DECEA - Departamento de Ciências Exatas e Aplicadas
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Navegando DECEA - Departamento de Ciências Exatas e Aplicadas por Assunto "Asynchronous SIR model"
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Item Epidemic outbreaks on random Voronoi–Delaunay triangulations.(2020) Alencar, David Santana Marques; Alves, Tayroni Francisco de Alencar; Alves, Gladstone de Alencar; Macedo Filho, Antonio de; Ferreira, Ronan SilvaWe study epidemic outbreaks on random Delaunay triangulations by applying the Asynchronous SIR (susceptible–infected–removed) dynamics coupled to two-dimensional Voronoi–Delaunay triangulations. In order to investigate the critical behavior of the model, we obtain the cluster size distribution by using Newman–Ziff algorithm, allowing to simulate random inhomogeneous lattices and measure any desired observable related to percolation. We numerically calculate the order parameter, defined as the wrapping cluster density, the mean cluster size, and Binder cumulant ratio defined for percolation in order to estimate the epidemic threshold. Our findings suggest that the system falls into two-dimensional dynamic percolation universality class and the quenched random disorder is irrelevant, in agreement with results for classical percolation.Item Epidemic outbreaks on two-dimensional quasiperiodic lattices.(2020) Santos, G. B. M.; Alves, Tayroni Francisco de Alencar; Alves, Gladstone de Alencar; Macedo Filho, Antonio de; Ferreira, Ronan SilvaWe present a novel kinetic Monte Carlo technique to study the susceptible-infected-removed model in order to simulate epidemic outbreaks on two quasiperiodic lattices, namely, Penrose and Ammann-Beenker. Our analysis around criticality is performed by investigating the order parameter, which is defined as the probability of growing a spanning cluster formed by removed sites, evolving from an initial system configuration with a single random chosen infective site. This system is studied by means of the cluster size distribution, obtained by the Newman-Ziff algorithm. Additionally, we obtained the mean cluster size, and a cumulant ratio to estimate the epidemic threshold. In spite of the quasiperiodic order moves the transition point, compared to periodic lattices, this is not able to alter the universality class of the model, leading to the same critical exponents. In addition, our technique can be generalized to study epidemic outbreaks in networks and diffusing populations.