Diffusive Epidemic Process Research Articles

Modified diffusive epidemic process on Apollonian networks.

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 [Formula: see text] and [Formula: see text], for the classes A and B, respectively, and obeying three diffusive regimes, i.e., [Formula: see text], [Formula: see text], and [Formula: see text]. 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 [Formula: see text], [Formula: see text], and [Formula: see text] 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.

Two-dimensional diffusive epidemic process in the presence of quasiperiodic and quenched disorder

This work considers the diffusive epidemic process model coupled to the square lattice, the Penrose quasiperiodic lattice, and the Voronoi–Delaunay random lattice. The main objective is to verify if spatial disorder influences critical behavior. According to the Harris–Barghathi–Vojta criterion, quenched or quasiperiodic disorder can change the critical behavior of the system, depending on the disorder decay exponent of the lattice. We employed extensive Monte Carlo simulations of the relevant quantities. Furthermore, we estimate the critical exponent ratios. Our results suggest that the disorder does not change the critical behavior when comparing the critical exponent ratios for the three studied lattice structures. In addition, the critical exponents depend on the three possible diffusion regimes: (1) where diffusion is dominated by susceptible individuals, (2) where infected and susceptible individuals have the same diffusion constant, and (3) where diffusion is dominated by the infected individuals.

Subdiffusive Activity Spreading in the Diffusive Epidemic Process.

The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in combination with finite-size scaling analyses we reveal two qualitatively different processes that characterize the critical dynamics: subdiffusive propagation of infection clusters and diffusive fluctuations in the healthy population. This suggests the presence of a strong-coupling regime and sheds new light on a long-standing debate about the theoretical classification of the system.

The diffusive epidemic process on Barabasi–Albert networks

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 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.

Diffusive epidemic process in 3D: a two-species reaction–diffusion phase transition

By the use of Monte Carlo simulation we study the critical behavior of a three-dimensional stochastic lattice model describing a diffusive epidemic propagation process. In this model, healthy (A) and sick (B) individuals diffuse on the lattice with diffusion constants d A and d B , respectively, and undergo reactions B → A and A + B → 2B. We determine the absorbing phase transition between a steady reactive state and a vacuum state. We obtained the order parameter, order parameter fluctuations, correlation length and their critical exponents by the use of steady state and short-time dynamics simulations. We studied three different diffusion regimes: the case of species A diffusing much slower than species B (d A ≪ d B ), the case of species with equal diffusion constants (d A = d B ) and the case of species A diffusing much faster than species B (d A ≫ d B ). We found only second order transition for all three cases. We did not identify any signal of first order transition for the case d A > d B as predicted by field theory in first order approximation.

Critical properties of a vector-mediated epidemic process

We study the critical behavior of an epidemic propagation model with interacting static individuals and diffusive vectors. The model presents a non-equilibrium phase transition from an absorbing vacuum state to an epidemic state at a critical vector density which depends on the recovery rates of infected individuals and vectors. The simulation was performed in a linear chain of the proposed model and the finite time scale hypothesis was explored to estimate the vector critical density and dynamic critical exponents. Our results show that the absorbing-state phase transition belongs to the universality class of the symmetric diffusive epidemic process irrespective to the relative values of the recovery rates. On the other hand, the critical vector density shows a much stronger dependence on the recovery rate of vectors than on the corresponding recovery rate of individuals.

Stationary and dynamical critical behavior of the three-dimensional Diffusive Epidemic Process

We investigate the critical behavior of a stochastic lattice model describing the hopping of two species that undergo reactions B→A and A+B→2B. We simulate the model defined on a 3D lattice and determine the threshold of the absorbing phase transition to the state at which species B is extinct. Using steady state and short-time dynamics simulations, we calculate the order parameter, order parameter fluctuations, correlation length and their critical exponents. We focus in the case of species A diffusing much faster than species B. We did not find signatures of a first-order transition that has been conjectured in the literature. We report a continuous transition with the perpendicular correlation exponent ν⊥≈0.61(6), in agreement with ν⊥=2∕D. Also, for this diffusion regime, we estimate β∕ν⊥=1.48, very close to the ϵ expansion prediction β∕ν⊥=D−ε∕82 (ε=4−D) for the regime of equally diffusing particles.

Nonperturbative renormalization group for the diffusive epidemic process.

