arXiv subjects

Federico Vazquez

Publications and source records attributed to Federico Vazquez.

At least 19 recordsLinked to original sources

arXiv2025

Decision-Making under Negativity Bias: Double Hysteresis in the Opinion-Dependent $q$-Voter Model

Negative information often exerts a disproportionately strong impact on human decision-making, a phenomenon known as the negativity bias. In behavioral economics, this effect is formally captured by Prospect Theory, which posits that losses loom larger than equivalent gains. For example, a single negative product review can outweigh numerous positive ones, reflecting this principle of loss aversion in consumer behavior. While this psychological effect has been widely documented, its implications for collective opinion dynamics, critical for understanding market stability and reputation dynamics, remain poorly understood. Here, we generalize the $q$-voter model with independence by introducing opinion-dependent influence group sizes, $q_+$ and $q_-$, which represent the social reinforcement needed to change an opinion from negative to positive and from positive to negative, respectively. We study two versions of this asymmetric model: a baseline model that reduces to the standard $q$-voter model when $q_+ = q_- = q$, and an extended model that incorporates an additional asymmetry expressed as a preference for one opinion. In its reduced version, this represents a minimal model in terms of non-linearity within the $q$-voter framework that allows for discontinuous phase transitions and hysteresis. Using mean-field analysis and computer simulations, we show that these modifications lead to rich collective behaviors, including double hysteresis, one form of which is irreversible, providing a mechanism for path-dependence and the sustained, irrecoverable damage to collective sentiment, brand equity, or market confidence.

physics.soc-ph↗

arXiv2024

Optimal control for a SIR model with limited hospitalised patients

This paper analyses the optimal control of infectious disease propagation using a classic susceptible-infected-recovered (SIR) model characterised by permanent immunity and the absence of available vaccines. The control is performed over a time-dependent mean reproduction number, in order to minimise the cumulative number of ever-infected individuals (recovered), under different constraints. We consider constraints on isolation measures ranging from partial lockdown to non-intervention, as well as the social and economic costs associated with such isolation, and the capacity limitations of intensive care units that limits the number of infected individuals to a maximum allowed value. We rigorously derive an optimal quarantine strategy based on necessary optimality conditions. The obtained optimal strategy is of a boundary-bang type, comprising three phases: an initial phase with no intervention, a second phase maintaining the infected population at its maximum possible value, and a final phase of partial lockdown applied over a single interval. The optimal policy is further refined by optimising the transition times between these phases. We show that these results are in excellent agreement with the numerical solution of the problem.

math.OC↗

arXiv2023

Ordering dynamics of nonlinear voter models

We study the ordering dynamics of nonlinear voter models with multiple states, also providing a discussion of the two-state model. The rate with which an individual adopts an opinion scales as the $q$-th power of the number of the individual's neighbours in that state. For $q>1$ the dynamics favor the opinion held by the most agents. The ordering to consensus is driven by deterministic drift, and noise only plays a minor role. For $q<1$ the dynamics favors minority opinions, and for multistate models the ordering proceeds through a noise-driven succession of metastable states. Unlike linear multi-state systems, the nonlinear model cannot be reduced to an effective two-state model. We find that the average density of active interfaces in the model with multiple opinion states does not show a single exponential decay in time for $q<1$, again at variance with the linear model. This highlights the special character of the conventional (linear) voter model, in which deterministic drift is absent. As part of our analysis, we develop a pair approximation for the multi-state model on graphs, valid for any positive real value of $q$, improving on previous approximations for nonlinear two-state voter models.

physics.soc-ph↗

arXiv2023

Contrarian Majority rule model with external oscillating propaganda and individual inertias

We study the Galam majority rule dynamics with contrarian behavior and an oscillating external propaganda, in a population of agents that can adopt one of two possible opinions. In an iteration step, a random agent interacts with other three random agents and takes the majority opinion among the agents with probability $p(t)$ (majority behavior) or the opposite opinion with probability $1-p(t)$ (contrarian behavior). The probability of following the majority rule $p(t)$ varies with the temperature $T$ and is coupled to a time-dependent oscillating field that mimics a mass media propaganda, in a way that agents are more likely to adopt the majority opinion when it is aligned with the sign of the field. We investigate the dynamics of this model on a complete graph and find various regimes as $T$ is varied. A transition temperature $T_c$ separates a bimodal oscillatory regime for $T T_c$ in which $m$ oscillates around zero. These regimes are characterized by the distribution of residence times that exhibits a unique peak for a resonance temperature $T^*$, where the response of the system is maximum. An insight into these results is given by a mean-field approach, which also shows that $T^*$ and $T_c$ are closely related.

