Epidemiological Models and Process Engineering

Abstract

The paper discusses the principles behind epidemiology models, with examples taken from the classic SIR (suspectible-infected-recovered) and SEIR (S-exposed-IR) models. Both continuous time deterministic and stochastic models are treated, where the stochastic models are based on Poisson-distributed events/reactions. These models use real approximations to the integers representing the number of people in each of the classes S, (E,) I, R. An alternative stochastic representation is the first reaction time description, where the variables are kept as integers, and where one instead computes the time between each event. The models are presented in a form compatible with standard chemical engineering models. Based on the model description, the SIR and SEIR models are fitted to a measles case study using the Markov Chain Monte Carlo approach. For the given data, the SIR model appears to give much smaller uncertainty in predicitons. The continuous time stochastic description and the firt reaction time approaches give similar variation in the models. An important measure of the state of epidemics is the reproduction number, R, which tells whether the infection is growing or decreasing from an initial infection. The development of an expression for Ris indicated both from eigenvalues and from the Next-Generation Approach, and it is shown that the expression for R is identical for the SIR and the SEIR model. The principles of epidemiology model development discussed in the paper are used in models ranging from HIV/AIDS to COVID-19.