The diffusive epidemic process on Barabasi–Albert networks. Issue 4 (7th April 2021)

• Record Type: Journal Article
• Authors: Alves, T F A; Alves, G A; Macedo-Filho, A; Ferreira, R S; Lima, F W S
• Is Part Of: Journal of statistical mechanics. Issue 4(2021:Apr.)
• Publication Date: 2021-04-07
• Subjects: absorbing states -- agent-based models -- critical exponents and amplitudes -- random graphs, networks; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/abefe4
• Languages: English
• ISSNs: 1742-5468

Abstract

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.