## 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)

- Anonymous. 1978. Influenza in a boarding school.
*British Medical Journal*1:587. - Blower, S.M., H. B. Gershengorn, R.M.. 2000. A tale of two futures: HIV and antiretroviral therapy in San Francisco.
*Science*287:650-654. - Grais, R.F., M.J. Ferrari, C. Dubray, O.N. Bjornstad, B.T. Grenfell, A. Djibo, F. Fermon, P.J. Guerin. 2006. Estimating transmission intensity for a measles epidemic in Niamey, Niger: Lessons for intervention.
*Transactions of the Royal Society of Tropical Medicine and Hygiene*100:867-873. - Legrand, J., R.F. Grais, P.Y. Boelle, A.J. Valleron, & A. Flahault. 2007. Understanding the dynamics of Ebola epidemics.
*Epidemiology & Infection*135:610-621. - Park, A.W., J.M. Daly, N.S. Lewis, D.J. Smith, J.L.N. Wood, B.T. Grenfell. 2009. Quantifying the impact of immune escape on transmission dynamics of influenza.
*Science*326:726-728. - Read, J., Lessler, J., Riley, S., Wang, S., Tan, L.J., Kwok, K.O., et al. 2014. Social mixing patterns in rural and urban areas of southern China.
*Proceedings of the Royal Society B: Biological Sciences*281:20140268. - Rohani, P., Zhong, X., & King, A. A. 2010. Contact network structure explains the changing epidemiology of pertussis.
*Science*330:982–985. - Schenzle, D. 1984. An age-structured model of pre- and post-vaccination measles transmissiont.
*IMA Journal of Mathematics Applied in Medicine and Biology*1:169–191.

## Suggested reading (modeling infectious diseases)

- Keeling, M.J. & P. Rohani. 2007.
*Modeling infectious diseases in humans and animals*. Princeton University Press. - Vynnyky, E., & R. White. 2010.
*An introduction to infectious disease modelling*. Oxford University Press. - Heesterbeek, J. A. P., & Roberts, M. G. 2007. The type-reproduction number T in models for infectious disease control.
*Mathematical Biosciences*206(1):3–10. - Diekmann, O., Heesterbeek, J. A. P., & Roberts, M. G. 2009. The construction of next-generation matrices for compartmental epidemic models.
*Journal of the Royal Society Interface*7:873–885. - Mossong, J. E. L., Hens, N., Jit, M., Beutels, P., Auranen, K., Mikolajczyk, R., et al. 2008. Social contacts and mixing patterns relevant to the spread of infectious diseases.
*PLoS Medicine*5:e74.

## 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.