The diffusive epidemic process on Barabasi–Albert networks

Abstract

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 β = 1, γ′ = 0 and ν ⊥ = 1/2. In addition, the system presents logarithmic corrections with pseudo-exponents β ̂ = γ ̂ ′ = − 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.

Modified diffusive epidemic process on Apollonian networks

“…Recently, the MDEP model was implemented on a Barabasi-Albert network [ 24 ]. Here, was analyzed a MDEP furnishing a continuous phase transition obeying the HMF critical exponents , , and , but with logarithmic corrections to order parameter and its fluctuations to all , , and studied regimes.…”

“…One can use the Gillespie algorithm to simulate the contamination and recovery processes inside a node. Next, we enumerate the following rules which define the MDEP model [ 24 ] applied to Apollonian networks: Initialization step: At the time , we distribute a population of walkers, given as a function of the concentration in Eq. 3 , in the nodes of an Apollonian network and we choose half of the population to be infected.…”

“…Thus, the primary modification to the canonical DEP definition was done in the reaction stage, simulating the reaction process as a chemical reaction. The MDEP dynamics have a finite threshold in the scale-free networks [ 24 ], which allows us to control and investigate the diffusion rates’ conditions to avoid epidemic spreading. The critical threshold is the minimal particle density, i.e., the concentration that allows an active endemic phase.…”

“…When coupling a population of random walkers to a network, one can make the compartments A ( i ) and B ( i ) of node i obeying Eq. 1 , where the reactions take place in a time while maintaining the discrete-time diffusion [ 24 ].…”

Diffusive Majority Vote Model

“…It is known that the models with local updates given by a contact process, when transport is dominated by brownian diffusion, can have different critical exponents in lower dimensions. The Diffusive Epidemic Process (DEP) [17][18][19][20][21][22][23][24][25][26] is an example of a system that presents a new universality class, where exponents in lower dimensions deviate from the exponents of the contact process (CP). The CP obeys the directed percolation (DP) universality class, and DEP in lower dimensions defines new universality classes [25].…”