Modified diffusive epidemic process on Apollonian networks

Abstract

We present an analysis of an epidemic spreading process on an Apollonian network that can describe an epidemic spreading in a non-sedentary population. We studied the modified diffusive epidemic process using the Monte Carlo method by computational analysis. Our model may be helpful for modeling systems closer to reality consisting of two classes of individuals: susceptible (A) and infected (B). The individuals can diffuse in a network according to constant diffusion rates \(D_{A}\) and \(D_{B}\), for the classes A and B, respectively, and obeying three diffusive regimes, i.e., \(D_{A}<D_{B}\), \(D_{A}=D_{B}\), and \(D_{A}>D_{B}\). Into the same site i, the reaction occurs according to the dynamical rule based on Gillespie’s algorithm. Finite-size scaling analysis has shown that our model exhibits continuous phase transition to an absorbing state with a set of critical exponents given by \(\beta /\nu =0.66(1)\), \(1/\nu =0.46(2)\), and \(\gamma '/\nu =-0.24(2)\) familiar to every investigated regime. In summary, the continuous phase transition, characterized by this set of critical exponents, does not have the same exponents of the mean-field universality class in both regular lattices and complex networks.