physics.soc-ph↗

arXiv2022

Modeling and analysis of social phenomena: challenges and possible research directions

This opening editorial aims to interest researchers and encourage novel research in the closely related fields of sociophysics and computational social science. We briefly discuss challenges and possible research directions in the study of social phenomena, with a particular focus on opinion dynamics. The aim of this special issue is to allow physicists, mathematicians, engineers and social scientists to show their current research interests in social dynamics, as well as to collect recent advances and new techniques in the analysis of social systems.

physics.soc-ph↗

arXiv2022

Contrarian Voter Model under the influence of an Oscillating Propaganda: Consensus, Bimodal behavior and Stochastic Resonance

We study the contrarian voter model for opinion formation in a society under the influence of an external oscillating propaganda and stochastic noise. Each agent of the population can hold one of two possible opinions on a given issue --against or in favor, and interacts with its neighbors following either an imitation dynamics (voter behavior) or an anti-alignment dynamics (contrarian behavior): each agent adopts the opinion of a random neighbor with a time-dependent probability $p(t)$, or takes the opposite opinion with probability $1-p(t)$. The imitation probability $p(t)$ is controlled by the social temperature $T$, and varies in time according to a periodic field that mimics the influence of an external propaganda, so that a voter is more prone to adopt an opinion aligned with the field. We simulate the model in complete graph and in lattices, and find that the system exhibits a rich variety of behaviors as $T$ is varied: opinion consensus for $T=0$, a bimodal behavior for $T T_c$, and full disorder for $T \gg 1$. The transition temperature $T_c$ vanishes with the population size $N$ as $T_c \simeq 2/\ln N$ in complete graph. Besides, the distribution of residence times $t_r$ in the bimodal phase decays approximately as $t_r^{-3/2}$. Within the oscillatory regime, we find a stochastic resonance-like phenomenon at a given temperature $T^*$. Also, mean-field analytical results show that the opinion oscillations reach a maximum amplitude at an intermediate temperature, and that exhibit a lag respect to the field that decreases with $T$.

physics.soc-ph↗

arXiv2022

Spatial effects in parasite induced marine diseases of immobile hosts

Emerging marine infectious diseases pose a substantial threat to marine ecosystems and the conservation of their biodiversity. Compartmental models of epidemic transmission in marine sessile organisms, available only recently, are based on non-spatial descriptions in which space is homogenised and parasite mobility is not explicitly accounted for. However, in realistic scenarios epidemic transmission is conditioned by the spatial distribution of hosts and the parasites mobility patterns, calling for a explicit description of space. In this work we develop a spatially-explicit individual-based model to study disease transmission by waterborne parasites in sessile marine populations. We investigate the impact of spatial disease transmission through extensive numerical simulations and theoretical analysis. Specifically, the effects of parasite mobility into the epidemic threshold and the temporal progression of the epidemic are assessed. We show that larger values of pathogen mobility imply more severe epidemics, as the number of infections increases, and shorter time-scales to extinction. An analytical expression for the basic reproduction number of the spatial model is derived as function of the non-spatial counterpart, which characterises a transition between a disease-free and a propagation phase, in which the disease propagates over a large fraction of the system.

q-bio.PE↗

arXiv2022

Bi-layer voter model: Modeling intolerant/tolerant positions and bots in opinion dynamics

