The diffusive epidemic process on Barabasi-Albert networks

We present a modified diffusive epidemic process (DEP) that has a finite threshold on scale-free graphs, motivated by the COVID-19 pandemic. The DEP describes the epidemic spreading of a disease in a non-sedentary population, which can describe the spreading of a real disease. Our main modification is to use the Gillespie algorithm with a reaction time t(max), exponentially distributed with mean inversely proportional to the node population in order to model the individuals' interactions. Our simulation results of the modified model on Barabasi-Albert networks are compatible with a continuous absorbing-active phase transition when increasing the average concentration. The transition obeys the mean-field critical exponents beta = 1, gamma' = 0 and nu(perpendicular to) = 1/2. In addition, the system presents logarithmic corrections with pseudo-exponents beta=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.