We consider the Diffusive Epidemic Process (DEP), a two-species reaction-diffusion process originally proposed to model disease spread within a population. This model exhibits a phase transition from an active epidemic to an absorbing state without sick individuals. Field-theoretic analyses suggest that this transition belongs to the universality class of Directed Percolation with a Conserved quantity (DP-C, not to be confused with conserved-directed percolation C-DP, appearing in the study of stochastic sandpiles). However, some exact predictions derived from the symmetries of DP-C seem to be in contradiction with lattice simulations. Here we revisit the field theory of both DP-C and DEP. We discuss in detail the symmetries present in the various formulations of both models. We then investigate the DP-C model using the derivative expansion of the nonperturbative renormalization group formalism. We recover previous results for DP-C near its upper critical dimension d_{c}=4, but show how the corresponding fixed point seems to no longer exist below d≲3. Consequences for the DEP universality class are considered.

Hyperuniformity of initial conditions and critical decay of a diffusive epidemic process belonging to the Manna class.

For a fixed-energy Manna sandpile model belonging to a Manna class in one dimension (d=1), we recently showed that the critical decay is different for random and regular initial conditions (ICs). Compared with previous results of natural IC for several models, we suggested for the Manna class that the critical decay depends on the characteristics of the three ICs. But the dependence on the random and regular ICs was shown only for a single model. In this work, we study the critical decay for the random and regular ICs for another model of the Manna class in d=1, a diffusive epidemic process. It is shown that the critical decay exponent agrees with the previous result for each IC, which verifies that IC dependence is a common feature of the Manna class. In addition, for the random and regular ICs, we measure the variance σ^{2}(r) of total particle density in a region of size r by increasing r up to system size and investigate its temporal evolution toward the value σ_{q}^{2}(r) of the quasisteady state at criticality. In d=1,σ^{2}(r) scales as σ^{2}(r)∼r^{-ψ} with ψ=1 for random distributions and 1<ψ≤2 for hyperuniform ones. The temporal evolution shows that σ^{2}(r) of the two ICs differently relax toward σ_{q}^{2}(r) and the regular IC becomes a hyperuniform distribution of ψ=2 in the beginning of the evolution. We estimate ψ=1.45(3) for both the quasisteady state and absorbing states, so the quasisteady state is also as hyperuniform as absorbing states. The hyperuniformity of the quasisteady state shows that the natural IC also should be hyperuniform as much as the quasisteady state, because the natural IC is obtained from particle configurations close to the quasisteady state. Consequently, the different ψ of the three ICs suggest that σ^{2}(r) can classify the characteristics of the three ICs in a unified way and the different degree of hyperuniformity of the ICs provides another explanation for the observed IC-dependent critical decay in a point of view of initial fluctuations and correlations.

Dynamical scaling behavior of the one-dimensional conserved directed-percolation universality class

We investigate the dynamical scaling behavior of the static diffusive epidemic process and a fixed-energy Manna sandpile model, undergoing nonequilibrium absorbing phase transitions in one dimension. These models belong to the so-called conserved directed-percolation or Manna universality class characterized by the conservation of the total particle number, activity coupled to a nondiffusive conserved field and infinitely many absorbing states. We measure the dynamical exponents of these models in one dimension by using the critical spreading simulation of a localized activity in absorbing configurations. In the spreading simulations, boundaries are never touched, so the results are free from the finite-size effects. In contrast to the scattered results for the different models from the previous finite-size scaling analyses, we obtain consistent estimates of the dynamical exponents for both models.

Critical properties of the diffusive epidemic process obtained via an automatic searchtechnique

The diffusive epidemic process DEP is composed of A and Bspecies that independently diffuse on a lattice with diffusion ratesDA andDB and follow the probabilistic dynamical rule and . This model belongs to the category of non-equilibrium systems with an absorbing state anda phase transition between active and inactive states. We investigate the critical behaviorof the one-dimensional DEP using an auto-adaptive algorithm to find critical points: themethod of automatic searching for critical points MASCP. We compare our results with theliterature and we find that the MASCP successfully finds the critical exponents1/ν and1/zν in all thecases DA = DB,DA < DB andDA > DB. The simulations show that the DEP has the same critical exponents as are expected fromfield-theoretical arguments. Moreover, we find that, contrary to a renormalization groupprediction, the system does not show a discontinuous phase transition in the regime ofDA > DB.

