Dynamics of epidemic diseases on a growing adaptive network

Nonlinear spreading behavior across multi-platform social media universe

Understanding how harmful content (mis/disinformation, hate, etc.) manages to spread among online communities within and across social media platforms represents an urgent societal challenge. We develop a non-linear dynamical model for such viral spreading, which accounts for the fact that online communities dynamically interconnect across multiple social media platforms. Our mean-field theory (Effective Medium Theory) compares well to detailed numerical simulations and provides a specific analytic condition for the onset of outbreaks (i.e., system-wide spreading). Even if the infection rate is significantly lower than the recovery rate, it predicts system-wide spreading if online communities create links between them at high rates and the loss of such links (e.g., due to moderator pressure) is low. Policymakers should, therefore, account for these multi-community dynamics when shaping policies against system-wide spreading.

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.

Dynamics of phase oscillator networks with synaptic weight and structural plasticity

We study the dynamics of Kuramoto oscillator networks with two distinct adaptation processes, one varying the coupling strengths and the other altering the network structure. Such systems model certain networks of oscillatory neurons where the neuronal dynamics, synaptic weights, and network structure interact with and shape each other. We model synaptic weight adaptation with spike-timing-dependent plasticity (STDP) that runs on a longer time scale than neuronal spiking. Structural changes that include addition and elimination of contacts occur at yet a longer time scale than the weight adaptations. First, we study the steady-state dynamics of Kuramoto networks that are bistable and can settle in synchronized or desynchronized states. To compare the impact of adding structural plasticity, we contrast the network with only STDP to one with a combination of STDP and structural plasticity. We show that the inclusion of structural plasticity optimizes the synchronized state of a network by allowing for synchronization with fewer links than a network with STDP alone. With non-identical units in the network, the addition of structural plasticity leads to the emergence of correlations between the oscillators' natural frequencies and node degrees. In the desynchronized regime, the structural plasticity decreases the number of contacts, leading to a sparse network. In this way, adding structural plasticity strengthens both synchronized and desynchronized states of a network. Second, we use desynchronizing coordinated reset stimulation and synchronizing periodic stimulation to induce desynchronized and synchronized states, respectively. Our findings indicate that a network with a combination of STDP and structural plasticity may require stronger and longer stimulation to switch between the states than a network with STDP only.

Moment closure approximations of susceptible-infected-susceptible epidemics on adaptive networks

The influence of people's individual responses to the spread of contagious phenomena, like the COVID-19 pandemic, is still not well understood. We investigate the Markovian Generalized Adaptive Susceptible-Infected-Susceptible (G-ASIS) epidemic model. The G-ASIS model comprises many contagious phenomena on networks, ranging from epidemics and information diffusion to innovation spread and human brain interactions. The connections between nodes in the G-ASIS model change adaptively over time, because nodes make decisions to create or break links based on the health state of their neighbors. Our contribution is fourfold. First, we rigorously derive the first-order and second-order mean-field approximations from the continuous-time Markov chain. Second, we illustrate that the first-order mean-field approximation fails to approximate the epidemic threshold of the Markovian G-ASIS model accurately. Third, we show that the second-order mean-field approximation is a qualitative good approximation of the Markovian G-ASIS model. Finally, we discuss the Adaptive Information Diffusion (AID) model in detail, which is contained in the G-ASIS model. We show that, similar to most other instances of the G-ASIS model, the AID model possesses a unique steady state, but that in the AID model, the convergence time toward the steady state is very large. Our theoretical results are supported by numerical simulations.

How do mobility restrictions and social distancing during COVID-19 affect oil price?

This paper provides an analysis of the effect of the COVID-19 outbreak on the crude oil price. Using a newly developed air mobility index and Apple's driving trends index, we assess the effect of human mobility restrictions and social distancing during the COVID-19 pandemic on the crude oil price. We apply a quantile regression model, which evaluates different quantiles of the crude oil price. We also conduct an extreme value modeling, which examines the lower tail of the crude oil price distribution. We find that both the air mobility index and driving trends index significantly influence lower and upper quantiles of the WTI crude oil price. The extreme value models suggest that there is a potential risk of a negative crude oil price for a sudden extreme fall of air mobility.

Impacts of COVID-19 local spread and Google search trend on the US stock market

We develop a novel temporal complex network approach to quantify the US county level spread dynamics of COVID-19. We use both conventional econometric and Machine Learning (ML) models that incorporate the local spread dynamics, COVID-19 cases and death, and Google search activities to assess if incorporating information about local spreads improves the predictive accuracy of models for the US stock market. The results suggest that COVID-19 cases and deaths, its local spread, and Google searches have impacts on abnormal stock prices between January 2020 to May 2020. Furthermore, incorporating information about local spread significantly improves the performance of forecasting models of the abnormal stock prices at longer forecasting horizons.

