Overview
Program: 3rd Annual IDEAS Workshop: Mathematical Models Module
Location: University of Georgia
Date: May 15-17, 2019
Instructors: Pejman Rohani (rohani@uga.edu) & John M. Drake (jdrake@uga.edu)
Class objectives: Outline
Data for exercises: data.zip
Class topics
- Outline: Objectives
- Lecture: Mathematical models of infectious diseases
- Exercise: Deterministic models (Slides) (Code) (Solutions)
- Lecture: Equilibrium stability analysis and next generation method
- 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) (Solutions) 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: Introduction to scientific programming in R (Code) (Solutions)
- 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. 2014. Introduction to scientific programming and simulation with R. Second edition. Chapman & Hall.