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Item Robustness and fragility of the susceptible- infected- susceptible epidemic models on complex networks(Physical Review E, 2018) Cota, Wesley; Mata, Angélica S.; Ferreira, Silvio C.We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models have the same epidemic thresholds in mean-field theories but depending on the network properties, simulations yield a dual scenario, in which the epidemic thresholds of the modified SIS models can be either dramatically altered or remain unchanged in comparison with the standard dynamics. For uncorrelated synthetic networks having a power-law degree distribution with exponent γ<5/2, the SIS dynamics are robust exhibiting essentially the same outcomes for all investigated models. A threshold in better agreement with the heterogeneous rather than quenched mean-field theory is observed in the modified dynamics for exponent γ>5/2. Differences are more remarkable for γ>3, where a finite threshold is found in the modified models in contrast with the vanishing threshold of the original one. This duality is elucidated in terms of epidemic lifespan on star graphs. We verify that the activation of the modified SIS models is triggered in the innermost component of the network given by a k-core decomposition for γ<3 while it happens only for γ<5/2 in the standard model. For γ>3, the activation in the modified dynamics is collective involving essentially the whole network while it is triggered by hubs in the standard SIS. The duality also appears in the finite-size scaling of the critical quantities where mean-field behaviors are observed for the modified but not for the original dynamics. Our results feed the discussions about the most proper conceptions of epidemic models to describe real systems and the choices of the most suitable theoretical approaches to deal with these models.Item Griffiths phases in infinite- dimensional, non- hierarchical modular networks(Scientific Reports, 2018) Cota, Wesley; Ódor, Géza; Ferreira, Silvio C.Griffiths phases (GPs), generated by the heterogeneities on modular networks, have recently been suggested to provide a mechanism, rid of fine parameter tuning, to explain the critical behavior of complex systems. One conjectured requirement for systems with modular structures was that the network of modules must be hierarchically organized and possess finite dimension. We investigate the dynamical behavior of an activity spreading model, evolving on heterogeneous random networks with highly modular structure and organized non-hierarchically. We observe that loosely coupled modules act as effective rare-regions, slowing down the extinction of activation. As a consequence, we find extended control parameter regions with continuously changing dynamical exponents for single network realizations, preserved after finite size analyses, as in a real GP. The avalanche size distributions of spreading events exhibit robust power-law tails. Our findings relax the requirement of hierarchical organization of the modular structure, which can help to rationalize the criticality of modular systems in the framework of GPs.Item Local roughness exponent in the nonlinear molecular-beam-epitaxy universality class in one dimension(Physical Review, 2019-02) Ferreira, Silvio C.; Luis, Edwin E. Mozo; Assis, Thiago A. de; Andrade, Roberto F. S.We report local roughness exponents, αloc, for three interface growth models in one dimension which are believed to belong to the nonlinear molecular-beam-epitaxy (nMBE) universality class represented by the Villain-Lais-Das Sarma (VLDS) stochastic equation. We applied an optimum detrended fluctuation analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801 (2017)] and compared the outcomes with standard detrending methods. We observe in all investigated models that ODFA outperforms the standard methods providing exponents in the narrow interval αloc∈[0.96,0.98] quantitatively consistent with two-loop renormalization group predictions for the VLDS equation. In particular, these exponent values are calculated for the Clarke-Vvdensky and Das Sarma-Tamborenea models characterized by very strong corrections to the scaling, for which large deviations of these values had been reported. Our results strongly support the absence of anomalous scaling in the nMBE universality class and the existence of corrections in the form αloc=1−ε of the one-loop renormalization group analysis of the VLDS equation.Item Eden model with nonlocal growth rules and kinetic roughening in biological systems(Physical Review, 2018-08) Ferreira, Silvio C.; Santalla, Silvia N.We investigate an off-lattice Eden model where the growth of new cells is performed with a probability dependent on the availability of resources coming externally towards the growing aggregate. The concentration of nutrients necessary for replication is assumed to be proportional to the voids connecting the replicating cells to the outer region, introducing therefore a nonlocal dependence on the replication rule. Our simulations point out that the Kadar–Parisi–Zhang (KPZ) universality class is a transient that can last for long periods in plentiful environments. For conditions of nutrient scarcity, we observe a crossover from regular KPZ to unstable growth, passing by a transient consistent with the quenched KPZ class at the pinning transition. Our analysis sheds light on results reporting on the universality class of kinetic roughening in akin experiments of biological growth.Item Activation thresholds in epidemic spreading with motile infectious agents on scale-free networks(Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018) Silva, Diogo H.; Ferreira, Silvio C.We investigate a fermionic susceptible-infected-susceptible model with the mobility of infected individuals on uncorrelated scale-free networks with power-law degree distributions P(k)∼k−γP(k)∼k−γ of exponents 2<γ<32<γ<3. Two diffusive processes with diffusion rate DD of an infected vertex are considered. In the standard diffusion, one of the nearest-neighbors is chosen with equal chance, while in the biased diffusion, this choice happens with probability proportional to the neighbor’s degree. A non-monotonic dependence of the epidemic threshold on DD with an optimum diffusion rate D∗D∗, for which the epidemic spreading is more efficient, is found for standard diffusion while monotonic decays are observed in the biased case. The epidemic thresholds go to zero as the network size is increased and the form that this happens depends on the diffusion rule and the degree exponent. We analytically investigated the dynamics using quenched and heterogeneous mean-field theories. The former presents, in general, a better performance for standard and the latter for biased diffusion models, indicating different activation mechanisms of the epidemic phases that are rationalized in terms of hubs or max kk-core subgraphs. Nowadays, we live in an interwoven world where information, goods, and people move through a complex structure with widely diversified types of interactions such as