Related papers: Exactly solvable SIR models, their extensions and …
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…
Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…
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…
The exact analytical solution in closed form of a modified SIR system where recovered individuals are removed from the population is presented. In this dynamical system the populations $S(t)$ and $R(t)$ of susceptible and recovered…
We consider a global (location independent) model of pandemic growth which generalizes the SIR model to accommodate important features of the COVID-19 pandemic, notably the implementation of pandemic reduction measures. This "SHIR" model is…
Mathematical models of infectious diseases exhibit robust dynamics such as stable endemic or a disease-free equilibrium, or convergence of the solutions to periodic epidemic waves. The present work shows that the accuracy of such dynamics…
Recently the A/H1N1-2009 virus pandemic appeared in Mexico and in other nations. We present a study of this pandemic in the Mexican case using the SIR model to describe epidemics. This model is one of the simplest models but it has been a…
The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modeling and forecasting. The SIR (Susceptible-Infected-Removed) model is a…
We consider the SIR epidemiological model applied to the evolution of COVID-19 with two approaches. In the first place we fit a global SIR model, with time delay, and constant parameters throughout the outbreak, including the contagion…
The SIR model is a classical model characterizing the spreading of infectious diseases. This model describes the time-dependent quantity changes among Susceptible, Infectious, and Recovered groups. By introducing space-depend effects such…
Predicting Pandemic evolution involves complex modeling challenges, often requiring detailed discrete mathematics executed on large volumes of epidemiological data. Differential equations have the advantage of offering smooth, well-behaved…
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…
The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common…
This paper extends the canonical model of epidemiology, the SIRD model, to allow for time-varying parameters for real-time measurement and prediction of the trajectory of the Covid-19 pandemic. Time variation in model parameters is captured…
We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…
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…
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…
This paper seeks to study the evolution of the COVID-19 pandemic based on daily published data from Worldometer website, using a time-dependent SIR model. Our findings indicate that this model fits well such data, for different chosen…
The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an…
The COVID-19 pandemic has had worldwide devastating effects on human lives, highlighting the need for tools to predict its development. Dynamics of such public-health threats can often be efficiently analysed through simple models that help…