Chaotic transients, riddled basins, and stochastic transitions in coupled periodic logistic maps

A system of two coupled map-based oscillators is studied. As units, we use identical logistic maps in two-periodic modes. In this system, increasing coupling strength significantly changes deterministic regimes of collective dynamics with coexisting periodic, quasiperiodic, and chaotic attractors. We study how random noise deforms these dynamical regimes in parameter zones of mono- and bistability, causes "order-chaos" transformations, and destroys regimes of in-phase and anti-phase synchronization. In the analytical study of these noise-induced phenomena, a stochastic sensitivity technique and a method of confidence domains for periodic and multi-band chaotic attractors are used. In this analysis, a key role of chaotic transients and geometry of "riddled" basins is revealed.

Infection spreading and recovery in a square lattice

We investigate spreading and recovery of disease in a square lattice, and, in particular, emphasize the role of the initial distribution of infected patches in the network on the progression of an endemic and initiation of a recovery process, if any, due to migration of both the susceptible and infected hosts. The disease starts in the lattice with three possible initial distribution patterns of infected and infection-free sites, viz., infected core patches (ICP), infected peripheral patches (IPP), and randomly distributed infected patches (RDIP). Our results show that infection spreads monotonically in the lattice with increasing migration without showing any sign of recovery in the ICP case. In the IPP case, it follows a similar monotonic progression with increasing migration; however, a self-organized healing process starts for higher migration, leading the lattice to full recovery at a critical rate of migration. Encouragingly, for the initial RDIP arrangement, chances of recovery are much higher with a lower rate of critical migration. An eigenvalue-based semianalytical study is made to determine the critical migration rate for realizing a stable infection-free lattice. The initial fraction of infected patches and the force of infection play significant roles in the self-organized recovery. They follow an exponential law, for the RDIP case, that governs the recovery process. For the frustrating case of ICP arrangement, we propose a random rewiring of links in the lattice allowing long-distance migratory paths that effectively initiate a recovery process. Global prevalence of infection thereby declines and progressively improves with the rewiring probability that follows a power law with the critical migration and leads to the birth of emergent infection-free networks.

Classification of link-breaking and link-creation updating rules in susceptible-infected-susceptible epidemics on adaptive networks

In the classical susceptible-infected-susceptible (SIS) model, a disease or infection spreads over a given, mostly fixed graph. However, in many real complex networks, the topology of the underlying graph can change due to the influence of the dynamical process. In this paper, besides the spreading process, the network adaptively changes its topology based on the states of the nodes in the network. An entire class of link-breaking and link-creation mechanisms, which we name Generalized Adaptive SIS (G-ASIS), is presented and analyzed. For each instance of G-ASIS using the complete graph as initial network, the relation between the epidemic threshold and the effective link-breaking rate is determined to be linear, constant, or unknown. Additionally, we show that there exist link-breaking and link-creation mechanisms for which the metastable state does not exist. We confirm our theoretical results with several numerical simulations.

Contact Adaption During Epidemics: A Multilayer Network Formulation Approach

People change their physical contacts as a preventive response to infectious disease propagations. Yet, only a few mathematical models consider the coupled dynamics of the disease propagation and the contact adaptation process. This paper presents a model where each agent has a default contact neighborhood set, and switches to a different contact set once she becomes alert about infection among her default contacts. Since each agent can adopt either of two possible neighborhood sets, the overall contact network switches among [Formula: see text] possible configurations. Notably, a two-layer network representation can fully model the underlying adaptive, state-dependent contact network. Contact adaptation influences the size of the disease prevalence and the epidemic threshold-a characteristic measure of a contact network robustness against epidemics-in a nonlinear fashion. Particularly, the epidemic threshold for the presented adaptive contact network belongs to the solution of a nonlinear Perron-Frobenius (NPF) problem, which does not depend on the contact adaptation rate monotonically. Furthermore, the network adaptation model predicts a counter-intuitive scenario where adaptively changing contacts may adversely lead to lower network robustness against epidemic spreading if the contact adaptation is not fast enough. An original result for a class of NPF problems facilitate the analytical developments in this paper.

Information Spread and Topic Diffusion in Heterogeneous Information Networks

Diffusion of information in complex networks largely depends on the network structure. Recent studies have mainly addressed information diffusion in homogeneous networks where there is only a single type of nodes and edges. However, some real-world networks consist of heterogeneous types of nodes and edges. In this manuscript, we model information diffusion in heterogeneous information networks, and use interactions of different meta-paths to predict the diffusion process. A meta-path is a path between nodes across different layers of a heterogeneous network. As its most important feature the proposed method is capable of determining the influence of all meta-paths on the diffusion process. A conditional probability is used assuming interdependent relations between the nodes to calculate the activation probability of each node. As independent cascade models, we consider linear threshold and independent cascade models. Applying the proposed method on two real heterogeneous networks reveals its effectiveness and superior performance over state-of-the-art methods.