- Module I: Literature searches with Google Scholar
- Module II: Extracting data from graphs in published literature
- Module III: Online sources of free data
- Module IV: The basics of the R statistical programming language

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Google Scholar is search engine that indexes the scholarly literature across an array of publishing formats and disciplines. It provides a very powerful means to find literature associated with pretty much any research topic you can think of.

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Connecting mathematical models to predicting reality usually involves comparing your model to data, and finding model parameters that make the model most closely match observations in data. And of course statistical models are wholly developed using sources of data.

Becoming adept at finding sources of data relevant to a model you are studying is a learned skill, but unfortunately one that isn’t taught in any textbook!

One thing to keep in mind is that any data that appears in a journal publication is fair game to use, even if it appears in graphical format only. If the data is in graphical format, there are free programs, such as DataThief, that can be used to extract the data into a numerical file.

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**[In this module we discuss methods for finding free sources of online data. We present examples of climate, population, and socio-economic data from a variety of online sources. Other sources of potentially useful data are also discussed. The data sources described here are by no means an exhaustive list of free online data that might be useful to use in a computational, statistical, or mathematical modeling study.]** Continue reading

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**[After you have read through this module, and have downloaded and worked through the provided R examples, you should be proficient enough in R to be able to download and run other R scripts that will be provided in other posts on this site. You should understand the basics of good programming practices (in any language, not just R). You will also have learned how to read data in a file into a table in R, and produce a plot.]**

**Contents:**

- Why use R for modelling?
- How to download R
- Some example R code with an overview of basic R commands
- Advancing on: programming constructs
- Good programming practices (in any language)
- Reading data files into R

**Why use R for modelling?**

I have programmed in many different computing and scripting languages, but the ones I most commonly use on a day to day basis are C++, Fortran, Perl, and R (with some Python, Java, and Ruby on the side). In particular, I use R every day because it is not only a programming language, but also has graphics and a very large suite of statistical tools. Connecting models to data is a process that requires statistical tools, and R provides those tools, plus a lot more.

Unlike SAS, Stata, SPSS, and Matlab, R is free and open source (it is hard to beat a package that is more comprehensive than pretty much any other product out there **and** is free!).

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**[After reading through this module you should have an intuitive understanding of how infectious disease spreads in the population, and how that process can be described using a compartmental model with flow between the compartments. You should be able to write down the differential equations of a simple disease model, and you will learn in this module how to numerically solve those differential equations in R to obtain the model estimate of the epidemic curve]**

**An excellent reference book with background material related to these lectures is Mathematical Epidemiology by Brauer et al. **

**Contents:**

- Introduction
- Basic dynamics of infectious disease spread
- The SIR compartmental model of disease spread
- The SIR model system of equations
- Numerically solving the SIR model system of equations in R
- R code to model an influenza pandemic with an SIR model
- Further things you can explore
- Summary

**Introduction**

Models of disease spread can yield insights into the mechanisms and dynamics most important to the spread of disease (especially when the models are compared to epidemic data). With this improved understanding, more effective disease intervention strategies can potentially be developed. Sometimes disease models are also used to forecast the course of an epidemic, and doing exactly that for the 2009 pandemic was my introduction to the field of computational epidemiology.

There are lots of different ways to model epidemics, and there are several modules on this site on the topic, but let’s begin with one of the simplest epidemic models for an infectious disease like influenza: the Susceptible, Infected, Recovered (SIR) model.

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**[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 the graphical Monte Carlo 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
- Least squares goodness-of-fit statistic
- Finding the model parameters that minimize the Least Squares statistic: why we can’t just use linear regression methods for the models we usually use
- Monte Carlo parameter sweep method
- R code to fit to 2007-2008 confirmed influenza cases in Midwest
- Parameter estimates have uncertainties
- Potential pitfalls of using Least Squares

**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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