Related papers: Social contact processes and the partner model
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barab\'asi-Albert (BA),…
Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process (CP) where the contagion is expanded at…
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…
We study the dynamics of secondary infections on networks, in which only the individuals currently carrying a certain primary infection are susceptible to the secondary infection. In the limit of large sparse networks, the model is mapped…
Real epidemic spreading networks often composed of several kinds of networks interconnected with each other, and the interrelated networks have the different topologies and epidemic dynamics. Moreover, most human diseases are derived from…
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…
We consider the extinction time of the contact process on increasing sequences of finite graphs obtained from a variety of random graph models. Under the assumption that the infection rate is above the critical value for the process on the…
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…
A bootstrap percolation process on a graph G is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round every uninfected node which has at least r infected neighbours…
Many infectious diseases can lead to re-infection. We examined the relationship between the prevalence of repeat infection and the basic reproductive number (R0). First we solved a generic, deterministic compartmental model of re-infection…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate $\lambda$. When a new pathogen is born, it has the same type as its parent with probability $1 - r$. With probability $r$, a…
In this paper, we study a reaction-diffusion vector-host epidemic model. We define the basic reproduction number $R_0$ and show that $R_0$ is a threshold parameter: if $R_0\le 1$ the disease free steady state is globally stable; if $R_0>1$…
The contact process, or SIS epidemic, is a continuous-time Markov process used to model the spread of infection on a graph. Each vertex is either healthy or infected, and each infected vertex independently infects each of its healthy…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
The basic and effective reproduction numbers are widely used metrics for characterizing the dynamics of infectious disease epidemics. However, the interpretation of these numbers is based on the assumption of homogeneous mixing and may not…
We develop a stochastic framework for viral population dynamics at the cellular level that explicitly incorporates the replication cycle with random stage durations. The model is formulated as a structured birth-death process coupled with a…
Accurate epidemic forecasting requires models that account for the layered and heterogeneous nature of real social interactions. The basic reproduction number $\mathcal R_0$ calculated from models that assume homogeneous mixing or…