Dynamics of annual influenza A epidemics with immuno-selection.

Abstract:

:The persistence of Influenza A in the human population relies on continual changes in the viral surface antigens allowing the virus to reinfect the same hosts every few years. The epidemiology of such a drifting virus is modeled by a discrete season-to-season map. During the epidemic season only one strain is present and its transmission dynamics follows a standard epidemic model. After the season, cross-immunity to next year's virus is determined from the proportion of hosts that were infected during the season. A partial analysis of this map shows the existence of oscillations where epidemics occur at regular or irregular intervals.

journal_name

J Math Biol

authors

Andreasen V

doi

10.1007/s00285-002-0186-2

keywords:

subject

Has Abstract

pub_date

2003-06-01 00:00:00

pages

504-36

issue

6

eissn

0303-6812

issn

1432-1416

journal_volume

46

pub_type

杂志文章
  • Stochastic selection in both haplophase and diplophase.

    abstract::A population genetic model incorporating the evolutionary forces of zygotic selection, gametic selection and non-Mendelian segregation has been analyzed for the case in which all selection coefficients and the segregation parameter are assumed to be random variables that are uncorrelated from generation to generation....

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF00275059

    authors: Hartl DL

    更新日期:1976-11-25 00:00:00

  • Mathematical model for rhythmic protoplasmic movement in the true slime mold.

    abstract::The plasmodium of the true slime mold Physarum polycephalum is a large amoeboid organism that displays "smart" behavior such as chemotaxis and the ability to solve mazes and geometrical puzzles. These amoeboid behaviors are based on the dynamics of the viscoelastic protoplasm and its biochemical rhythms. By incorporat...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-006-0007-0

    authors: Kobayashi R,Tero A,Nakagaki T

    更新日期:2006-08-01 00:00:00

  • Implications of immune-mediated metastatic growth on metastatic dormancy, blow-up, early detection, and treatment.

    abstract::Metastatic seeding of distant organs can occur in the very early stages of primary tumor development. Once seeded, these micrometastases may enter a dormant phase that can last decades. Curiously, the surgical removal of the primary tumor can stimulate the accelerated growth of distant metastases, a phenomenon known a...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-020-01521-x

    authors: Rhodes A,Hillen T

    更新日期:2020-09-01 00:00:00

  • A numerical scheme for the early steps of nucleation-aggregation models.

    abstract::In the formation of large clusters out of small particles, the initializing step is called the nucleation, and consists in the spontaneous reaction of agents which aggregate into small and stable polymers called nuclei. After this early step, the polymers are involved in a number of reactions such as polymerization, f...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-016-1026-0

    authors: Banks HT,Doumic M,Kruse C

    更新日期:2017-01-01 00:00:00

  • Theory of a microfluidic serial dilution bioreactor for growth of planktonic and biofilm populations.

    abstract::We present the theory of a microfluidic bioreactor with a two-compartment growth chamber and periodic serial dilution. In the model, coexisting planktonic and biofilm populations exchange by adsorption and detachment. The criteria for coexistence and global extinction are determined by stability analysis of the global...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-015-0913-0

    authors: Hsu SB,Yang YT

    更新日期:2016-04-01 00:00:00

  • Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis.

    abstract::The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spat...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-012-0532-y

    authors: Faye G,Rankin J,Chossat P

    更新日期:2013-05-01 00:00:00

  • Equilibria in systems of interacting structured populations.

    abstract::The existence of a stable positive equilibrium density for a community of k interacting structured species is studied as a bifurcation problem. Under the assumption that a subcommunity of k-1 species has a positive equilibrium and under only very mild restrictions on the density dependent vital growth rates, it is sho...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF00275507

    authors: Cushing JM

    更新日期:1987-01-01 00:00:00

  • Translating stochastic density-dependent individual behavior with sensory constraints to an Eulerian model of animal swarming.

    abstract::Density-dependent social behaviors such as swarming and schooling determine spatial distribution and patterns of resource use in many species. Lagrangian (individual-based) models have been used to investigate social groups arising from hypothetical algorithms for behavioral interactions, but the Lagrangian approach i...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF00160177

    authors: Grünbaum D

    更新日期:1994-01-01 00:00:00

  • An ant navigation model based on Weber's law.

    abstract::We analyze an ant navigation model based on Weber's law, where the ants move across a pheromone landscape sensing the area using two antennae. The key parameter of the model is the angle [Formula: see text] representing the span of the ant's sensing area. We show that when [Formula: see text] ants are able to follow (...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-018-1298-7

    authors: Amorim P,Goudon T,Peruani F

    更新日期:2019-03-01 00:00:00

  • Competition in the presence of a virus in an aquatic system: an SIS model in the chemostat.

