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 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.

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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 the disease dynamics is affected by the two types of awareness. Numerical simulations are performed to illustrate the behaviour of the system in different dynamical regimes.

-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.Introduction. -Time-delayed couplings arise naturally in many types of networks, for instance in coupled lasers [1], neural networks [2-4], electronic circuits [5], or genetic oscillators [6], due to finite signal transmission and processing times, and memory and latency effects. While investigating real-world systems, it is necessary to take time delay into account, since the presence of time delay is an inherent property of the vast majority of processes that occur in nature [7,8]. Moreover, time-delayed coupling and feedback represent an important aspect of control [9]. Previous theoretical and experimental works have shown that time delay can be treated as a control parameter and can stabilize initially unstable states. In particular, time-delayed feedback has been used to stabilize unstable periodic orbits embedded in a deterministic chaotic attractor [10,11], or generated by a Hopf bifurcation [12], unstable steady states [13], spatio-temporal patterns [14][15][16], or control the coherence and timescales of stochastic motion [17]. In coupled nonlinear systems and networks time-delayed couplings represent an ubiquitous feature [18] which can also be used to control stability.

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.

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.

This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes. This implies that the new model is exact on the ensemble of configuration model networks of infinite size. For the case of Markovian transmission the message passing model is re-parametrised into a pairwise-like model which is then used to derive many well-known pairwise models for regular networks, or when the infectious period is exponentially distributed or is of a fixed length.