Dalla Lana School of Public Health

Special Topics: Mathematical Epidemiology: Methods and Applications

Course Description

This course is designed to equip students with the foundational and advanced tools required to model the transmission dynamics of infectious diseases. Through a progression from basic compartmental models to complex, structured, and disease-specific models, students will gain a deep understanding of how mathematical frameworks can be used to describe, analyze, and predict the spread of infectious diseases. Key learning objectives include the ability to derive and analyze classical and extended epidemiological models, estimate key parameters using Bayesian inference, incorporate behavioral and structural heterogeneities into models, and assess intervention strategies. By the end of the course, students will be able to develop and apply tailored mathematical models to real-world public health challenges, contributing to informed decision-making in outbreak response and disease control.

Course Objectives

By the end of this course, students will be able to:

1. Construct and analyze compartmental models (e.g., SIS, SIR, SEIR, SEAIR, SEAQIR) to describe the transmission dynamics of infectious diseases.
2. Calculate and interpret key epidemiological quantities, including the basic and effective reproduction numbers, and assess their implications for outbreak potential and control.
3. Apply parameter estimation techniques, including Bayesian inference using Stan, to calibrate disease models with epidemiological data and quantify uncertainty in model parameters.
4. Conduct sensitivity analyses to determine the robustness of model outcomes to changes in key parameters and assumptions.
5. Critically evaluate the impact of pharmaceutical and non-pharmaceutical interventions on disease dynamics, including vaccine rollout and public health measures, using mathematical modeling.
6. Incorporate human behavioral responses (e.g., risk perception, adaptive behavior) into epidemic models and analyze their effects on intervention outcomes.
7. Develop and assess advanced model structures, including multi-patch, age-structured, and risk-structured models, to capture population heterogeneity and spatial dynamics.
8. Model complex disease systems, including co-infections, multi-stage progression, and seasonal effects, to reflect realistic transmission and control scenarios.
9. Estimate the true burden of disease by accounting for underreporting and incomplete surveillance data within modeling frameworks.
10. Design and critique disease-specific models for a range of infections (e.g., COVID-19, HIV, malaria, cholera), evaluating their assumptions, limitations, and utility for public health decision-making.
11. Communicate model results effectively to both technical and non-technical audiences through written reports, presentations, or visualizations, demonstrating the relevance of findings to public health decision-making.

Methods of Assessment

Participation	10%
Assignment 1 – build, analyze, and interpret basic epidemic models	20%
Assignment 2 – apply advanced modeling techniques	20%
Final Project: – presentation – report	10% 40%