IDEAS: Mathematical Models of Infectious Diseases

Overview

Program: 1st Annual IDEAS Workshop: Mathematical Models of Infectious Diseases
Location: University of Georgia
Date: May 17-19, 2017
Instructors: Pejman Rohani (rohani@uga.edu) & John M. Drake (jdrake@uga.edu)
Class objectives: This module covers the principles of dynamic models of infectious diseases. The module will focus on the dynamics of compartmental models such as the susceptible-infected-recovered (SIR) model and variants (SI,SIRS, and SEIR). Topics include incorporating different types of heterogeneities in transmission (resulting from age-structure, behavior or, seasonality), exact stochastic birth-death models, sensitivity analysis, and fitting of simple models to data. The module will alternate between lectures and computer labs. Programming will be done in R.
Data for exercises: data.zip

Class topics

Outline: Objectives
Lecture: Mathematical models of infectious diseases
Exercise: Introduction to scientific programming in R (Code) (Solutions)
Lecture: Equilibrium stability analysis and next generation method
Exercise: Deterministic models (Code) (Solutions)
Lecture: Infectious disease management
Exercise: Pulsed vaccination (Code) (Solutions), Social distancing (Code) (Solutions)
Lecture: Parameter estimation
Exercise: Estimation (Code) (Solutions)
Lecture: Stochastic models
Exercise: Stochastic simulation (Code) (Solutions)
Lecture: Parameter uncertainty
Exercise: Sensitivity analysis of deterministic models through latin hypercube sampling – Ebola example (Code) Sensitivity analysis of deterministic models through latin hypercube sampling – HIV example (Code)
Lecture: Heterogeneities in contact
Exercise: Structured models for host heterogeneities (Code) (Solutions)

Further exercises

Exercise:  Estimating model parameters through maximum likelihood (Code)
Exercise:  The distribution of outbreak sizes: Immune escape and transmission of equine influenza (Code)
Exercise:  Seasonally forced epidemics (Code)

Suggested reading (case studies)

Suggested reading (modeling infectious diseases)

Suggested reading (programming in R)

  • Crawley, M.J. 2007. The R book. Wiley.
  • Matloff, N. 2011. The Art of R Programming. No Starch Press.
  • Venables, W.N., & B.D Ripley. 2002. Modern Applied Statistics with S. 4th edition. Springer.
  • Jones, O., R. Maillardet, & A. Robinson. 2009. Introduction to scientific programming and simulation with R. Chapman & Hall.