Epidemic spreading with awareness on multi-layer activity-driven networks

Dynamics of COVID-19 spreading model with social media public health awareness diffusion over multiplex networks: Analysis and control

In human society, individual interactions intrinsically change, with profound implications for epidemics. The activity-driven model, a type of temporal network, offers an excellent framework to study epidemic processes in dynamical interaction. In this work, we study how social attitudes affect the transmission of infectious diseases in activity-driven networks. Here, we divide a population into “risk-ignorant” and “risk-averse”, in which risk-averse individuals will reduce their social intensity (Social intensity refers to the number of social contacts in the social process) and risk-ignorant individuals will not. A parameter p controls the proportion of risk-averse individuals, and therefore risk-ignorant individuals by 1-p. With the aid of mean-field theory, we calculate epidemic thresholds, as well as validate theoretical predictions with extensive Monte Carlo simulations. It is shown numerically and theoretically that reducing the social intensity and increasing the number of risk-averse individuals are effective ways of controlling epidemic outbreaks. An appropriate proportion of the risk-averse individual will lead to an epidemic die-out, which is based on a small spreading rate. Our research provides a new perspective for understanding the effect of the population with different social attitudes in the epidemic process.

Epidemic spreading processes on multiplex networks have richer dynamical properties than those on single layered networks. To describe the intertwined processes on such networks, heterogeneous mean field (HMF) approach for continuous-time processes and microscopic Markov chain approach for discrete-time processes have been proposed. However, it has been shown that the time evolution of infected individuals and the final epidemic size obtained from these approaches have noticeable discrepancy comparing to those from Monte Carlo simulations. In this paper, we extend the approach of effective degree theory (EDT) on multiplex networks. We will show that predictions obtained from the EDT have excellent agreement with Monte Carlo simulations. Moreover, since the dynamics on multiplex networks involve more dynamical variables, which may invoke more computations, to reduce the computational burden, we further develop an approach based on partial effective degree theory (PEDT) for analyzing the dynamics on multiplex networks, where one layer adopts EDT and the other layer adopts the HMF. Our results show that PEDT has a good performance in predicting the target dynamical process.

Despite intensive studies on epidemic spreading in metapopulation networks, the infection process is normally assumed to be a Markovian process without considering time-dependent infectivity. In this paper, a reaction-diffusion SIRS epidemic model with non-Markovian infection processes is constructed on metapopulation networks, where the infection rate function associated with the sojourn time in the infected state is obtained by constructing the generation time distribution of the emerging infection process. Meanwhile, the recurrent mobility patterns are incorporated by the metapopulation model. By Lyapunov stability analysis, the epidemic outbreak condition is derived theoretically. The results show that the non-Markovian infection characteristics can significantly alter the transient behavior of epidemic spreading under the same basic reproduction number. Furthermore, with the increase in the average time for an infected individual to generate secondary cases in the non-Markovian process, the impact of mobility rate on transient epidemic spreading behavior will be reduced. Finally, mobility can have a suppressing effect on epidemic spreading dynamics when the population distribution exhibits significant asymmetry. The results can sharpen our understanding of the role of real-world non-Markovian infection processes in epidemic outbreaks.

Traffic-driven SIR epidemic spread dynamics on scale-free networks

We study the effect of heterogeneous temporal activations on epidemic spreading in temporal networks. We focus on the susceptible-infected-susceptible model on activity-driven networks with burstiness. By using an activity-based mean-field approach, we derive a closed analytical form for the epidemic threshold for arbitrary activity and inter-event time distributions. We show that, as expected, burstiness lowers the epidemic threshold while its effect on prevalence is twofold. In low-infective systems burstiness raises the average infection probability, while it weakens epidemic spreading for high infectivity. Our results can help clarify the conflicting effects of burstiness reported in the literature. We also discuss the scaling properties at the transition, showing that they are not affected by burstiness.

Diffusion of resources and their impact on epidemic spreading in multilayer networks with simplicial complexes

An improved susceptible-infected-susceptible (SIS) model in the local-world evolving network model is presented to study the epidemic spreading behavior with time delay, which is added into the infected phase. The local-world evolving model displays a transition from the exponential network to the scale-free network with respect to the degree distribution. Two typical delay regimes, i.e., uniform and degree-dependent delays are incorporated into the SIS epidemic model to investigate the epidemic infection processes in the local-world network model. The results indicate that the infection delay will promote the epidemic outbreaks, increase the prevalence and reduce the critical threshold of epidemic spreading. It is also found that local-world size M will considerably influence the epidemic spreading behavior with time delay in the local-world network through large-scale numerical simulations. Simulation results are also of relevance to fight epidemic outbreaks.

