Tricritical behavior in epidemic dynamics with vaccination

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 formulation reveals that MVE model exhibits either continuous or discontinuous active-to-absorbing phase transition, accompanied by bistability tricritical point. However, on square lattices, we detect no signs of bistability, disclose state transition has invariance critical exponents compatible with directed percolation universality class. Additionally, our findings indicate crossover behaviors belong to class percolation.