    abstract::Recent research indicates that viruses are much more prevalent in aquatic environments than previously imagined. We derive a model of competition between two populations of bacteria for a single limiting nutrient in a chemostat where a virus is present. It is assumed that the virus can only infect one of the populatio...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-011-0439-z

    authors: Northcott K,Imran M,Wolkowicz GS

    更新日期:2012-05-01 00:00:00

  • A note on the statistical properties of animal locations.

    abstract::A statistical model of the successive locations of an animal in the plane induces a statistical model of the relative positions of successive locations. A common locational model is that the Cartesian coordinates of successive locations in the plane are independent bivariate normal random variables. This note gives th...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF00168178

    authors: Solow AR

    更新日期:1990-01-01 00:00:00

  • Continuous and discrete modeling of HIV-1 decline on therapy.

    abstract::Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582-1586, 1996) and Perelson and Nelson (SIAM Rev 41:3-44, 1999) on time scales, i.e., a nonempty closed subset of real...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-020-01492-z

    authors: Akın E,Yeni G,Perelson AS

    更新日期:2020-07-01 00:00:00

  • A model for macromolecular selection in complementary instructing systems.

    abstract::In this paper we consider a model for the selection and evolution of biological macromolecules when their reproduction is based on complementary instruction. The model is an extension of one of Eigen's models for selection and takes in account explicitly the formation of both single stranded and double stranded molecu...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF00276350

    authors: Jones BL

    更新日期:1977-02-28 00:00:00

  • Mathematical modelling of stem cell differentiation: the PU.1-GATA-1 interaction.

    abstract::The transcription factors PU.1 and GATA-1 are known to be important in the development of blood progenitor cells. Specifically they are thought to regulate the differentiation of progenitor cells into the granulocyte/macrophage lineage and the erythrocyte/megakaryocite lineage. While several mathematical models have b...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-011-0419-3

    authors: Duff C,Smith-Miles K,Lopes L,Tian T

    更新日期:2012-02-01 00:00:00

  • Combinatorial vector fields and the valley structure of fitness landscapes.

    abstract::Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vecto...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-010-0326-z

    authors: Stadler BM,Stadler PF

    更新日期:2010-12-01 00:00:00

  • On the formulation and analysis of general deterministic structured population models. II. Nonlinear theory.

    abstract::This paper is as much about a certain modelling methodology, as it is about the constructive definition of future population states from a description of individual behaviour and an initial population state. The key idea is to build a nonlinear model in two steps, by explicitly introducing the environmental condition ...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s002850170002

    authors: Diekmann O,Gyllenberg M,Huang H,Kirkilionis M,Metz JA,Thieme HR

    更新日期:2001-08-01 00:00:00

  • Dispersal and settling of translocated populations: a general study and a New Zealand amphibian case study.

    abstract::Translocations are widely used to reintroduce threatened species to areas where they have disappeared. A continuum multi-species model framework describing dispersal and settling of translocated animals is developed. A variety of different dispersal and settling mechanisms, which may depend on local population density...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-007-0096-4

    authors: Trewenack AJ,Landman KA,Bell BD

    更新日期:2007-10-01 00:00:00

  • On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations.

    abstract::The expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population is mathematically defined as the dominant eigenvalue of a positive linear operator. It is shown that in certain special cases one can easily compute or esti...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF00178324

    authors: Diekmann O,Heesterbeek JA,Metz JA

    更新日期:1990-01-01 00:00:00

  • Mixture distributions in a stochastic gene expression model with delayed feedback: a WKB approximation approach.

    abstract::Noise in gene expression can be substantively affected by the presence of production delay. Here we consider a mathematical model with bursty production of protein, a one-step production delay (the passage of which activates the protein), and feedback in the frequency of bursts. We specifically focus on examining the ...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-020-01512-y

    authors: Bokes P,Borri A,Palumbo P,Singh A

    更新日期:2020-07-01 00:00:00

  • Stationary multiple spots for reaction-diffusion systems.

    abstract::In this paper, we review analytical methods for a rigorous study of the existence and stability of stationary, multiple spots for reaction-diffusion systems. We will consider two classes of reaction-diffusion systems: activator-inhibitor systems (such as the Gierer-Meinhardt system) and activator-substrate systems (su...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-007-0146-y

    authors: Wei J,Winter M

    更新日期:2008-07-01 00:00:00

  • Mathematical models for CFSE labelled lymphocyte dynamics: asymmetry and time-lag in division.

