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Sep 23, 2013
09/13

by
K. B. Blyuss

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In the studies of dynamics of pathogens and their interactions with a host immune system, an important role is played by the structure of antigenic variants associated with a pathogen. Using the example of a model of antigenic variation in malaria, we show how many of the observed dynamical regimes can be explained in terms of the symmetry of interactions between different antigenic variants. The results of this analysis are quite generic, and have wider implications for understanding the...

Source: http://arxiv.org/abs/1202.4290v1

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Sep 19, 2013
09/13

by
K. B. Blyuss

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Stationary wave solutions of the perturbed Korteweg-de Vries equation are considered in the presence of external hamiltonian perturbations. Conditions of their chaotic behaviour are studied with the help of Melnikov theory. For the homoclinic chaos Poincar\'e sections are constructed to demonstrate the complicated behaviour, and Lyapunov exponents are also numerically calculated.

Source: http://arxiv.org/abs/nlin/0206019v1

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Sep 23, 2013
09/13

by
K. B. Blyuss

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This paper considers properties of nonlinear waves and solitons of Korteweg-de Vries equation in the presence of external perturbation. For time-periodic hamiltonian perturbation the width of the stochastic layer is calculated. The conclusions about chaotic behaviour in long-period waves and solitons are inferred. Obtained theoretical results find experimental confirmation in experiments with the propagation of ion-acoustic waves in plasma.

Source: http://arxiv.org/abs/patt-sol/9904001v3

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Sep 19, 2013
09/13

by
K. B. Blyuss

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In this work the Melnikov method for perturbed Hamiltonian wave equations is considered in order to determine possible chaotic behaviour in the systems. The backbone of the analysis is the multi-symplectic formulation of the unperturbed PDE and its further reduction to travelling waves. In the multi-symplectic approach two separate symplectic operators are introduced for the spatial and temporal variables, which allow one to generalise the usual symplectic structure. The systems under...

Source: http://arxiv.org/abs/nlin/0206020v1

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Sep 18, 2013
09/13

by
K. B. Blyuss; S. Gupta

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We examine the properties of a recently proposed model for antigenic variation in malaria which incorporates multiple epitopes and both long-lasting and transient immune responses. We show that in the case of a vanishing decay rate for the long-lasting immune response, the system exhibits the so-called "bifurcations without parameters" due to the existence of a hypersurface of equilibria in the phase space. When the decay rate of the long-lasting immune response is different from...

Source: http://arxiv.org/abs/1201.4591v1

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Sep 18, 2013
09/13

by
K. B. Blyuss; L. B. Nicholson

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It has been known for some time that human autoimmune diseases can be triggered by viral infections. Several possible mechanisms of interactions between a virus and immune system have been analysed, with a prevailing opinion being that the onset of autoimmunity can in many cases be attributed to "molecular mimicry", where linear peptide epitopes, processed from viral proteins, mimic normal host self proteins, thus leading to a cross-reaction of immune response against virus with host...

Source: http://arxiv.org/abs/1209.4487v1

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Sep 18, 2013
09/13

by
K. B. Blyuss; Y. N. Kyrychko

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Effects of immune delay on symmetric dynamics are investigated within a model of antigenic variation in malaria. Using isotypic decomposition of the phase space, stability problem is reduced to the analysis of a cubic transcendental equation for the eigenvalues. This allows one to identify periodic solutions with different symmetries arising at a Hopf bifurcation. In the case of small immune delay, the boundary of the Hopf bifurcation is found in a closed form in terms of system parameters. For...

Source: http://arxiv.org/abs/1209.4475v1

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Sep 18, 2013
09/13

by
K. B. Blyuss; Y. N. Kyrychko

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An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is...

Source: http://arxiv.org/abs/1201.4587v1

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2.0

Jun 29, 2018
06/18

by
N. Sherborne; K. B. Blyuss; I. Z. Kiss

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This paper presents a compact pairwise model that describes the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian models with exponentially distributed infectious period and epidemics with a constant infectious period. We show how the compact approach leads to a system of equations whose size is independent of the range of node degrees, thus significantly reducing the...

Topics: Quantitative Biology, Quantitative Methods, Populations and Evolution

Source: http://arxiv.org/abs/1602.05227

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3.0

Jun 27, 2018
06/18

by
N. Sherborne; K. B. Blyuss; I. Z. Kiss

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This paper investigates the dynamics of infectious diseases with a non-exponentially distributed infectious period. This is achieved by considering a multi-stage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the...

Topics: Nonlinear Sciences, Quantitative Biology, Populations and Evolution, Physics and Society,...

Source: http://arxiv.org/abs/1503.08676

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Sep 18, 2013
09/13

by
Y. N. Kyrychko; K. B. Blyuss; E. Schoell

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This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in terms of average frequency, frequency detuning and parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insight into the dynamics inside amplitude death...

Source: http://arxiv.org/abs/1209.0133v1

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Sep 19, 2013
09/13

by
K. B. Blyuss; T. J. Bridges; G. Derks

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The stability properties of line solitary wave solutions of the (2+1)-dimensional Boussinesq equation with respect to transverse perturbations and their consequences are considered. A geometric condition arising from a multi-symplectic formulation of this equation gives an explicit relation between the parameters for transverse instability when the transverse wavenumber is small. The Evans function is then computed explicitly, giving the eigenvalues for transverse instability for all transverse...

