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During the ongoing COVID-19 pandemic, mathematical models of epidemic spreading have emerged as powerful tools to produce valuable predictions of the evolution of the pandemic, helping public health authorities decide which intervention…
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach…
We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant…
In this paper, we study the interplay between individual behaviors and epidemic spreading in a dynamical network. We distribute agents on a square-shaped region with periodic boundary conditions. Every agent is regarded as a node of the…
This paper investigates a behavioral-feedback SIR model in which the infection rate adapts dynamically based on the fractions of susceptible and infected individuals. We introduce an invariant of motion and we characterize the peak of…
Malware spread among websites and between websites and clients is an increasing problem. Search engines play an important role in directing users to websites and are a natural control point for intervening, using mechanisms such as…
We introduce a modified SIR model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states susceptible (${\bf S}$), infected (${\bf I}$) or recovered (${\bf R}$). In…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary network of contacts by investing on disease awareness throughout the network. We model the effect of agent awareness on the dynamics of an…
Understanding interactions between the spread of multiple pathogens during an epidemic is crucial to assessing the severity of infections in human communities. In this paper, we introduce two new Multiplex Bi-Virus Reaction-Diffusion models…
We study epidemic arrival times in meta-population disease models through the lens of front propagation into unstable states. We demonstrate that several features of invasion fronts in the PDE context are also relevant to the network case.…
Self-adaptive dynamics occurs in many physical systems such as socio-economics, neuroscience, or biophysics. We formalize a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the…
The outcome of SIR epidemics with heterogeneous infective lifetimes, or heterogeneous susceptibilities, can be mapped onto a directed percolation process on the underlying contact network. In this paper we study SIR models where…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
In this paper we present a model describing Susceptible-Infected-Susceptible (SIS) type epidemics spreading on a dynamic contact network with random link activation and deletion where link ac- tivation can be locally constrained. We use and…
The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could…
Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by…
In epidemiology, an epidemic is defined as the spread of an infectious disease to a large number of people in a given population within a short period of time. In the marketing context, a message is viral when it is broadly sent and…
Two crucial elements facilitate the understanding and control of communicable disease spread within a social setting. These components are, the underlying contact structure among individuals that determines the pattern of disease…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…