Related papers: Exact solution of a stochastic SIR model
We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also…
In this work, we discuss the SIR epidemiological model and different variations of it applied to the propagation of the COVID-19 pandemia; we employ the data of the state of Guanajuato and of Mexico. We present some considerations that can…
We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from…
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…
In this paper, a susceptible-infected-susceptible (SIS) model with identical infectivity, where each node is assigned with the same capability of active contacts, $A$, at each time step, is presented. We found that on scale-free networks,…
We introduce an extension to Kermack and McKendrick's classic susceptible-infected-recovered (SIR) model in epidemiology, whose underlying mechanism of infection consists of individuals attending randomly generated social gatherings. This…
The non-population conserving SIR (SIR-NC) model to describe the spread of infections in a community is proposed and studied. Unlike the standard SIR model, SIR-NC does not assume population conservation. Although similar in form to the…
In this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre-vaccine era. We considered a stochastic SIR model on dynamical networks that involve local and global contacts among…
Motivated by our intention to use SIR-type epidemiological models in the context of dynamic networks as provided by large-scale highly interacting inhomogeneous human crowds, we investigate in this framework possibilities to reduce the…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
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…
The recent COVID-19 pandemic has shown that when the reproduction number is high and there are no proper measurements in place, the number of infected people can increase dramatically in a short time, producing a phenomenon that many…
A probabilistic approach to the epidemic evolution on realistic social-contact networks allows for characteristic differences among subjects, including the individual number and structure of social contacts, and the heterogeneity of the…
This paper is concerned with SIR (susceptible $\to$ infected $\to$ removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an…
We introduce an epidemic model with varying infectivity and general exposed and infectious periods, where the infectivity of each individual is a random function of the elapsed time since infection, those function being i.i.d. for the…
Two factors that are often ignored but could play a crucial role in the progression of an infectious disease are the distributions of inherent susceptibility ($\sigma_{inh}$) and external infectivity ($\iota_{ext}$), in a given population.…
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…
Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the…
I estimate the Susceptible-Infected-Recovered (SIR) epidemic model for Coronavirus Disease 2019 (COVID-19). The transmission rate is heterogeneous across countries and far exceeds the recovery rate, which enables a fast spread. In the…
We propose a nonstandard finite difference scheme for the Susceptible-Infected-Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution.…