Stochastic Epidemic Models with Inference
Meeting Times:
- Monday, July 29, 8:30 AM – 5:00 PM
- Tuesday July 30, 8:30 AM – 5:00 PM
- Wednesday July 31, 8:30 AM – 12:00 PM
Classroom: Randall Rollins Building (RR 226)
Module Summary:
The course first studies some basic stochastic models for the spread of an infectious disease and presents large population results for them including threshold phenomenon (Ro), distribution of the final number infected, and the critical vaccination coverage (the fraction needed to vaccinate to avoid future epidemics). Several extensions towards realism are then discussed: different types of individuals and social structures in the community including households and networks.
Then focus shifts towards statistics and how to obtain estimates of relevant model parameters from epidemic data. The course will give the theoretical background but also numerous examples from empirical situations including estimation of various vaccine efficacies. There will be class exercises during the course.
Prerequisites:
This module assumes knowledge of probability and inference covered in an introductory statistical course. Familiarity with regression modeling, survival analysis and R programming is recommended.
Module Content:
- Introduction to stochastic epidemic models; notation, properties, examples
- Important properties of epidemics and endemic situations
- Inference on stochastic epidemic models
- Modeling using networks and other heterogeneities, computer simulations
- Different models for vaccine mechanisms
- Stochastic models for small groups such as households
- Continuation, Heterogeneities, inference from big outbreaks
- COVID-19 analysis
- Study designs for evaluating vaccine efficacy
- Design and analysis of randomized vaccine trials for emerging infectious disease epidemics: From cholera to Ebola to COVID 19
Instructors
Ira Longini, PhD
Professor, Department of Biostatistics, University of Florida
Dr. Longini’s research interests are in the area of stochastic processes applied to epidemiological problems. He has specialized in the mathematical and statistical theory of epidemics–a process that involves constructing and analyzing mathematical models of disease transmission, disease progression and the analysis of infectious disease data based on these models. He works extensively in the design and analysis of vaccine and infectious disease prevention trials and observational studies.
Dr. Longini has worked on the analysis of epidemics of COVID-19, Ebola, influenza, HIV, tuberculosis, cholera, dengue fever, malaria, rhinovirus, rotavirus, measles and other infectious agents, with the WHO, CDC and other organizations.
Tom Britton, PhD
Professor of Mathematical Statistics, Stockholm University
Dr. Britton’s research interests lie in applied probability models and statistical inference for such, in particular epidemic models, networks and applications towards genetics and molecular biology including phylogenetics.
Required Software:
- R
Recommended Reading:
- Books:
- Halloran ME, Longini IM and Struchiner CJ: The Design and Analysis of Vaccine Studies. Springer, New York, 387 pp. (2009).
- Diekmann O, Heesterbeek H and Gritton T: Mathematical Tools for Understanding Infectious Disease Dynamics. Princeton U Press, 520 pp (2012)
- Held L, Hens N, O’Neill P and Wallinga J (eds): Handbook of Infectious Disease Data Analysis. Chapman and Hall, 554 pp (2019)
