Lecture: Mathematical Modeling for Epidemiology and Ecology

Speaker: Glenn Ledder, University of Nebraska-Lincoln
Focus: Overview of a new book on mathematical modeling for life sciences, specifically epidemiology and ecology.

Introduction to the Book

• Title: Mathematical Modeling for Epidemiology and Ecology
• Purpose:
  • Textbook for undergraduate courses in mathematical modeling or biology.
  • Source for problems and methods to supplement modeling courses.
• Special Features:
  • Unique topics not commonly covered elsewhere.
  • Emphasis on designing and analyzing mathematical models.
  • Focus on scientific computation with practical programming exercises.

Key Features of the Book

• Model Derivations:
  • Alternatives for biological assumptions discussed.
  • Problems often include symbolic parameters.
  • Biological interpretation of model results required in many exercises.
  • Emphasis on hands-on modeling projects.
• Scientific Computation:
  • Supports learning to use programming environments.
  • Includes 22 MATLAB programs with no prior programming needed.
  • Programs structured for easy modification and experimentation.

Overview of Contents

• Mechanistic Modeling (Chapter 3):
  • Longest chapter, focusing on transition processes and interaction processes.
  • Case studies, including COVID-19 scenarios.
• Single Populations (Chapter 4):
  • Covers various topics related to population dynamics.
• Topics Highlighted in Lecture:
  • Vaccination models.
  • Transition processes.
  • Adding demographics to disease models.

Detailed Discussion of Selected Topics

Vaccination Models

• Issues with Standard Models:
  • Entire population is assumed susceptible.
  • Assumes unlimited vaccine supply and instantaneous distribution.
• Improved Models:
  • Accounts for limited acceptance, supply, and distribution capacity.
  • Use of realistic parameters to simulate real-world vaccination scenarios.

Transition Processes

• Single vs. Multi-Phase Transitions:
  • Example: disease recovery.
  • Multi-phase transitions provide a more realistic model than single-phase.

Adding Demographics

• SIR Model with Demographics:
  • Incorporates natural death and disease-induced death.
  • Improves realism by adding birth rate mechanics reflecting natural population changes.

Innovative Teaching Tools

• Phase Line Analysis with Structures:
  • Use of function decomposition for better insight into parameter effects.
  • Simplifies modeling by separating increase and decrease components.

Conclusion

• Book Release: Anticipated by April.
• Linked Problem Sets: Further discussions in future talks.

Q&A Highlights

• COVID-19 Modeling Challenges:
  • Difficulty in predicting long-term outcomes due to variable reproduction numbers.
  • Mechanistic modeling offers solutions to empirical challenges.
• Communication with Non-Technical Audiences:
  • Importance of technical writing for mathematical modelers.

Additional Resources Mentioned

• Akaike Information Criterion (AIC):
  • Implementation of Occam's Razor in modeling.
  • Balances accuracy with model complexity.

Contact Information

• Glenn Ledder available for further discussion during the Expo or via email.