Evolution | Life Sciences | Human health and pathology | SantÃ© publique et Ã©pidÃ©miologie | Dynamical Systems

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 10/2017, Volume 23, Issue 10, pp. 1694 - 1706

We show that the solutions of nonlinear higher order difference equations may have convergent subsequences, even when the solution as a whole does not...

subsequences of solution | 39A30 | higher order equation | 92D25 | planar systems | population dynamics | Convergence | POPULATION-MODELS | MATHEMATICS, APPLIED | Nonlinear equations | Difference equations | Dynamical systems | Mathematics - Dynamical Systems

subsequences of solution | 39A30 | higher order equation | 92D25 | planar systems | population dynamics | Convergence | POPULATION-MODELS | MATHEMATICS, APPLIED | Nonlinear equations | Difference equations | Dynamical systems | Mathematics - Dynamical Systems

Journal Article

Journal of Difference Equations and Applications, ISSN 1023-6198, 04/2019, Volume 25, Issue 4, pp. 583 - 596

This article investigates the global behaviour of May's host-parasitoid model [R.M. May, Host-parasitoid systems in patchy environments: A phenomenological...

39A30 | May's host-parasitoid model | Difference equations | global behaviour | 92D25 | host-parasitoid model | Initial conditions

39A30 | May's host-parasitoid model | Difference equations | global behaviour | 92D25 | host-parasitoid model | Initial conditions

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 2/2013, Volume 66, Issue 3, pp. 423 - 476

Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations....

37H15 | 60H10 | Dominant Lyapunov exponent | Mathematical and Computational Biology | Spatial and temporal heterogeneity | Mathematics | Stochastic population growth | Single large or several small debate | Ideal free movement | 92D25 | Evolution of dispersal | Habitat fragmentation | Applications of Mathematics | SINK HABITATS | DISPERSAL RATES | PERSISTENCE | EQUATIONS | INVARIANT-MEASURES | VARYING ENVIRONMENTS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | CORRELATED ENVIRONMENTS | EVOLUTIONARY BETS | EXTINCTION | Animals | Population Growth | Stochastic Processes | Endangered Species | Models, Biological | Ecosystem | Measurement | Stochastic differential equations | Usage | Growth | Population | Research | Computational biology

37H15 | 60H10 | Dominant Lyapunov exponent | Mathematical and Computational Biology | Spatial and temporal heterogeneity | Mathematics | Stochastic population growth | Single large or several small debate | Ideal free movement | 92D25 | Evolution of dispersal | Habitat fragmentation | Applications of Mathematics | SINK HABITATS | DISPERSAL RATES | PERSISTENCE | EQUATIONS | INVARIANT-MEASURES | VARYING ENVIRONMENTS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | CORRELATED ENVIRONMENTS | EVOLUTIONARY BETS | EXTINCTION | Animals | Population Growth | Stochastic Processes | Endangered Species | Models, Biological | Ecosystem | Measurement | Stochastic differential equations | Usage | Growth | Population | Research | Computational biology

Journal Article

Dynamical Systems, ISSN 1468-9367, 10/2017, Volume 32, Issue 4, pp. 490 - 503

In this paper, the exponential stability of travelling waves solutions for nonlinear cellular neural networks with distribute delays in the lattice is studied....

weighted energy method | 92D25 | travelling waves solutions | 34K13 | Cellular neural networks | exponential stability | 35C07 | FRONTS | MATHEMATICS, APPLIED | NICHOLSONS BLOWFLIES EQUATION | PHYSICS, MATHEMATICAL | GLOBAL ASYMPTOTIC STABILITY | Control systems | Traveling waves | Stability analysis | Cellular communication | Neural networks

weighted energy method | 92D25 | travelling waves solutions | 34K13 | Cellular neural networks | exponential stability | 35C07 | FRONTS | MATHEMATICS, APPLIED | NICHOLSONS BLOWFLIES EQUATION | PHYSICS, MATHEMATICAL | GLOBAL ASYMPTOTIC STABILITY | Control systems | Traveling waves | Stability analysis | Cellular communication | Neural networks

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 03/2016, Volume 72, Issue 4, pp. 877 - 908

In this paper we characterize the stability boundary in the (Formula presented.) -plane, for fixed (Formula presented.) with (Formula presented.) , for the...

