SIR model of epidemic spread with accumulated exposure

Rich dynamics of an SIR epidemic model

Over the past one hundred years, mathematics has been used to understand and predict the spread of diseases, relating important public-health questions to basic transmission parameters. From prehistory to the present day, diseases have been a source of fear and superstition. A comprehensive picture of disease dynamics requires a variety of mathematical tools, from model creation to solving diff...

Stochastic Model of SIR Epidemic Modelling

Threshold theorem is probably the most important development of mathematical epidemic modelling. Unfortunately, some models may not behave according to the threshold. In this paper, we will focus on the final outcome of SIR model with demography. The behaviour of the model approached by deteministic and stochastic models will be introduced, mainly using simulations. Furthermore, we will also in...

Behavior of a Discrete SIR Epidemic Model

I. Introduction Infections and infectious diseases are a great burden on many societies, including the countries. An epidemic may be described as a sudden outbreak of a disease that infects a substantial portion of the population in a region before it disappears. In the nineteenth century, recurrent waves of cholera killed millions in India. The influenza epidemic of 1918-1919 killed at least 2...

Modeling and analysis of the spread of the COVID-19 pandemic using the classical SIR model

In this paper modeling, analysis and prediction of novel epidemic of COVID-19 are concerned to identify effective spread parameters of it in Iran. For this purpose, the basic susceptible-infected-removed (SIR) model is used which has two parameters: the infection rate and remove rate. The occurrence of several maximum points in the Iranian data and the single peak of the SIR model makes it impo...

Existence of a Nonautonomous SIR Epidemic Model with Age Structure