Social interaction, which is intricate and time-varying, has emerged as a pivotal consideration in epidemic spreading. In this paper, we devise a UAU–SIS model for simulating awareness diffusion and epidemic spreading on temporal multiplex networks. Drawing inspiration from individuals’ self-protection behaviors, a novel adaptive update mechanism is developed. To provide a more precise representation of the collective social interactions encompassing individuals, we introduce the higher-order network structure encompassing temporal variability. Building upon the established framework of the microscopic Markov chain approach (MMCA) for static networks, we extend its applicability to the condition of temporal networks and derive the threshold within the coupled dynamics. Our extensive simulations illuminate the dual role of awareness in epidemic mitigation. Beyond solely diminishing infection probabilities through self-protective measures, individual awareness additionally facilitates to change the network structure to separate them from the infected. By elucidating these fundamental characteristics, our research contributes to advancing more effective strategies for epidemic mitigation and containment.

We investigate the role of migration patterns on the spread of epidemics in complex networks. We enhance the SIS-diffusion model on metapopulations to a nonlinear diffusion. Specifically, individuals move randomly over the network but at a rate depending on the population of the departure patch. In the absence of epidemics, the migration-driven equilibrium is described by quantifying the total number of individuals living in heavily or lightly populated areas. Our analytical approach reveals that strengthening the migration from populous areas contains the infection at the early stage of the epidemic. Moreover, depending on the exponent of the nonlinear diffusion rate, epidemic outbreaks do not always occur in the most populated areas as one might expect.

In many developing countries, public transit plays an important role in daily life. However, few existing methods have considered the influence of public transit in their models. In this work, we present a dual-perspective view of the epidemic spreading process of the individual that involves both contamination in places (such as work places and homes) and public transit (such as buses and trains). In more detail, we consider a group of individuals who travel to some places using public transit, and introduce public transit into the epidemic spreading process. Our simulation results suggest that individuals with a high public transit trip contribution rate will increase the volume of infectious people when an infectious disease outbreak occurs by affecting the social network through the public transit trip contribution rate.KeywordsCommunity structureSubway systemEarly prediction

The influence of individual emotions on the coupled model of unconfirmed information propagation and epidemic spreading in multilayer networks

Technological advances have led to a strong increase in the number of data collection efforts aimed at measuring co-presence of individuals at different spatial resolutions. It is however unclear how much co-presence data can inform us on actual face-to-face contacts, of particular interest to study the structure of a population in social groups or for use in data-driven models of information or epidemic spreading processes. Here, we address this issue by leveraging data sets containing high resolution face-to-face contacts as well as a coarser spatial localisation of individuals, both temporally resolved, in various contexts. The co-presence and the face-to-face contact temporal networks share a number of structural and statistical features, but the former is (by definition) much denser than the latter. We thus consider several down-sampling methods that generate surrogate contact networks from the co-presence signal and compare them with the real face-to-face data. We show that these surrogate networks reproduce some features of the real data but are only partially able to identify the most central nodes of the face-to-face network. We then address the issue of using such down-sampled co-presence data in data-driven simulations of epidemic processes, and in identifying efficient containment strategies. We show that the performance of the various sampling methods strongly varies depending on context. We discuss the consequences of our results with respect to data collection strategies and methodologies.

The structure of complex networks has long been understood to play a role in transmission and spreading phenomena on a graph. Such networks form an important part of the structure of society, including transportation networks. As society fights to control the COVID-19 pandemic, an important question is how to choose the optimum balance between the full opening of transport networks and the control of epidemic spread. In this work we investigate the interplay between network dismantling and epidemic spread rate as a proxy for the imposition of travel restrictions to control disease spread. For network dismantling we focus on the weighted and unweighted forms of metrics that capture the topological and informational structure of the network. Our results indicate that there is benefit to a directed approach to imposing travel restrictions, but we identify that more detailed models of the transport network are necessary for definitive results.

Acknowledging the significance of awareness diffusion and behavioral response in contagion outbreaks has been regarded as an indispensable prerequisite for a complete understanding of epidemic spreading. Recent studies from the research community have accumulated overwhelming evidence for the incessantly evolving structure of the underlying networks. Thus there is an impelling need to capture the interplay between the epidemic spreading and awareness diffusion on time-varying networks. In this paper, we consider a behavioral model in which susceptible individuals become alert and adopt a preventive behavior under the local risk perception characterized by a decision-making threshold. The impact of awareness diffusion on the epidemic threshold is investigated under the framework of activity-driven network. Results show that the local epidemic situation in risk perception and the duration of preventive effect are crucial for raising the epidemic threshold. The analytical results are corroborated by Monte Carlo simulations.