  We scrutinize the phenomenology arising from a minimal vaccination-epidemic
(MVE) dynamics using three methods: mean-field approach, Monte Carlo
simulations, and finite-size scaling analysis. The mean-field formulation
reveals that the MVE model exhibits either a continuous or a discontinuous
active-to-absorbing phase transition, accompanied by bistability and a
tricritical point. However, on square lattices, we detect no signs of
bistability, and we disclose that the active-to-absorbing state transition has
a scaling invariance and critical exponents compatible with the continuous
transition of the directed percolation universality class. Additionally, our
findings indicate that the tricritical and crossover behaviors of the MVE
dynamics belong to the universality class of mean-field tricritical directed
percolation.