Critical behavior of a model for catalyzed autoamplification

We examine the critical behavior of a model of catalyzed autoamplification inspired by a common motif in genetic networks. Similar to models in the directed percolation (DP) universality class, a phase transition between an absorbing state with no copies of the autoamplifying species A and an active state with a finite amount of A occurs at the point at which production and removal of A are balanced. A suitable coordinate transformation shows that this model corresponds to one with three fields, one of which relaxes exponentially, one of which displays critical behavior, and one of which has purely diffusive dynamics but exerts an influence on the critical field. Using stochastic simulations that account for discrete molecular copy numbers in one, two, and three dimensions, we show that this model has exponents that are distinct from previously studied reaction-diffusion systems, including the few with more than one field (unidirectionally coupled DP processes and the diffusive epidemic process). Thus the requirement of a catalyst changes the fundamental physics of autoamplification. Estimates for the exponents of the diffusive epidemic process in two dimensions are also presented.

The nature of the absorbing-state phase transition in the diffusive epidemic process

In the diffusive epidemic process (DEP), particles of two species (A and B) hop on a lattice and undergo reactions B → A and A + B → 2B; the B-free state is absorbing. Renormalization group analysis predicts a continuous phase transition to the absorbing state when the hopping rate of B particles, DB, is greater than or equal to that of A particles, and a discontinuous transition for DA > DB. Monte Carlo simulations of the one-dimensional DEP suggest that, on the contrary, the transition is continuous in all cases. Here we present strong evidence for a continuous transition for DA > DB in the two-dimensional model as well. Our results suggest that hysteresis is absent in both the one- and two-dimensional cases.

Diffusive epidemic process: theory and simulation

We study the continuous absorbing-state phase transition in the one-dimensional diffusiveepidemic process via mean-field theory and Monte Carlo simulation. In this model,particles of two species (A and B) hop on a lattice and undergo reactions and ; the total particle number is conserved. We formulate the model as a continuous-timeMarkov process described by a master equation. A phase transition between the(absorbing) B-free state and an active state is observed as the parameters (reaction anddiffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising,nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles.A computational realization of the process that is faithful to the transition rates definingthe model is devised, allowing for direct comparison with theory. Using the quasi-stationarysimulation method we determine the order parameter and the survival time in systems ofup to 4000 sites. Due to strong finite-size effects, the results converge only for large systemsizes. We find no evidence for a discontinuous transition. Our results are consistentwith the existence of three distinct universality classes, depending on whether Aparticles diffusive more rapidly, less rapidly or at the same rate as B particles. Wealso perform quasi-stationary simulations of the triplet creation model, whichyield results consistent with a discontinuous transition at high diffusion rates.

Monte Carlo study of the critical behavior of a diffusive epidemic process

We perform Monte Carlo simulations of a symmetric 1D diffusive epidemic propagation process. The system presents a continuous phase transition between a stationary vacuum state and a steady reactive state. Renormalization group calculations have predicted that the dynamical critical exponent z=2 and the correlation exponent ν=2. However, recent numerical results have reported ν=2.21. In this work we employ a finite size scaling analysis of order parameter and relaxation time data at the vicinity of the critical point and show that, once corrections to scaling are taken into account, the numerical data are consistent with the RG results. Further, we report a precise estimate for β/ ν.

Critical behavior of a one-dimensional diffusive epidemic process.

We investigate the critical behavior of a one-dimensional diffusive epidemic propagation process by means of a Monte Carlo procedure. In the model, healthy (A) and sick (B) individuals diffuse on a lattice with diffusion constants D(A) and D(B), respectively. According to a Wilson renormalization calculation, the system presents a second-order phase transition between a steady reactive state and a vacuum state, with distinct universality classes for the cases D(A)=D(B) and D(A)<D(B). A first-order transition has been conjectured for D(A)>D(B). In this work we perform a finite size scaling analysis of order parameter data at the vicinity of the critical point in dimension d=1. Our results show no signature of a first-order transition in the case of D(A)>D(B). A finite size scaling typical of second-order phase transitions fits well the data from all three regimes. We found that the correlation exponent nu=2 as predicted by field-theoretical arguments. Estimates for beta/nu are given for all relevant regimes.