65L03 | 92D25 | 37N25 | 45D05 | 34K20 | QUIESCENCE | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY

65L03 | 92D25 | 37N25 | 45D05 | 34K20 | QUIESCENCE | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 5/2011, Volume 62, Issue 5, pp. 655 - 683

Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and...

60H10 | Mathematics | Mathematical Biology in General | 60J05 | Applications of Mathematics | 92D25 | VARIABILITY | POPULATION-MODELS | PREDATION | COEXISTENCE | APPARENT COMPETITION | DYNAMICAL-SYSTEMS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | STOCHASTICITY | POLYMORPHISM | ROBUST PERMANENCE | HYPERCYCLES | Markov Chains | Population Growth | Biota | Probability | Genotype | Genetic Variation | Algorithms | Genetic Fitness | Stochastic Processes | Models, Biological | Population Density | Statistical Distributions | Environment | Population Dynamics | Fluctuations (Physics) | Population biology | Research

60H10 | Mathematics | Mathematical Biology in General | 60J05 | Applications of Mathematics | 92D25 | VARIABILITY | POPULATION-MODELS | PREDATION | COEXISTENCE | APPARENT COMPETITION | DYNAMICAL-SYSTEMS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | STOCHASTICITY | POLYMORPHISM | ROBUST PERMANENCE | HYPERCYCLES | Markov Chains | Population Growth | Biota | Probability | Genotype | Genetic Variation | Algorithms | Genetic Fitness | Stochastic Processes | Models, Biological | Population Density | Statistical Distributions | Environment | Population Dynamics | Fluctuations (Physics) | Population biology | Research

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 2/2018, Volume 74, Issue 2, pp. 1060 - 1090

We consider a quasilinear degenerate diffusionâ€“reaction system that describes biofilm formation. The model exhibits two non-linear effects: a power law...

Computational Mathematics and Numerical Analysis | Primary 35K65 | 65M08 | Secondary 68U20 | Theoretical, Mathematical and Computational Physics | Mathematics | Time adaptivity | Algorithms | Degenerate diffusionâ€“reaction equation | 92D25 | Mathematical and Computational Engineering | Biofilm | Quorum sensing | Semi-discretization | Regularization | MATHEMATICS, APPLIED | SIMULATION | CULTURE | FLOW | SCHEME | MATHEMATICAL-MODEL | Degenerate diffusion-reaction equation | QUORUM | GROWTH | RESISTANCE | BACTERIAL BIOFILM | EQUATION | Differential equations | Mathematics - Numerical Analysis

Computational Mathematics and Numerical Analysis | Primary 35K65 | 65M08 | Secondary 68U20 | Theoretical, Mathematical and Computational Physics | Mathematics | Time adaptivity | Algorithms | Degenerate diffusionâ€“reaction equation | 92D25 | Mathematical and Computational Engineering | Biofilm | Quorum sensing | Semi-discretization | Regularization | MATHEMATICS, APPLIED | SIMULATION | CULTURE | FLOW | SCHEME | MATHEMATICAL-MODEL | Degenerate diffusion-reaction equation | QUORUM | GROWTH | RESISTANCE | BACTERIAL BIOFILM | EQUATION | Differential equations | Mathematics - Numerical Analysis

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 4/2017, Volume 27, Issue 2, pp. 425 - 452

This paper proposes a new definition of permanence for stochastic population models, which overcomes some limitations and deficiency of the existing ones....

