Physica A.2017 Feb;467:21-29

Susceptible-infected-recovered model with recurrent infection

Flávia M.Ruziska, Tânia Tomé, Mário Oliveira

Instituto de Física, Universidade de São Paulo, Rua do Matão, 1371, 05508-090 São Paulo, SP, Brazil



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.

Keywords: Epidemic models, Nonequilibrium phase transitions, Dynamic percolation; SIR model

DOI: 10.1016/j.physa.2016.09.010