    abstract::Since their invention in 1994, fluorescent dyes such as carboxyfluorescein diacetate succinimidyl ester (CFSE) are used for cell proliferation analysis in flow cytometry. Importantly, the interpretation of such assays relies on the assumption that the label is divided equally between the daughter cells upon cell divis...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-013-0741-z

    authors: Luzyanina T,Cupovic J,Ludewig B,Bocharov G

    更新日期:2014-12-01 00:00:00

  • Memory and adaptive behavior in population dynamics: anti-predator behavior as a case study.

    abstract::Memory allows organisms to forecast the future on the basis of experience, and thus, in some form, is important for the development of flexible adaptive behavior by animal communities. To model memory, we use the concept of hysteresis, which mathematically is described by the Preisach operator. As a case study, we con...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-016-1065-6

    authors: Pimenov A,Kelly TC,Korobeinikov A,O'Callaghan MJ,Rachinskii D

    更新日期:2017-05-01 00:00:00

  • Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model.

    abstract::Providing an analytical treatment to the stochastic feature of neurons' dynamics is one of the current biggest challenges in mathematical biology. The noisy leaky integrate-and-fire model and its associated Fokker-Planck equation are probably the most popular way to deal with neural variability. Another well-known for...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-016-1002-8

    authors: Dumont G,Henry J,Tarniceriu CO

    更新日期:2016-12-01 00:00:00

  • Input-output relationship of the Leaky-integrator neuron model.

    abstract::This paper presents a method of calculating the spike sequence at the output of the Leaky-Integrator Neuron Model (LIM) in response to an arbitrary input stimulus. The calculations have revealed new properties of the initial transient behavior of the LIM, as well as new constraints upon necessary and sufficient condit...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF00275835

    authors: Scharstein H

    更新日期:1979-12-01 00:00:00

  • Stability of the steady-state size distribution in a model of cell growth and division.

    abstract::The approach to steady-state size distribution is studied for a growing population of cells. The model incorporates cell growth at a linear rate and division into two equal daughters after a random time composed of an exponentially distributed phase and a constant deterministic phase. ...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF00276487

    authors: Hannsgen KB,Tyson JJ

    更新日期:1985-01-01 00:00:00

  • Central pattern generators for bipedal locomotion.

    abstract::Golubitsky, Stewart, Buono and Collins proposed two models for the achitecture of central pattern generators (CPGs): one for bipeds (which we call leg) and one for quadrupeds (which we call quad). In this paper we use symmetry techniques to classify the possible spatiotemporal symmetries of periodic solutions that can...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-006-0021-2

    authors: Pinto CM,Golubitsky M

    更新日期:2006-09-01 00:00:00

  • Stochastic models for cell motion and taxis.

    abstract::Certain biological experiments investigating cell motion result in time lapse video microscopy data which may be modeled using stochastic differential equations. These models suggest statistics for quantifying experimental results and testing relevant hypotheses, and carry implications for the qualitative behavior of ...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-003-0220-z

    authors: Ionides EL,Fang KS,Isseroff RR,Oster GF

    更新日期:2004-01-01 00:00:00

  • Counting glycans revisited.

    abstract::We present an algorithm for counting glycan topologies of order n that improves on previously described algorithms by a factor n in both time and space. More generally, we provide such an algorithm for counting rooted or unrooted d-ary trees with labels or masses assigned to the vertices, and we give a "recipe" to est...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-013-0721-3

    authors: Böcker S,Wagner S

    更新日期:2014-10-01 00:00:00

  • Coexistence phenomena and global bifurcation structure in a chemostat-like model with species-dependent diffusion rates.

    abstract::We study the competition of two species for a single resource in a chemostat. In the simplest space-homogeneous situation, it is known that only one species survives, namely the best competitor. In order to exhibit coexistence phenomena, where the two competitors are able to survive, we consider a space dependent situ...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-012-0633-7

    authors: Castella F,Madec S

    更新日期:2014-01-01 00:00:00

  • Predicting coexistence of plants subject to a tolerance-competition trade-off.

    abstract::Ecological trade-offs between species are often invoked to explain species coexistence in ecological communities. However, few mathematical models have been proposed for which coexistence conditions can be characterized explicitly in terms of a trade-off. Here we present a model of a plant community which allows such ...

    journal_title:Journal of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s00285-013-0692-4

    authors: Haegeman B,Sari T,Etienne RS

    更新日期:2014-06-01 00:00:00