Mathematics and the Quest for Vaccine-Induced Herd Immunity Threshold

Explore a comprehensive lecture on the mathematical principles behind vaccine-induced herd immunity thresholds. Delve into the history, applications, and mathematical models used to understand this crucial concept in epidemiology. Learn about infectious compartment equations, model extensions, and important factors affecting herd immunity, including heterogeneities and linear optimization. Gain insights into the application of these concepts to COVID-19, understanding key terms such as R0 and vaccine efficacy. Discover the current progress in achieving herd immunity and potential future research directions. Engage with a Q&A session following the presentation to deepen your understanding of this vital topic in public health and mathematics.

Introduction
Acknowledgement
Outline
Questions
Concepts
History
Applications
Model
Infectious compartment equation
Mathematical analysis
Model extension
Conclusion
Important concept
Heterogeneities
Linear Optimization
Factors affecting herd immunity
Covid19 and herd immunity
What is the R naught
What is vaccine efficacy
Duration of protection
How are we doing
Future research
Summary
QA