Related papers: Analysis of a network--based SIR model
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the…
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which…
Networks have become an important tool for infectious disease epidemiology. Most previous theoretical studies of transmission network models have either considered simple Markovian dynamics at the individual level, or have focused on the…
Realistic human contact networks capable of spreading infectious disease, for example studied in social contact surveys, exhibit both significant degree heterogeneity and clustering, both of which greatly affect epidemic dynamics. To…
We formulate a multi-group and multi-vector epidemic model in which hosts' dynamics is captured by staged-progression $SEIR$ framework and the dynamics of vectors is captured by an $SI$ framework. The proposed model describes the evolution…
We investigate the long-time dynamics of a SIR epidemic model in the case of a population of pathogens infecting a homogeneous host population. The pathogen population is structured by a genotypic variable. When the initial mass of the…
In this paper, we study the dynamics of the susceptible-infected-recovered (SIR) model on a network with community structure, namely the stochastic block model (SBM). As usual, the SIR model is a stochastic model for an epidemic where…
In this work, we study the epidemic SIR model on a system which takes into consideration face-to-face interaction networks. This approach has been used as prototype to describe people interactions in different kinds of social organizations…
We propose a novel SIR epidemic model which is driven by the transmission of infection packets in networks. Specifically, infected nodes generate and deliver infection packets causing the spread of the epidemic, while recovered nodes block…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
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…
Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks…
Since the last century, deterministic compartmental models have emerged as powerful tools to predict and control epidemic outbreaks, in many cases helping to mitigate their impacts. A key quantity for these models is the so-called Basic…
Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with…
Most real networks are characterized by connectivity patterns that evolve in time following complex, non-Markovian, dynamics. Here we investigate the impact of this ubiquitous feature by studying the Susceptible-Infected-Recovered (SIR) and…
In this paper, we focus on the node-based epidemic modeling for networks, introduce the propagation medium and propose a node-based Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model with infective media. Theoretical…
The ever-changing world of disease study heavily relies on mathematical models. They are key in finding and controlling infectious diseases. We aim to explore these mathematical tools used for studying disease spread in biology. The SEIR…
We analyze the ordering dynamics of the voter model in different classes of complex networks. We observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks. We also find…
The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an…
Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories…