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We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from…
Compartmental epidemic models are among the most popular ones in epidemiology. For the parameters (e.g., the transmission rate) characterizing these models, the majority of researchers simplify them as constants, while some others manage to…
Many dynamic processes on complex networks, from disease outbreaks to cascading failures, can rapidly accelerate once a critical threshold is exceeded, potentially leading to severe social and economic costs. Therefore, in order to develop…
A pandemic is the spread of a disease across large regions, and can have devastating costs to the society in terms of health, economic and social. As such, the study of effective pandemic mitigation strategies can yield significant positive…
The integration of empirical data in computational frameworks to model the spread of infectious diseases poses challenges that are becoming pressing with the increasing availability of high-resolution information on human mobility and…
Partial differential equation (PDE) models for infectious diseases, while less common than their ordinary differential equation (ODE) counterparts, have found successful applications for many years. Such models are typically of…
One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the…
The evolution of network structure and the spreading of epidemic are common coexistent dynamical processes. In most cases, network structure is treated either static or time-varying, supposing the whole network is observed in a same time…
This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set…
We study a susceptible-infected-recovered (SIR) epidemic model on a network of $n$ interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
Delayed neural field models can be viewed as a dynamical system in an appropriate functional analytic setting. On two dimensional rectangular space domains, and for a special class of connectivity and delay functions, we describe the…
Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading,…
A dynamic model of a society is studied where each person is an uncorrelated and non-interacting random walker. A dynamical random graph represents the acquaintance network of the society whose nodes are the individuals and links are the…
We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all…
We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models…
The SIS (susceptible-infected-susceptible) epidemic model on an arbitrary network, without making approximations, is a $2^n$-state Markov chain with a unique absorbing state (the all-healthy state). This makes analysis of the SIS model and,…
We study the Susceptible-Infected-Recovered (SIR) and the Susceptible-Exposed-Infected-Recovered (SEIR) models of epidemics, with possibly time-varying rates, on a class of networks that are locally tree-like, which includes sparse…
We consider an SIR-type (Susceptible $\to$ Infected $\to$ Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model…
An integrable discretization of the SIR model with vaccination is proposed. The conserved quantities of the continuous model are inherited to the discrete model through the discretization, since the discretization is based on the…