An analytical framework for the study of epidemic models on activity driven networks

Abstract

Network theory has greatly contributed to an improved understanding of epidemic processes, offering an empowering framework for the analysis of real-world data, prediction of disease outbreaks, and formulation of containment strategies. However, the current state of knowledge largely relies on time-invariant networks, which are not adequate to capture several key features of a number of infectious diseases. Activity driven networks (ADNs) constitute a promising modelling framework to describe epidemic spreading over time varying networks, but a number of technical and theoretical gaps remain open. Here, we lay the foundations for a novel theory to model general epidemic spreading processes over time-varying, ADNs. Our theory derives a continuous-time model, based on ordinary differential equations (ODEs), which can reproduce the dynamics of any discrete-time epidemic model evolving over an ADN. A rigorous, formal framework is developed, so that a general epidemic process can be systematically mapped, at first, on a Markov jump process, and then, in the thermodynamic limit, on a system of ODEs. The obtained ODEs can be integrated to simulate the system dynamics, instead of using computationally intensive Monte Carlo simulations. An array of mathematical tools for the analysis of the proposed model is offered, together with techniques to approximate and predict the dynamics of the epidemic spreading, from its inception to the endemic equilibrium. The theoretical framework is illustrated step-by-step through the analysis of a susceptible–infected–susceptible process. Once the framework is established, applications to more complex epidemic models are presented, along with numerical results that corroborate the validity of our approach. Our framework is expected to find application in the study of a number of critical phenomena, including behavioural changes due to the infection, unconscious spread of the disease by exposed individuals, or the removal of nodes from the network of contacts.

Backbone reconstruction in temporal networks from epidemic data

“…The propagation of the disease may occur with probability λ ∈ [0, 1] along each link of the RADN independently of the others, such that Following the recovery mechanism, instead, each node i that is infected at time t, recovers at time t + 1 with probability μ ∈ [0, 1], becoming again susceptible to the epidemics. The generality of our theoretical approach suggests that our algorithm could be extended to more complex epidemic models on ADNs [29,57].…”

Risk assessment of vector-borne disease transmission using spatiotemporal network model and climate data with an application of dengue in Bangladesh

“…Y i is the set of infected neighbors of node i within the spatiotemporal network at time t. The parameter δ is the intrinsic incubation rate, which governs the transition from exposed to infected state. The transition from infected to removed state is expressed with the removal rate γ. Incubation rate δ and removal rate γ is node-based transition rates, whose values are assumed equal to 0.17 and 0.14 respectively, and are time-invariant in this work [44,45]. These values of δ and γ reflect the means of exponentially distributed parameter values used in the spatiotemporal spreading process.…”

Risk assessment of Ebola virus disease spreading in Uganda using a two-layer temporal network

“…used an ADN to emulate the dynamics of EVD in Liberia and offer a one-year prediction 21 . The effect on contact tracing on the spreading dynamics has also been quantified using an ADN 38,39 . An activity-driven network has a limitation as it randomly creates new links every time.…”