Source: http://arxiv.org/abs/nlin/0208046v2

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3.0

Jun 29, 2018
06/18

by
G. Neofytou; Y. N. Kyrychko; K. B. Blyuss

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Cross-protection, which refers to a process whereby artificially inoculating a plant with a mild strain provides protection against a more aggressive isolate of the virus, is known to be an effective tool of disease control in plants. In this paper we derive and analyse a new mathematical model of the interactions between two competing viruses with particular account for RNA interference. Our results show that co-infection of the host can either increase or decrease the potency of individual...

Topics: Quantitative Biology, Quantitative Methods, Chaotic Dynamics, Nonlinear Sciences, Populations and...

Source: http://arxiv.org/abs/1612.01561

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2.0

Jun 28, 2018
06/18

by
G. Neofytou; Y. N. Kyrychko; K. B. Blyuss

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In the studies of plant infections, the plant immune response is known to play an essential role. In this paper we derive and analyse a new mathematical model of plant immune response with particular account for post-transcriptional gene silencing (PTGS). Besides biologically accurate representation of the PTGS dynamics, the model explicitly includes two time delays to represent the maturation time of the growing plant tissue and the non-instantaneous nature of the PTGS. Through analytical and...

Topics: Quantitative Biology, Chaotic Dynamics, Quantitative Methods, Nonlinear Sciences

Source: http://arxiv.org/abs/1511.05475

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7.0

Jun 30, 2018
06/18

by
Y. N. Kyrychko; K. B. Blyuss; E. Schoell

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This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of Stuart-Landau oscillators, it is shown how the stability of synchronized solutions in networks with distributed delay coupling can be determined through a semi-analytic computation of Floquet exponents. The analysis of stability of fully synchronized and of...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1406.5428

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3.0

Jun 30, 2018
06/18

by
G. O. Agaba; Y. N. Kyrychko; K. B. Blyuss

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This paper analyses the dynamics of infectious disease with a concurrent spread of disease awareness. The model includes local awareness due to contacts with aware individuals, as well as global awareness due to reported cases of infection and awareness campaigns. We investigate the effects of time delay in response of unaware individuals to available information on the epidemic dynamics by establishing conditions for the Hopf bifurcation of the endemic steady state of the model. Analytical...

Topics: Populations and Evolution, Quantitative Biology, Chaotic Dynamics, Nonlinear Sciences, Quantitative...

Source: http://arxiv.org/abs/1704.05912

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2.0

Jun 30, 2018
06/18

by
G. O. Agaba; Y. N. Kyrychko; K. B. Blyuss

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This paper analyses an SIRS-type model for infectious diseases with account for behavioural changes associated with the simultaneous spread of awareness in the population. Two types of awareness are included into the model: private awareness associated with direct contacts between unaware and aware populations, and public information campaign. Stability analysis of different steady states in the model provides information about potential spread of disease in a population, and well as about how...

Topics: Populations and Evolution, Quantitative Biology, Chaotic Dynamics, Nonlinear Sciences, Quantitative...

Source: http://arxiv.org/abs/1702.04999

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42

Sep 18, 2013
09/13

by
Y. N. Kyrychko; K. B. Blyuss; P. Hoevel; E. Schoell

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Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived exact stability boundary. The approximate and exact stability borders agree quite well for the large time delay, and the inclusion of a time-delayed velocity feedback improves this agreement for small delays. Theoretical results are complemented by a numerically...

Source: http://arxiv.org/abs/1201.5957v1

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48

Sep 18, 2013
09/13

by
K. B. Blyuss; Y. N. Kyrychko; P. Hoevel; E. Schoell

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We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a corresponding characteristic equation with two time delays. An analytic expression for the stabilizing control strength is derived in terms of original system parameters and the time delay of the control. Theoretical and numerical results show that the interplay...

Source: http://arxiv.org/abs/1201.5964v1

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3.0

Jun 28, 2018
06/18

by
K. Parmar; K. B. Blyuss; Y. N. Kyrychko; S. J. Hogan

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In this review we discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.

Topics: Molecular Networks, Quantitative Biology, Quantitative Methods

Source: http://arxiv.org/abs/1510.08513

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36

Sep 18, 2013
09/13

by
Y. N. Kyrychko; K. B. Blyuss; S. J. Hogan; E. Schoell

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This paper studies the effects of a time-delayed feedback control on the appearance and development of spatiotemporal patterns in a reaction-diffusion system. Different types of control schemes are investigated, including single-species, diagonal, and mixed control. This approach helps to unveil different dynamical regimes, which arise from chaotic state or from traveling waves. In the case of spatiotemporal chaos, the control can either stabilize uniform steady states or lead to bistability...

Source: http://arxiv.org/abs/1201.6151v1

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3.0

Jun 29, 2018
06/18

by
N. Sherborne; J. C. Miller; K. B. Blyuss; I. Z. Kiss

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This paper presents a novel extension of the edge-based compartmental model for epidemics with arbitrary distributions of transmission and recovery times. Using the message passing approach we also derive a new pairwise-like model for epidemics with Markovian transmission and an arbitrary recovery period. The new pairwise-like model allows one to formally prove that the message passing and edge-based compartmental models are equivalent in the case of Markovian transmission and arbitrary...

Topics: Quantitative Biology, Quantitative Methods, Populations and Evolution

Source: http://arxiv.org/abs/1611.04030