Four States Epidemiologic model (FSEM) in the random transverse-field Ising universality class

We analyze the critical properties of a four states epidemic model by a mean field pair approximation and by Monte Carlo simulations on a cubic lattice. The mean field pair approximation solution suggests that this model spreads the infection in two different steps. The first step decides which sites can be infected, and the second step spreads the infection among those sites. Comparing these mean field equations with those of the Susceptible-Exposed-Infected (SEI) model and the Contact Process (CP), we conclude that the first step generates clusters according to the SEI rules and the second simulates the CP in those clusters. Since the SEI model is in the Dynamical Percolation universality class, this mean field solution suggests that this four states epidemic model should be in the same universality class of the CP with quenched disorder, which is expected to be in the random transverse field Ising (RTFI) universality class. By performing Monte Carlo simulations near the critical point, we are able to verify this hypothesis and estimate the critical exponents which are compatible with those in the random transverse field Ising model.