Dynamic vaccination games and variational inequalities on time-dependent sets
Annamaria Barbagallo1, Monica-Gabriela Cojocaru
1Department of Mathematics and Computer Science, University of Catania, Viale Andrea Doria n. 6 - Catania, Italy.
Journal of Biological Dynamics
|August 14, 2012
Summary
This study models dynamic vaccination games in diverse groups with varying risk perceptions. It introduces a novel approach to calculate optimal vaccination strategies and coverage levels, accounting for changing population dynamics.
Area of Science:
- Game Theory
- Mathematical Modeling
- Public Health
Background:
- Vaccination decisions are influenced by perceived risks and population-level coverage.
- Heterogeneity in risk perception across population groups impacts vaccination dynamics.
- Existing models often lack dynamic and time-varying population structures.
Purpose of the Study:
- To develop a dynamic game model for vaccination decisions in heterogeneous populations.
- To analyze vaccination strategies in a repeated game with time-varying group sizes.
- To compute optimal vaccination strategies and resulting coverage levels without prior assumptions.
Main Methods:
- A parametric variational inequality approach is employed to solve the dynamic game.
- The model analyzes a repeated game over a finite time horizon.
- Theoretical results ensure the existence, uniqueness, and regularity of solutions.
Main Results:
- The model computes vaccine coverage levels as an outcome, not an input.
- It demonstrates the evolution of optimal vaccination strategies for each group.
- The approach accommodates time-varying population group sizes and distinct risk perceptions.
Conclusions:
- The proposed dynamic game model offers a robust framework for understanding vaccination behavior in heterogeneous populations.
- It provides a method to predict vaccine coverage scenarios based on perceived risks.
- The model's theoretical underpinnings support the computation of optimal and evolving vaccination strategies.
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