相关论文: Exact equations for SIR epidemics on tree graphs
A Markovian SIR (Susceptible-Infectious-Recovered) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours.…
We investigate what structural aspects of a collection of twelve empirical temporal networks of human contacts are important to disease spreading. We scan the entire parameter spaces of the two canonical models of infectious disease…
We consider a very general stochastic model for an SIR epidemic on a network which allows an individual's infectious period, and the time it takes to contact each of its neighbours after becoming infected, to be correlated. We write down…
We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions…
The Susceptible-Infectious-Recovered (SIR) model is the canonical model of epidemics of infections that make people immune upon recovery. Many of the open questions in computational epidemiology concern the underlying contact structure's…
In this paper we study a susceptible infectious recovered (SIR) model with asymptomatic patients, contact tracing and isolation on a configuration network. Using degree based approximation, we derive a system of differential equations for…
This paper is concerned with the growth rate of SIR (Susceptible-Infectious-Recovered) epidemics with general infectious period distribution on random intersection graphs. This type of graph is characterized by the presence of cliques…
In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on…
We propose a new network-based SIR epidemic model in which transmission is modulated by a curvature-weighted contact matrix that encodes structural and geometric features of the underlying graph. The formulation encompasses both…
We investigate the expected time to extinction in the susceptible-infectious-susceptible (SIS) model of disease spreading. Rather than using stochastic simulations, or asymptotic calculations in network models, we solve the extinction time…
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…
This paper provides an additional probabilistic interpretation of the limiting functions for the SIR epidemic on the configuration model derived in the paper by Janson, Luczak and Windridge (2014).
We study the stochastic susceptible-infected-recovered (SIR) model with time-dependent forcing using analytic techniques which allow us to disentangle the interaction of stochasticity and external forcing. The model is formulated as a…
We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of a Markovian regime-switching. We first prove the existence of a unique global positive solution, and find a positive invariant…
We study the spread of an SIRS-type epidemic with vaccination on network. Starting from an exact Markov description of the model, we investigate the mean epidemic lifetime by providing a sufficient condition for fast extinction that depends…
Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for 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…
To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a…
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…
Over the years numerous models of SIS (susceptible - infected - susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general…