  We introduce the generalized diffusive epidemic process, which is a
metapopulation model for an epidemic outbreak where a non-sedentary population
of walkers can jump along lattice edges with diffusion rates $D_S$ or $D_I$ if
they are susceptible or infected, respectively, and recovered individuals
possess permanent immunity. Individuals can be contaminated with rate $\mu_c$
if they share the same lattice node with an infected individual and recover
with rate $\mu_r$, being removed from the dynamics. Therefore, the model does
not have the conservation of the active particles composed of susceptible and
infected individuals. The reaction-diffusion dynamics are separated into two
stages: (i) Brownian diffusion, where the particles can jump to neighboring
nodes, and (ii) contamination and recovery reactions. The dynamics are mapped
into a growing process by activating lattice nodes with successful
contaminations where activated nodes are interpreted as infection sources. In
all simulations, the epidemic starts with one infected individual in a lattice
filled with susceptibles. Our results indicate a phase transition in the
dynamic percolation universality class controlled by the population size,
irrespective of diffusion rates $D_S$ and $D_I$ and a subexponential growth of
the epidemics in the percolation threshold.
