Related papers: A note on Exact solution of SIR and SIS epidemic m…

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…

The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…

Exact solutions of the SEIR epidemic model are derived, and various properties of solutions are obtained directly from the exact solution. In this paper Abel differential equations play an important role in establishing the exact solution…

We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a…

We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove the asymptotic stability of the extinction and disease-free…

Mathematical modelling of the spread of epidemics has been an interesting challenge in the field of epidemiology. The SIR Model proposed by Kermack and McKendrick in 1927 is a prototypical model of epidemiology. However, it has its…

We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…

Assuming a general distribution for the sojourn time in the in- fectious class, we consider an SIS type epidemic model formulated as a scalar integral equation. We prove that the endemic equilibrium of the model is globally asymptotically…

An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et. al, 2017, Q. Jl Mech. Appl. Math, 70 (1), 21-48). The solution is created by analytically continuing the divergent…

This report is based on the work in (1). We first review definitions and notation developped there and provide derivations for the exact mathematical description of an SIS epidemic on a hypergraph. We then generalise the work in (1) to a…

In this paper, the exact analytical solution of the Susceptible-Infected-Recovered (SIR) epidemic model is obtained in a parametric form. By using the exact solution we investigate some explicit models corresponding to fixed values of the…

This brief note highlights a largely overlooked similarity between the SIR ordinary differential equations used for epidemics on the configuration model of a Poisson network and the classical mass-action SIR equations introduced nearly a…

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the…

In this paper we introduce an agent-based epidemiological model that generalizes the classical SIR model by Kermack and McKendrick. We further provide a multiscale approach to the derivation of a macroscopic counterpart via the mean-field…

Several exact expansions as well as lower and upperbounds of the Kermack and McKendrick SIR equations are presented.

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…

We present an exact analytical solution to a one-dimensional model of the Susceptible-Infected-Recovered (SIR) epidemic type, with infection rates dependent on nearest-neighbor occupations. We use a quantum mechanical approach, transforming…

We revisit the classic Susceptible-Infected-Recovered (SIR) epidemic model and one of its nonlocal variations recently developed in \cite{Guan}. We introduce several new approaches to derive exact analytical solutions in the classical…

This work considers an extension of the SIR equations from epidemiology that includes a spatial variable. This model, referred to as the Kermack-McKendrick equations (KM), is a pair of diffusive partial differential equations, and methods…

We propose an approach to model spatial heterogeneity in SIR-type models for the spread of epidemics via \emph{nonlocal aggregation terms}. More precisely, we first consider an SIR model with spatial movements driven by nonlocal aggregation…