SISMID 2014: Mathematical Modeling of Infectious Diseases


Program: 6th Annual Summer Institute in Statistical Modeling of Infectious Diseases
Location: University of Washington
Date: July 7-9, 2014
Instructors: Pejman Rohani ( & John M. Drake (
Class objectives: Outline
Data for exercises:

Class topics

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 (Code) (Solutions)
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.
  • 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. M., 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 transmission. 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.