Persistence | 60H10 | 60H30 | 92D25 | Analysis | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Appl.Mathematics/Computational Methods of Engineering | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | White noises | Random time change | MATHEMATICS, APPLIED | FLUCTUATING ENVIRONMENTS | BEHAVIOR | PHYSICS, MATHEMATICAL | RANDOM PERTURBATION | MECHANICS | MODELS | COMPETITIVE SYSTEM | POPULATION-DYNAMICS | EXTINCTION | EQUATION

Persistence | 60H10 | 60H30 | 92D25 | Analysis | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Appl.Mathematics/Computational Methods of Engineering | Economic Theory/Quantitative Economics/Mathematical Methods | Mathematics | White noises | Random time change | MATHEMATICS, APPLIED | FLUCTUATING ENVIRONMENTS | BEHAVIOR | PHYSICS, MATHEMATICAL | RANDOM PERTURBATION | MECHANICS | MODELS | COMPETITIVE SYSTEM | POPULATION-DYNAMICS | EXTINCTION | EQUATION

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 2/2015, Volume 70, Issue 3, pp. 399 - 435

This paper proposes an approach for building epidemiological models that incorporate the intra-host pathogen-immunity dynamics. The infected population is...

Epidemic modelling | 92D30 | Immune response | 92D25 | Mathematical and Computational Biology | Pathogen dynamics | 35L04 | Mathematics | Applications of Mathematics | Structured population models | EVOLUTION | IMMUNOEPIDEMIOLOGY | MODELS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | WITHIN-HOST | INFECTION | VIRULENCE | Models, Immunological | Animals | Communicable Diseases - epidemiology | Humans | Communicable Diseases - immunology | Mathematical Concepts | Epidemics - statistics & numerical data | Host-Pathogen Interactions - immunology | Population Dynamics | Usage | Models | Mathematical models | Prevalence studies (Epidemiology)

Epidemic modelling | 92D30 | Immune response | 92D25 | Mathematical and Computational Biology | Pathogen dynamics | 35L04 | Mathematics | Applications of Mathematics | Structured population models | EVOLUTION | IMMUNOEPIDEMIOLOGY | MODELS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | WITHIN-HOST | INFECTION | VIRULENCE | Models, Immunological | Animals | Communicable Diseases - epidemiology | Humans | Communicable Diseases - immunology | Mathematical Concepts | Epidemics - statistics & numerical data | Host-Pathogen Interactions - immunology | Population Dynamics | Usage | Models | Mathematical models | Prevalence studies (Epidemiology)

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 7/2019, Volume 79, Issue 2, pp. 731 - 764

In the previous paper (Inaba in J Math Biol 65:309â€“348, 2012), we proposed a new (most biologically natural) definition of the basic reproduction number...

Cone spectral radius | Basic reproduction number | 92D30 | Orbital spectral radius | 92D25 | Mathematical and Computational Biology | Mathematics | Applications of Mathematics | Generation evolution operator

Cone spectral radius | Basic reproduction number | 92D30 | Orbital spectral radius | 92D25 | Mathematical and Computational Biology | Mathematics | Applications of Mathematics | Generation evolution operator

Journal Article

Japanese Journal of Mathematics, ISSN 0289-2316, 03/2007, Volume 2, Issue 1, pp. 197 - 227

We describe a setting where convergence to consensus in a population of autonomous agents can be formally addressed and prove some general results establishing...

91D30 | 92D25 | emergence | Mathematics, general | flocking | consensus reaching | Mathematics | 92D50 | History of Mathematics | Consensus reaching | Flocking | Emergence | MATHEMATICS

91D30 | 92D25 | emergence | Mathematics, general | flocking | consensus reaching | Mathematics | 92D50 | History of Mathematics | Consensus reaching | Flocking | Emergence | MATHEMATICS

Journal Article

SpringerPlus, ISSN 2193-1801, 12/2016, Volume 5, Issue 1, p. 452

Motivated by (Goyal and Murray in PLoS One 9(10):e110143, 2014) we consider a partially age-structured model simulating the dynamic of two infectious diseases...

Basic reproduction rate | Vaccination | Differential infectivity

Basic reproduction rate | Vaccination | Differential infectivity

Journal Article