Susceptible–infected–recovered model with recurrent infection

We analyze a stochastic lattice model describing the spreading of a disease among a community composed by susceptible, infected and removed individuals. A susceptible individual becomes infected catalytically. An infected individual may, spontaneously, either become recovered, that is, acquire a permanent immunization, or become again susceptible. The critical properties including the phase diagram is obtained by means of mean-field theories as well as numerical simulations. The model is found to belong to the universality class of dynamic percolation except when the recovering rate vanishes in which case the model belongs to the directed percolation universality class.