The diffusion of opinions in Social Networks is a relevant process for adopting positions and attracting potential voters in political campaigns. Opinion polarization, bias, targeted diffusion, and the radicalization of postures are key elements for understanding voting dynamics. In particular, social bots are a new element that can have a pronounced effect on the formation of opinions during elections by, for instance, creating fake accounts in social networks to manipulate elections. Here we propose a voter model incorporating bots and radical or intolerant individuals in the decision-making process. The dynamics of the system occur in a multiplex network of interacting agents composed of two layers, one for the dynamics of opinions where agents choose between two possible alternatives, and the other for the tolerance dynamics, in which agents adopt one of two tolerance levels. The tolerance accounts for the likelihood to change opinion in an interaction, with tolerant (intolerant) agents switching opinion with probability $1.0$ ($γ\le 1$). We find that intolerance leads to a consensus of tolerant agents during an initial stage that scales as $τ^+ \sim γ^{-1} \ln N$, who then reach an opinion consensus during the second stage in a time that scales as $τ\sim N$, where $N$ is the number of agents. Therefore, very intolerant agents ($γ\ll 1$) could considerably slow down dynamics towards the final consensus state. We also find that the inclusion of a fraction $σ_{\mathbb{B}}^-$ of bots breaks the symmetry between both opinions, driving the system to a consensus of intolerant agents with the bots' opinion. Thus, bots eventually impose their opinion to the entire population, in a time that scales as $τ_B^- \sim γ^{-1}$ for $γ\ll σ_{\mathbb{B}}^-$ and $τ_B^- \sim 1/σ_{\mathbb{B}}^-$ for $σ_{\mathbb{B}}^- \ll γ$.

physics.soc-ph↗

arXiv2021

Random multi-player games

The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many situations, however, interactions between different numbers of players in each round could take place, and this case can not be reduced to pairwise interactions. In this work we formalize and generalize the definition of evolutionary stable strategy (ESS) to be able to include a scenario in which the game is played by two players with probability $p$, and by three players with the complementary probability $1-p$. We show the existence of equilibria in pure and mixed strategies depending on the probability $p$, on a concrete example of the duel-truel game. We find a range of $p$ values for which the game has a mixed equilibrium and the proportion of players in each strategy depends on the particular value of $p$. We prove that each of these mixed equilibrium points are ESS. A more realistic way to study this dynamics with high-order interactions is to look at how it evolves in complex networks. We introduce and study an agent-based model on a network with a fixed number of nodes, which evolves as the replicator equation predicts. By studying the dynamics of this model on random networks we find that the phase transitions between the pure and mixed equilibria depend on the probability $p$ and also on the mean degree of the network.

physics.soc-ph↗

arXiv2021

Noisy multistate voter model for flocking in finite dimensions

We study a model for the collective behavior of self-propelled particles subject to pairwise copying interactions and noise. Particles move at a constant speed $v$ on a two--dimensional space and, in a single step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle, with the addition of a perturbation of amplitude $η$ (noise). We investigate how the global level of particles' alignment (order) is affected by their motion and the noise amplitude $η$. In the static case scenario $v=0$ where particles are fixed at the sites of a square lattice and interact with their first neighbors, we find that for any noise $η_c>0$ the system reaches a steady state of complete disorder in the thermodynamic limit, while for $η=0$ full order is eventually achieved for a system with any number of particles $N$. Therefore, the model displays a transition at zero noise when particles are static, and thus there are no ordered steady states for a finite noise ($η>0$). We show that the finite-size transition noise vanishes with $N$ as $η_c^{1D} \sim N^{-1}$ and $η_c^{2D} \sim \left(N \ln N \right)^{-1/2}$ in one and two--dimensional lattices, respectively, which is linked to known results on the behavior of a type of noisy voter model for catalytic reactions. When particles are allowed to move in the space at a finite speed $v>0$, an ordered phase emerges, characterized by a fraction of particles moving in a similar direction. The system exhibits an order-disorder phase transition at a noise amplitude $η_c>0$ that is proportional to $v$, and that scales approximately as $η_c \sim v \, (-\ln v)^{-1/2}$ for $v \ll 1$. These results show that the motion of particles is able to sustain a state of global order in a system with voter-like interactions.

physics.soc-ph↗

arXiv2021

Species exclusion and coexistence in a noisy voter model with a competition-colonization tradeoff

We introduce an asymmetric noisy voter model to study the joint effect of immigration and a competition-dispersal tradeoff in the dynamics of two species competing for space in regular lattices. Individuals of one species can invade a nearest-neighbor site in the lattice, while individuals of the other species are able to invade sites at any distance but are less competitive locally, i.e., they establish with a probability $g \le 1$. The model also accounts for immigration, modeled as an external noise that may spontaneously replace an individual at a lattice site by another individual of the other species. This combination of mechanisms gives rise to a rich variety of outcomes for species competition, including exclusion of either species, mono-stable coexistence of both species at different population proportions, and bi-stable coexistence with proportions of populations that depend on the initial condition. Remarkably, in the bi-stable phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to a half loop dynamics associated to a cusp catastrophe, which causes the irreversible loss of the species with the shortest dispersal range.

