# Dynamic Vaccination Game in a Heterogeneous Mixing Population

## TL;DR

This paper models voluntary vaccination decisions in a heterogeneous population during an epidemic, analyzing how individual choices impact overall outbreak risk and evaluating different vaccination strategies through a novel dynamic epidemic model and game theory.

## Contribution

It introduces a new epidemic dynamics model incorporating dynamic vaccination and heterogeneity, along with an efficient method to evaluate epidemic outcomes and analyze vaccination game equilibria.

## Key findings

- Vaccination decisions significantly influence epidemic risk.
- Early vaccination schemes can effectively reduce outbreak probability.
- Heterogeneity in population affects vaccination behavior and epidemic dynamics.

## Abstract

Opposition to vaccination has long been a non-negligible public health phenomenon resulted from people's varied perceptions toward vaccination (e.g., vaccine-phobia). This paper investigates the voluntary vaccination behavior of a heterogeneous population during an epidemic outbreak, where each individual makes its own vaccination decision to minimize its expected disutility from both vaccine-phobia and the risk of infection. Such a problem is known as a vaccination game, as people's vaccination decisions not only affect their own disutilities but those of all others through probabilistic disease transmissions. To study the vaccination game, the susceptible-infected-removed disease propagation process is generalized into a new epidemic dynamics model to allow dynamic vaccination and immunity activation in a heterogeneous mixing population. An efficient computation method is proposed to evaluate the final state of the dynamic epidemic system. Then, a classic game-theoretical equilibrium model is built upon these results to examine the impacts of people's vaccination behavior on the overall risk of epidemic outbreak. A hypothetical case study is used to validate the dynamics model and the derived results, and extensive numerical experiments are conducted to identify the key factors that affect people's vaccination decisions and the risk of an outbreak. Moreover, three alternative vaccination schemes are also studied to examine the effects of early and non-differential vaccination treatments, respectively.