  We present a modified diffusive epidemic process that has a finite threshold
on scale-free graphs. The diffusive epidemic process describes the epidemic
spreading in a non-sedentary population, and it is a reaction-diffusion
process. In the diffusion stage, the individuals can jump between connected
nodes, according to different diffusive rates for the infected and susceptible
individuals. In the reaction stage, the contagion can happen if there is an
infected individual sharing the same node, and infected individuals can
spontaneously recover. Our main modification is to turn the number of
individuals' interactions independent on the population size by using Gillespie
algorithm with a reaction time $t_\mathrm{max}$, exponentially distributed with
mean inversely proportional to the node concentration. Our simulation results
of the modified model on Barabasi-Albert networks are compatible with a
continuous phase transition with a finite threshold from an absorbing phase to
an active phase when increasing the concentration. The transition obeys the
mean-field critical exponents of the order parameter, its fluctuations and the
spatial correlation length, whose values are $\beta=1$, $\gamma'=0$ and
$\nu_\perp=1/2$, respectively. In addition, the system presents logarithmic
corrections with pseudo-exponents $\widehat{\beta}=\widehat{\gamma}'=-3/2$ on
the order parameter and its fluctuations, respectively. The most evident
implication of our simulation results is if the individuals avoid social
interactions in order to not spread a disease, this leads the system to have a
finite threshold in scale-free graphs, allowing for epidemic control.

Physics and Society;Statistical Mechanics;Populations and Evolution