q-bio.PE↗

arXiv2020

Disease and information spreading at different speeds in multiplex networks

Nowadays, one of the challenges we face when carrying out modeling of epidemic spreading is to develop methods to control disease transmission. In this article we study how the spreading of knowledge of a disease affects the propagation of that disease in a population of interacting individuals. For that, we analyze the interaction between two different processes on multiplex networks: the propagation of an epidemic using the susceptible-infected-susceptible dynamics and the dissemination of information about the disease --and its prevention methods-- using the unaware-aware-unaware dynamics, so that informed individuals are less likely to be infected. Unlike previous related models where disease and information spread at the same time scale, we introduce here a parameter that controls the relative speed between the propagation of the two processes. We study the behavior of this model using a mean-field approach that gives results in good agreement with Monte Carlo simulations on homogeneous complex networks. We find that increasing the rate of information dissemination reduces the disease prevalence, as one may expect. However, increasing the speed of the information process as compared to that of the epidemic process has the counter intuitive effect of increasing the disease prevalence. This result opens an interesting discussion about the effects of information spreading on disease propagation.

physics.soc-ph↗

arXiv2020

A model for the competition between political mono-polarization and bi-polarization

We investigate the phenomena of political bi-polarization in a population of interacting agents by means of a generalized version of the model introduced in PRE E 101, 012101 (2020) for the dynamics of voting intention. Each agent has a propensity $p$ in $[0,1]$ to vote for one of two political candidates. In an iteration step, two agents $i$ and $j$ with respective propensities $p_i$ and $p_j$ interact, and then $p_i$ either increases by an amount $h>0$ with a probability that is a nonlinear function of $p_i$ and $p_j$ or decreases by $h$ with the complementary probability. We study the behavior of the system under variations of a parameter $q \ge 0$ that measures the nonlinearity of the propensity update rule. We focus on the stability properties of the two distinct stationary states: mono-polarization in which all agents share the same extreme propensity ($0$ or $1$), and bi-polarization where the population is divided into two groups with opposite and extreme propensities. We find that the bi-polarized state is stable for $q q_c$, where $q_c$ is a transition value that decreases as $h$ decreases. We develop a rate equation approach whose stability analysis reveals that $q_c$ vanishes when $h$ becomes infinitesimally small. This result is supported by the analysis of a transport equation derived in the continuum $h \to 0$ limit. We also show by Monte Carlo simulations that the mean time $τ$ to reach mono-polarization in a system of size $N$ scales as $τ\sim N^α$ at $q_c$ , where $α(h)$ is a non-universal exponent.

physics.soc-ph↗

arXiv2019

Epidemic spreading with awareness and different timescales in multiplex networks

One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to stop a disease from spreading or to reduce its burden, as individuals aware of the presence of a disease can take measures to reduce their exposure to contagion. In this paper, we propose a mathematical model for the spread of diseases with awareness in complex networks. Unlike previous models, the information is propagated following a generalized Maki-Thompson rumor model. Flexibility on the timescale between information and disease spreading is also included. We verify that the velocity characterizing the diffusion of information awareness greatly influences the disease prevalence. We also show that a reduction in the fraction of unaware individuals does not always imply a decrease of the prevalence, as the relative timescale between disease and awareness spreading plays a crucial role in the systems' dynamics. This result is shown to be independent of the network topology. We finally calculate the epidemic threshold of our model, and show that it does not depend on the relative timescale. Our results provide a new view on how information influence disease spreading and can be used for the development of more efficient methods for disease control.

