Numerical methods to solve ordinary differential equations

After going through this module, students will be familiar with the Euler and Runge-Kutta methods for numerical solution of systems of ordinary differential equations.  Examples are provided to show students how complementary R scripts can be written to help debug Runge-Kutta methods implemented in C++.

Contents

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ASU AML 610 Module IX: Introduction to C++ for computational epidemiologists

After going through this module, students should be familiar with basic skills in C++ programming, including the structure of a basic program, variable types, scope, functions (and function overloading), control structures, and the standard template library.

So far in this course we have used R to explore methods related to fitting model parameters to data (in particular, we explored the Simplex method for parameter estimation).  As we’ve shown, parameter estimation can be a very computationally intensive process.

When you use R, it gives you a prompt, and waits for you to input commands, either directly through the command line, or through an R script that you source.  Because R is a non-compiled language, and instead interprets code step-by-step, it does not have the ability to optimize calculations by pre-processing the code.

In contrast, compiled programming languages like C, java, or C++ (to name just a few) use a compiler to process the code, and optimize the computational algorithms.  In fact, most compilers have optional arguments related to the level of optimization you desire (with the downside that the optimization process can be computationally intensive).  Optimized code runs faster than non-optimized code.

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ASU AML 610 Module VIII: Fitting to initial exponential rise of epidemic curves

In this module students will compare the performance of several fitting methods (Least squares, Pearson chi-squared, and likelihood fitting methods) in estimating the rate of exponential rise in initial epidemic incidence data.  Students will learn about the properties of good estimators (bias and efficiency).

A good reference source for this material is Statistical Data Analysis, by G.Cowan

Another good reference source (in a very condensed format) for statistical data analysis methods can be found here.

Contents:
Introduction
Properties of good estimators
Generating simulated exponential rise data
Estimation of the rate of exponential rise: Least Squares
Estimation of the rate of exponential rise: Pearson chi-squared
The Poisson maximum likelihood method
Estimation of parameter confidence intervals: any maximum likelihood method
Estimation of the rate of exponential rise: Poisson maximum likelihood method
Testing for over- or under-dispersion.
Correcting for over- or under-dispersion
Better method for determination of parameter estimates and their covariance when using the Pearson chi-squared method

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