Fitting the parameters of an SIR model to influenza data using Least Squares and the Monte Carlo parameter sweep method

[After reading this module, students should understand the Least Squares goodness-of-fit statistic.   Students will be able to read an influenza data set from a comma delimited file into R, and understand the basic steps involved in a Monte Carlo parameter sweep method to fit an SIR model to the data to estimate the R0 of the influenza strain by minimizing the Least Squares statistic.  Students will be aware that parameter estimates have uncertainties associated with them due to stochasticity (randomness) in the data.]

A really good reference for statistical data analysis (including fitting) is Statistical Data Analysis, by G.Cowan.

Contents:

Introduction

When a new virus starts circulating in the population, one of the first questions that epidemiologists and public health officials want answered is the value of the reproduction number of the spread of the disease in the population (see, for instance, here and here).

The length of the infectious period can roughly be estimated from observational studies of infected people, but the reproduction number can only be estimated by examination of the spread of the disease in the population.  When early data in an epidemic is being used to estimate the reproduction number, I usually refer to this as “real-time” parameter estimation (ie; the epidemic is still ongoing at the time of estimation).

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