physics.soc-ph↗

arXiv2019

The role of voting intention in public opinion polarization

We introduce and study a simple model for the dynamics of voting intention in a population of agents that have to choose between two candidates. The level of indecision of a given agent is modeled by its propensity to vote for one of the two alternatives, represented by a variable $p \in [0,1]$. When an agent $i$ interacts with another agent $j$ with propensity $p_j$, then $i$ either increases its propensity $p_i$ by $h$ with probability $P_{ij}=ωp_i+(1-ω)p_j$, or decreases $p_i$ by $h$ with probability $1-P_{ij}$, where $h$ is a fixed step. We analyze the system by a rate equation approach and contrast the results with Monte Carlo simulations. We found that the dynamics of propensities depends on the weight $ω$ that an agent assigns to its own propensity. When all the weight is assigned to the interacting partner ($ω=0$), agents' propensities are quickly driven to one of the extreme values $p=0$ or $p=1$, until an extremist absorbing consensus is achieved. However, for $ω>0$ the system first reaches a quasi-stationary state of symmetric polarization where the distribution of propensities has the shape of an inverted Gaussian with a minimum at the center $p=1/2$ and two maxima at the extreme values $p=0,1$, until the symmetry is broken and the system is driven to an extremist consensus. A linear stability analysis shows that the lifetime of the polarized state, estimated by the mean consensus time $τ$, diverges as $τ\sim (1-ω)^{-2} \ln N$ when $ω$ approaches $1$, where $N$ is the system size. Finally, a continuous approximation allows to derive a transport equation whose convection term is compatible with a drift of particles from the center towards the extremes.

physics.soc-ph↗

arXiv2019

A multi-state voter model with imperfect copying

The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here we introduce and study a variant of the multi-state voter model in mean-field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise; a minimalistic model for flocking. We found that the ordering properties of this multi-state noisy voter model, measured by a parameter $ψ$ in [0, 1], depend on the amplitude $η$ of the copying error or noise and the population size N. In the case of perfect copying $η=0$ the system reaches an absorbing configuration with complete order ($ψ=1$) for all values of N. However, for any degree of imperfection $η>0$, we show that the average value of $ψ$ at the stationary state decreases with N as $\langle ψ\rangle \simeq 6/(π^2 η^2 N)$ for $η\ll 1$ and $η^2 N \gtrsim 1$, and thus the system becomes totally disordered in the thermodynamic limit $N \to \infty$. We also show that $\langle ψ\rangle \simeq 1-1.64 \, η^2 N$ in the vanishing small error limit $η\to 0$, which implies that complete order is never achieved for $η> 0$. These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.

physics.soc-ph↗

arXiv2019

Flocking dynamics with voter-like interactions

We study the collective motion of a large set of self-propelled particles subject to voter-like interactions. Each particle moves on a two-dimensional space at a constant speed in a direction that is randomly assigned initially. Then, at every step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle. We investigate the time evolution of the global alignment of particles measured by the order parameter $φ$, until complete order $φ=1.0$ is reached (polar consensus). We find that $φ$ increases as $t^{1/2}$ for short times and approaches exponentially fast to $1.0$ for long times. Also, the mean time to consensus $τ$ varies non-monotonically with the density of particles $ρ$, reaching a minimum at some intermediate density $ρ_{\tiny \mbox{min}}$. At $ρ_{\tiny \mbox{min}}$, the mean consensus time scales with the system size $N$ as $τ_{\tiny \mbox{min}} \sim N^{0.765}$, and thus the consensus is faster than in the case of all-to-all interactions (large $ρ$) where $τ=2N$. We show that the fast consensus, also observed at intermediate and high densities, is a consequence of the segregation of the system into clusters of equally-oriented particles which breaks the balance of transitions between directional states in well mixed systems.

physics.soc-ph↗

arXiv2018

Opinion dynamics in two dimensions: domain coarsening leads to stable bi-polarization and anomalous scaling exponents

We study an opinion dynamics model that explores the competition between persuasion and compromise in a population of agents with nearest-neighbor interactions on a two-dimensional square lattice. Each agent can hold either a positive or a negative opinion orientation, and can have two levels of intensity --moderate and extremist. When two interacting agents have the same orientation become extremists with persuasion probability $p$, while if they have opposite orientations become moderate with compromise probability $q$. These updating rules lead to the formation of same-opinion domains with a coarsening dynamics that depends on the ratio $r=p/q$. The population initially evolves to a centralized state for small $r$, where domains are composed by moderate agents and coarsening is without surface tension, and to a bi-polarized state for large $r$, where domains are formed by extremist agents and coarsening is driven by curvature. Consensus in an extreme opinion is finally reached in a time that scales with the population size $N$ and $r$ as $τ\simeq r^{-1} \ln N$ for small $r$ and as $τ\sim r^2 N^{1.64}$ for large $r$. Bi-polarization could be quite stable when the system falls into a striped state where agents organize into single-opinion horizontal, vertical or diagonal bands. An analysis of the stripes dynamics towards consensus allows to obtain an approximate expression for $τ$ which shows that the exponent $1.64$ is a result of the diffusion of the stripe interfaces combined with their roughness properties.

physics.soc-ph↗