on-line friendship and airport connections. These and many other systems of completely distinct nature can be equally suited in a theoretical representation called complex networks, in which the elements are represented by vertices and the interactions among them by edges connecting these vertices. The study of epidemic processes on complex networks represents one of the cornerstones in modern network science and can aid the prevention (or even stimulation) of disease or misinformation spreading. The relevance of the interplay between diffusion and epidemic spreading in real systems is self-evident since hosts of infectious agents, such as people and mobile devices, are constantly moving, being the carriers that promote the quick transition from a localized outbreak to a large scale epidemic scenario. In this work, we perform a theoretical analysis and report nontrivial roles played by mobility of infected agents on the efficiency of epidemic spreading running on the top of complex networks. We expect that our results will render impacts for forthcoming research related to the area.Item Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks(Computer Physics Communications, 2017-10) Cota, Wesley; Ferreira, Silvio C.Numerical simulation of continuous-time Markovian processes is an essential and widely applied tool in the investigation of epidemic spreading on complex networks. Due to the high heterogeneity of the connectivity structure through which epidemic is transmitted, efficient and accurate implementations of generic epidemic processes are not trivial and deviations from statistically exact prescriptions can lead to uncontrolled biases. Based on the Gillespie algorithm (GA), in which only steps that change the state are considered, we develop numerical recipes and describe their computer implementations for statistically exact and computationally efficient simulations of generic Markovian epidemic processes aiming at highly heterogeneous and large networks. The central point of the recipes investigated here is to include phantom processes, that do not change the states but do count for time increments. We compare the efficiencies for the susceptible–infected–susceptible, contact process and susceptible–infected–recovered models, that are particular cases of a generic model considered here. We numerically confirm that the simulation outcomes of the optimized algorithms are statistically indistinguishable from the original GA and can be several orders of magnitude more efficient.Item Origins of scaling corrections in ballistic growth models(Physical Review E, 2014-11-20) Alves, Sidiney G.; Oliveira, Tiago J.; Ferreira, Silvio C.We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes strong corrections to the scaling, comes from the fluctuations in the height increments along deposition events. Accounting for this correction in the scaling analysis, we obtain scaling exponents in excellent agreement with the KPZ class. We also propose a method to suppress these corrections, which consists in dividing the surface in bins of size ε and using only the maximal height inside each bin to do the statistics. Again, scaling exponents in remarkable agreement with the KPZ class are found. The binning method allows the accurate determination of the height distributions of the ballistic models in both growth and steady-state regimes, providing the universal underlying fluctuations foreseen for KPZ class in 2 + 1 dimensions. Our results provide complete and conclusive evidences that the ballistic model belongs to the KPZ universality class in 2 + 1 dimensions. Potential applications of the methods developed here, in both numerics and experiments, are discussed.Item Quasistationary analysis of the contact process on annealed scale-free networks(Statistical Mechanics, 2011-06-20) Ferreira, Silvio C.; Ferreira, Ronan S.; Pastor-Satorras, RomualdoWe present an analysis of the quasistationary (QS) state of the contact process (CP) on annealed scale-free networks using a mapping of the CP dynamics in a one-step process and analyzing numerically and analytically the corresponding master equation. The relevant QS quantities determined via the master equation exhibit an excellent agreement with direct QS stochastic simulations of the CP. The high accuracy of the resulting data allows a probe of the strong corrections to scaling present in both the critical and supercritical regions, corrections that mask the correct finite-size scaling obtained analytically by applying an exact heterogeneous mean-field approach. Our results represent a promising starting point for a deeper understanding of the contact process and absorbing phase transitions on real (quenched) complex networks.Item Phase transitions with infinitely many absorbing states in complex networks(Physical Review E, 2013-02-27) Sander, Renan S.; Ferreira, Silvio C.; Pastor-Satorras, RomualdoWe investigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite-size scaling exponents characterizing the transition are obtained in a heterogeneous mean-field (HMF) approximation and compared with extensive simulations, particularly in the case of heterogeneous scale-free networks. We observe that the TCP exhibits the same critical properties as the contact process, which undergoes an absorbing-state phase transition to a single absorbing state. The accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a HMF theory is a universal feature of absorbing-state phase transitions in complex networks, depending only on the locality of the interactions and independent of the number of absorbing states. The conditions for the applicability of the conjecture are discussed considering a parallel with the susceptible-infected-susceptible epidemic spreading model, which in fact belongs to a different universality class in complex networks.Item Multiscale model for the effects of adaptive immunity suppression on the viral therapy of cancer(Physical Biology, 2013-03-15) Paiva, Leticia R .; Silva, Hallan S.; Ferreira, Silvio C.; Martins, Marcelo L.Oncolytic virotherapy—the use of viruses that specifically kill tumor cells—is an innovative and highly promising route for treating cancer. However, its therapeutic outcomes are mainly impaired by the host immune response to the viral infection. In this paper, we propose a multiscale mathematical model to study how the immune response interferes with the viral oncolytic activity. The model assumes that cytotoxic T cells can induce apoptosis in infected cancer cells and that free viruses can be inactivated by neutralizing antibodies or cleared at a constant rate by the innate immune response. Our simulations suggest that reprogramming the immune microenvironment in tumors could substantially enhance the oncolytic virotherapy in immune-competent hosts. Viable routes to such reprogramming are either in situ virus-mediated impairing of CD8 + T cells motility or blockade of B and T lymphocytes recruitment. Our theoretical results can shed light on the design of viral vectors or new protocols with neat potential impacts on the clinical practice.