  The general epidemic process (GEP), also known as
susceptible-infected-recovered model (SIR), describes how an epidemic spreads
within a population of susceptible individuals who acquire permanent
immunization upon recovery. This model exhibits a second-order absorbing state
phase transition, commonly studied assuming immobile healthy individuals. We
investigate the impact of mobility on disease spreading near the extinction
threshold by introducing two generalizations of GEP, where the mobility of
susceptible and recovered individuals is examined independently. In both cases,
including mobility violates GEP's rapidity reversal symmetry and alters the
number of absorbing states. The critical dynamics of the models are analyzed
through a perturbative renormalization group approach and large-scale
stochastic simulations using a Gillespie algorithm. The renormalization group
analysis predicts both models to belong to the same novel universality class
describing the critical dynamics of epidemic spreading when the infected
individuals interact with a diffusive species and gain immunization upon
recovery. At the associated renormalization group fixed point, the immobile
species decouples from the dynamics of the infected species, dominated by the
coupling with the diffusive species. Numerical simulations in two dimensions
affirm our renormalization group results by identifying the same set of
critical exponents for both models. Violation of the rapidity reversal symmetry
is confirmed by breaking the associated hyperscaling relation. Our study
underscores the significance of mobility in shaping population spreading
dynamics near the extinction threshold.
