Mathematical Models of Infectious Diseases
Meeting Times:
- Monday, July 15, 8:30 AM – 5:00 PM
- Tuesday July 16, 8:30 AM – 5:00 PM
- Wednesday July 17, 8:30 AM – 12:00 PM
Classroom: TBA
Module Summary:
This module covers the principles of dynamic models of infectious diseases. This module will focus on developing and analyzing compartmental models such as the susceptible-infected-recovered (SIR) model. Topics include deriving the basic reproductive ratio using the next generation method, incorporating different mechanisms of heterogeneity in transmission (for instance, age-structure, behavior or seasonality), formulating exact stochastic birth-death models, carrying out sensitivity analysis and statistical fitting of simple models to data. The module will alternate between lectures and computer labs.
Prerequisites:
Students are expected to have a working knowledge of the R computing environment. Programming will be in R. Students new to R should complete a tutorial before the module. Students are expected to have exposure to the notation of differential equations and basic statistics.
Module Content:
- Day 1:
- Introduction to Modeling
- Basics of SIR Models
- Herd Immunity and Vaccination
- Day 2:
- Heterogeneity in Models
- Age Structured Models
- Parameter Estimation
- Day 3:
- Confronting Models with Data
- Stochastic models
Instructors
Micaela Martinez, PhD
Director of Environmental Health, We Act for Environmental Justice
Dr. Micaela E. Martinez is a Chicana scientist, artist, and justice advocate. She is the newly appointed Director of Environmental Health at WE ACT for Environmental Justice, in New York City. She is responsible for advancing efforts to improve environmental health in communities of color and low-income communities by conducting research, promoting public health awareness, education, coalition-building, and advocacy.
Matt Ferrari, PhD
Director of the Center for Infectious Disease Dynamics, Professor of Biology, Pennsylvania State University
Dr. Ferrari's lab does research on both the application of quantitative modeling and analysis to inform public health policy and the basic ecology of parasites and infectious diseases at the Center for Infectious Disease Dynamics at The Pennsylvania State University.
Required Software:
Students are expected to have knowledge of RStudio and a basic text editor downloaded prior to the course. Please install the following packages prior to the course: tidyverse, deSolve, diagram, gt, ggtext, here, rio. Information on installing these packages will be provided along with the “Introduction to R” tutorial that students will be asked to complete prior to the course.
Recommended Reading:
- Keeling & Rohani (2008) Modeling Infectious Diseases in Humans and Animals, Princeton University Press.
