相关论文: The SIR model of an epidemic

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…

We analytically study the SEIR (Susceptible Exposed Infectious Removed) epidemic model. The aim is to provide simple analytical expressions for the peak and asymptotic values and their characteristic times of the populations affected by the…

Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that…

Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. The model is described by a system of integro-differential equations. Parameters of our model…

We propose a stochastic SIR model, specified as a system of stochastic differential equations, to analyse the data of the Italian COVID-19 epidemic, taking also into account the under-detection of infected and recovered individuals in the…

Epidemiological models for the spread of pathogens in a population are usually only able to describe a single pathogen. This makes their application unrealistic in cases where multiple pathogens with similar symptoms are spreading…

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…

Compartmental models are valuable tools for investigating infectious diseases. Researchers building such models typically begin with a simple structure where compartments correspond to individuals with different epidemiological statuses,…

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…

We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…

The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…

We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations…

The celebrated Kermack-McKendric model of epidemics studies the transmission of a disease in a population where each individual is initially susceptible (S), may become infective (I) and then removed or recovered (R) and plays no further…

We present three data driven model-types for COVID-19 with a minimal number of parameters to provide insights into the spread of the disease that may be used for developing policy responses. The first is exponential growth, widely studied…

Compartmental models like the Susceptible-Infected-Recovered (SIR)\cite{Kermack1927} and its extensions such as the Susceptible-Exposed-Infected-Recovered (SEIRS)\cite{Ottar2020,Ignazio2021,Grimm2021,Paoluzzi2021} are commonly used to model…

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…

We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For the associated random dynamical system, we prove the existence…

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…

We propose an SIR epidemic model coupled with opinion dynamics to study an epidemic and opinions spreading in a network of communities. Our model couples networked SIR epidemic dynamics with opinions towards the severity of the epidemic,…

A plethora of prediction models of SARS-CoV-2 pandemic were proposed in the past. Prediction performances not only depend on the structure and features of the model, but also on its parametrization. Official databases are often biased due…