  The COVID-19 pandemic has devastated the world in an unprecedented way,
causing enormous loss of life. Time and again, public health authorities have
urged people to become vaccinated to protect themselves and mitigate the spread
of the disease. However, vaccine hesitancy has stalled vaccination levels in
the United States. This study explores the effect of vaccine hesitancy on the
spread of disease by introducing an SIRS-V$_\kappa$ model, with compartments of
susceptible (S), infected (I), recovered (R), and vaccinated (V). We leverage
the concept of carrying capacity to account for vaccine hesitancy by defining a
vaccine confidence level $\kappa$, which is the maximum number of people that
will become vaccinated during the course of a disease. The inverse of vaccine
confidence is vaccine hesitance, $(\frac{1}{\kappa})$. We explore the
equilibria of the SIRS-V$_\kappa$ model and their stability, and illustrate the
impact of vaccine hesitance on epidemic spread analytically and via
simulations.
