Epidemic processes over adaptive state-dependent networks

Fixation probability in evolutionary dynamics on switching temporal networks

Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of selection, and those that suppress the spreading of fitter mutants are called suppressors of selection. Research in the past two decades has found various families of amplifiers while suppressors still remain somewhat elusive. It has also been discovered that most networks are amplifiers of selection under the birth-death updating combined with uniform initialization, which is a standard condition assumed widely in the literature. In the present study, we extend the birth-death processes to temporal (i.e., time-varying) networks. For the sake of tractability, we restrict ourselves to switching temporal networks, in which the network structure deterministically alternates between two static networks at constant time intervals or stochastically in a Markovian manner. We show that, in a majority of cases, switching networks are less amplifying than both of the two static networks constituting the switching networks. Furthermore, most small switching networks, i.e., networks on six nodes or less, are suppressors, which contrasts to the case of static networks.

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.

Data-driven methods for present and future pandemics: Monitoring, modelling and managing

This survey analyses the role of data-driven methodologies for pandemic modelling and control. We provide a roadmap from the access to epidemiological data sources to the control of epidemic phenomena. We review the available methodologies and discuss the challenges in the development of data-driven strategies to combat the spreading of infectious diseases. Our aim is to bring together several different disciplines required to provide a holistic approach to epidemic analysis, such as data science, epidemiology, and systems-and-control theory. A 3M-analysis is presented, whose three pillars are: Monitoring, Modelling and Managing. The focus is on the potential of data-driven schemes to address three different challenges raised by a pandemic: (i) monitoring the epidemic evolution and assessing the effectiveness of the adopted countermeasures; (ii) modelling and forecasting the spread of the epidemic; (iii) making timely decisions to manage, mitigate and suppress the contagion. For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics, such as Covid-19, as well as their potential application to future epidemics.

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.

Spectral Analysis of Epidemic Thresholds of Temporal Networks

Many complex systems can be modeled as temporal networks with time-evolving connections. The influence of their characteristics on epidemic spreading is analyzed in a susceptible-infected-susceptible epidemic model illustrated by the discrete-time Markov chain approach. We develop the analytical epidemic thresholds in terms of the spectral radius of weighted adjacency matrix by averaging temporal networks, e.g., periodic, nonperiodic Markovian networks, and a special nonperiodic non-Markovian network (the link activation network) in time. We discuss the impacts of statistical characteristics, e.g., bursts and duration heterogeneity, as well as time-reversed characteristic on epidemic thresholds. We confirm the tightness of the proposed epidemic thresholds with numerical simulations on seven artificial and empirical temporal networks and show that the epidemic threshold of our theory is more precise than those of previous studies.

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.

Disease Spreading in Time-Evolving Networked Communities

Human communities are organized in complex webs of contacts that may be represented by a graph or network. In this graph, vertices identify individuals and edges establish the existence of some type of relations between them. In real communities, the possible edges may be active or not for variable periods of time. These so-called temporal networks typically result from an endogenous social dynamics, usually coupled to the process under study taking place in the community. For instance, disease spreading may be affected by local information that makes individuals aware of the health status of their social contacts, allowing them to reconsider maintaining or not their social contacts. Here we investigate the impact of such a dynamical network structure on disease dynamics, where infection occurs along the edges of the network. To this end, we define an endogenous network dynamics coupled with disease spreading. We show that the effective infectiousness of a disease taking place along the edges of this temporal network depends on the population size, the number of infected individuals in the population and the capacity of healthy individuals to sever contacts with the infected, ultimately dictated by availability of information regarding each individual’s health status. Importantly, we also show how dynamical networks strongly decrease the average time required to eradicate a disease.