Konstantin B. Blyuss

Immunological serotype interactions and their effect on the epidemiological pattern of dengue

Long-term epidemiological data reveal multi-annual fluctuations in the incidence of dengue fever and dengue haemorrhagic fever, as well as complex cyclical behaviour in the dynamics of the four serotypes of the dengue virus. It has previously been proposed that these patterns are due to the phenomenon of the so-called antibody-dependent enhancement (ADE) among dengue serotypes, whereby viral replication is increased during secondary infection with a heterologous serotype; however, recent studies have implied that this positive reinforcement cannot account for the temporal patterns of dengue and that some form of cross-immunity or external forcing is necessary. Here, we show that ADE alone can produce the observed periodicities and desynchronized oscillations of individual serotypes if its effects are decomposed into its two possible manifestations: enhancement of susceptibility to secondary infections and increased transmissibility from individuals suffering from secondary infections. This decomposition not only lowers the level of enhancement necessary for realistic disease patterns but also reduces the risk of stochastic extinction. Furthermore, our analyses reveal a time-lagged correlation between serotype dynamics and disease incidence rates, which could have important implications for understanding the irregular pattern of dengue epidemics.

Real-time dynamic substructuring in a coupled oscillator-pendulum system

Real-time dynamic substructuring is a powerful testing method, which brings together analytical, numerical and experimental tools for the study of complex structures. It consists of replacing one part of the structure with a numerical model, which is connected to the remainder of the physical structure (the substructure) by a transfer system. In order to provide reliable results, this hybrid system must remain stable during the whole test. A primary mechanism for destabilization of these type of systems is the delays which are naturally present in the transfer system. In this paper, we apply the dynamic substructuring technique to a nonlinear system consisting of a pendulum attached to a mechanical oscillator. The oscillator is modelled numerically and the transfer system is an actuator. The system dynamics is governed by two coupled second-order neutral delay differential equations. We carry out local and global stability analyses of the system and identify the delay dependent stability boundaries for this type of system. We then perform a series of hybrid experimental tests for a pendulum–oscillator system. The results give excellent qualitative and quantitative agreement when compared to the analytical stability results.

Stability and Bifurcations in an Epidemic Model with Varying Immunity Period

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 performed using DDE-BIFTOOL and traceDDE to investigate different dynamical regimes in the model using numerical continuation for different values of system parameters and different integral kernels.

Amplitude death in systems of coupled oscillators with distributed-delay coupling

This paper studies the effects of coupling with distributed delay on the suppression of oscillations in a system of coupled Stuart-Landau oscillators. Conditions for amplitude death are obtained in terms of strength and phase of the coupling, as well as the mean time delay and the width of the delay distribution for uniform and gamma distributions. Analytical results are confirmed by numerical computation of the eigenvalues of the corresponding characteristic equations. These results indicate that larger widths of delay distribution increase the regions of amplitude death in the parameter space. In the case of a uniformly distributed delay kernel, for sufficiently large width of the delay distribution it is possible to achieve amplitude death for an arbitrary value of the average time delay, provided that the coupling strength has a value in the appropriate range. For a gamma distribution of delay, amplitude death is also possible for an arbitrary value of the average time delay, provided that it exceeds a certain value as determined by the coupling phase and the power law of the distribution. The coupling phase has a destabilizing effect and reduces the regions of amplitude death.

Control of spatiotemporal patterns in the Gray–Scott model

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 between a trivial steady state and a propagating traveling wave. Furthermore, when the basic state is a stable traveling pulse, the control is able to advance stationary Turing patterns or yield the above-mentioned bistability regime. In each case, the stability boundary is found in the parameter space of the control strength and the time delay, and numerical simulations suggest that diagonal control fails to control the spatiotemporal chaos.

Modelling meningococcal meningitis in the African meningitis belt

SUMMARYMeningococcal meningitis is a major public health problem in a large area of sub-Saharan Africa known as the meningitis belt. Disease incidence increases every dry season, before dying out with the first rains of the year. Large epidemics, which can kill tens of thousands of people, occur frequently but unpredictably every 6-14 years. It has been suggested that these patterns may be attributable to complex interactions between the bacteria, human hosts and the environment. We used deterministic compartmental models to investigate how well simple model structures with seasonal forcing were able to qualitatively capture these patterns of disease. We showed that the complex and irregular timing of epidemics could be caused by the interaction of temporary immunity conferred by carriage of the bacteria together with seasonal changes in the transmissibility of infection. This suggests that population immunity is an important factor to include in models attempting to predict meningitis epidemics.

On a basic model of a two-disease epidemic

This paper considers a basic model for a spread of two diseases in a population. The equilibria of the model are found, and their stability is investigated. In particular, we prove the stability result for a disease-free and a one-disease steady-states. Bifurcation diagrams are used to analyse the stability of possible branches of equilibria, and also they indicate the existence of a co-infected equilibrium with both diseases present. Finally, numerical simulations of the model are performed to study the behaviour of the solutions in different regions of the parameter space.

Master-equation approach to understanding multistate phase-change memories and processors

A master-equation approach is used to perform dynamic modeling of phase-transformation processes that define the operating regimes and performance attributes of electronic (and optical) processors and multistate memory devices based on phase-change materials. The predictions of the so-called energy accumulation and direct-overwrite regimes, prerequisites for processing and memory functions, respectively, emerge in detail from the model, providing a theoretical framework for future device design and evaluation.

Amplitude and phase dynamics in oscillators with distributed-delay coupling

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, the conditions for amplitude death are obtained in terms of average frequency, frequency detuning and the 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 insights into the dynamics inside amplitude death regions, the eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated, using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions.

Time delay control of symmetry-breaking primary and secondary oscillation death

We show that oscillation death as a specific type of oscillation suppression, which implies symmetry breaking, can be controlled by introducing time-delayed coupling. In particular, we demonstrate that time delay influences the stability of an inhomogeneous steady state, providing the opportunity to modulate the threshold for oscillation death. Additionally, we find a novel type of oscillation death representing a secondary bifurcation of an inhomogeneous steady state.