Role of Time Scales in the Coupled Epidemic-Opinion Dynamics on Multiplex Networks

Modelling the epidemic’s spread on multiplex networks, considering complex human behaviours, has recently gained the attention of many scientists. In this work, we study the interplay between epidemic spreading and opinion dynamics on multiplex networks. An agent in the epidemic layer could remain in one of five distinct states, resulting in the SIRQD model. The agent’s attitude towards respecting the restrictions of the pandemic plays a crucial role in its prevalence. In our model, the agent’s point of view could be altered by either conformism mechanism, social pressure, or independent actions. As the underlying opinion model, we leverage the q-voter model. The entire system constitutes a coupled opinion–dynamic model where two distinct processes occur. The question arises of how to properly align these dynamics, i.e., whether they should possess equal or disparate timescales. This paper highlights the impact of different timescales of opinion dynamics on epidemic spreading, focusing on the time and the infection’s peak.

Relay interlayer synchronisation: invariance and stability conditions

In this paper, the existence (invariance) and stability (locally and globally) of relay interlayer synchronisation (RIS) are investigated in a chain of multiplex networks. The local dynamics of the nodes in the symmetric positions layers on both sides of the non-identical middlemost layer(s) are identical. The local and global stability conditions for this synchronisation state are analytically derived based on the master stability function approach and by constructing a suitable Lyapunov function, respectively. We propose an appropriate demultiplexing process for the existence of the RIS state. Then the variational equation transverse to the RIS manifold for demultiplexed networks is derived. In numerical simulations, the impact of interlayer and intralayer coupling strengths, variations of the system parameter in the relay layers and demultiplexing on the emergence of RIS in triplex and pentaplex networks are explored. Interestingly, in this multiplex network, enhancement of RIS is observed when a type of impurity via parameter mismatch in the local dynamics of the nodes is introduced in the middlemost layer. A common time-lag with small amplitude shift between the symmetric positions and central layers plays an important role for the enhancing of relay interlayer synchrony. This analysis improves our understanding of synchronisation states in multiplex networks with nonidentical layers.

Orientations and matrix function-based centralities in multiplex network analysis of urban public transport

We study urban public transport systems by means of multiplex networks in which stops are represented as nodes and each line is represented by a layer. We determine and visualize public transport network orientations and compare them with street network orientations of the 36 largest German as well as 18 selected major European cities. We find that German urban public transport networks are mainly oriented in a direction close to the cardinal east-west axis, which usually coincides with one of two orthogonal preferential directions of the corresponding street network. While this behavior is present in only a subset of the considered European cities it remains true that none but one considered public transport network has a distinct north-south-like preferential orientation. Furthermore, we study the applicability of the class of matrix function-based centrality measures, which has recently been generalized from single-layer networks to layer-coupled multiplex networks, to our more general urban multiplex framework. Numerical experiments based on highly efficient and scalable methods from numerical linear algebra show promising results, which are in line with previous studies. The centrality measures allow detailed insights into geometrical properties of urban systems such as the spatial distribution of major transport axes, which can not be inferred from orientation plots. We comment on advantages over existing methodology, elaborate on the comparison of different measures and weight models, and present detailed hyper-parameter studies. All results are illustrated by demonstrative graphical representations.