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.