Related papers: Exact solution of a stochastic SIR model
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…
Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node…
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…
The SIR model with spatially inhomogeneous infection rate is studied with numerical simulations in one, two, and three dimensions, considering the case that the infection spreads inhomogeneously in densely populated regions or hot spots. We…
In general, the rates of infection and removal (whether through recovery or death) are nonlinear functions of the number of infected and susceptible individuals. One of the simplest models for the spread of infectious diseases is the SIR…
The infection dynamics of a population under stationary isolation conditions is modeled. It is underlined that the stationary character of the isolation measures can be expected to imply that an effective SIR model with constant parameters…
In a collection of particles performing independent random walks on $\mathbb Z^d$ we study the spread of an infection with SIR dynamics. Susceptible particles become infected when they meet an infected particle. Infected particles heal and…
We consider a Susceptible-Infective-Recovered (SIR) model, where the mechanism for the renewal of susceptibles is demographic, on a ring with next nearest neighbour interactions, and a family of correlated pair approximations (CPA),…
A stochastic SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a social network is analysed. The underlying social network is described by an Erd\H{o}s-R\'{e}nyi random graph but, during the course of the epidemic,…
We consider the SIR model and study the first time the number of infected individuals begins to decrease and the first time this population is below a given threshold. We interpret these times as functions of the initial susceptible and…
Based on the classical continuous system initially proposed by Bailey in 1975, we present a novel Susceptible--Infected--Removed (SIR) model defined in quantum time, where the temporal evolution is governed by a non-uniform time grid. An…
Exact solution of the Susceptible-Infectious-Recovered (SIR) epidemic model is derived, and various properties of solution are obtained directly from the exact solution. It is shown that there exists an exact solution of an initial value…
In this work, some new exact and approximate analytical solutions are obtained for the SIR epidemic model, which is formulated in terms of dimensionless variables and parameters. The susceptibles population (S) is in this way explicitly…
A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing…
Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size $n$. A Markovian SIR (susceptible $\to$ infective $\to$ recovered) infectious disease,…
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…
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the…
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…