Graphical Monte Carlo method: choosing ranges over which to sample parameters

In this module we will discuss how to choose ranges over which to sample parameters using the graphical Monte Carlo method for fitting the parameters of a mathematical model to data.  We will also discuss the importance of using the Normal negative log-likelihood statistic (equivalent to Least Squares) when doing Least Squares fitting, rather than the Least Squares statistic itself.

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Contagion models with non-exponentially distributed sojourn times in the infectious state

Compartmental models of infectious disease transmission inherently assume that the time spent (“sojourn time”) in the infectious state is Exponentially distributed.  As we will discuss in this module, this is a highly unrealistic assumption.  We will show that the “linear chain rule” can be used to incorporate more realistic probability distributions for state sojourn times into compartmental mathematical models.

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Example LaTex and BibTex documents

In this module, I provide an example LaTex document that cites references within a BibTex file, and also includes examples of how to include equations, figures, and tables.

The files for this worked example can be found in my GitHub repository


The repository contains the main LaTex document example_latex.tex, along with the bibtex file example_latex.bib.  In order to compile the document, you also need to download the example_latex_histogram_plot.eps, which is the figure included in the file.  To compile the document, run LaTex once, then BibTex, then LaTex twice (which should resolve all references).

This should produce the file example_latex.pdf

Note that the encapsulated postscript (EPS) figure for the paper was produced with the R script example_latex.R  (you need to install the R extrafont library before running the script) The R script also shows you how to automatically output results from your analysis code that can be included as \newcommands in your latex file that allow you to copy and paste the results to your LaTex file so that reference those results in the text of your paper without having to manually transcribe numbers (which can lead to unnecessary transcription errors).

Data and R code repositories in GitHub

GitHub is a web-based version-control and collaboration platform for software developers.

Git, an open source code management system, is used to store the source code for a project and track the complete history of all changes to that code. It allows developers to collaborate on a project more effectively by providing tools for managing possibly conflicting changes from multiple developers. GitHub allows developers to change, adapt and improve software from its public repositories for free.  Repositories can have multiple collaborators and can be either public or private.

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AML 612 Spring 2019: List of modules

Computational and statistical methods for mathematical biologists and epidemiologists.


This course is meant to provide students in applied mathematics with the broad skill-set needed to optimize the parameters of dynamical mathematical models to relevant biological or epidemic data. The course will almost entirely be based on material posted on this website. Continue reading