相关论文: The SIR model of an epidemic

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 SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…

We develop a multiple compartment Susceptible-Infected-Recovered (SIR) model to analyze the spread of several infectious diseases through different geographic areas. Additionally, we propose a data-quality sensitive optimization framework…

We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic…

We investigate the SIR epidemic on a dynamic inhomogeneous Erd\H{o}s-R\'enyi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large…

The rapidly spreading Covid-19 that affected almost all countries, was first reported at the end of 2019. As a consequence of its highly infectious nature, countries all over the world have imposed extremely strict measures to control its…

We have derived the governing equations for an SIR model with delay terms in both the infectivity and recovery of the disease. The equations are derived by modelling the dynamics as a continuous time random walk, where individuals move…

Infection spread among individuals is modelled with a continuous time Markov chain, in which subject interactions depend on their distance in space. The well known SIR model and non local variants of the latter are then obtained as large…

A pandemic is the spread of a disease across large regions, and can have devastating costs to the society in terms of health, economic and social. As such, the study of effective pandemic mitigation strategies can yield significant positive…

In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…

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, 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…

The Susceptible-Infected-Recovered (SIR) epidemic model as well as its generalizations are extensively used for the study of the spread of infectious diseases, and for the understanding of the dynamical evolution of epidemics. From SIR type…

There is increasing evidence that one of the most difficult problems in trying to control the ongoing COVID-19 epidemic is the presence of a large cohort of asymptomatic infectives. We develop a SIR-type model taking into account the…

Dynamic properties of spreading infection through a heterogeneous population are studied numerically and analytically using a dynamic variant of Watts and Strogatz Small World Network-based stochastic Susceptible-Exposed-Infectious-Removed…

Traditional epidemic models consider that individual processes occur at constant rates. That is, an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly fails…

In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite…

Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic…

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…

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…