arXiv subjects

Martina Alutto

Publications and source records attributed to Martina Alutto.

11 recordsLinked to original sources

arXiv2026

Network Behavioral-Feedback SIR Epidemic Model

We propose a network behavioral-feedback Susceptible-Infected-Recovered (SIR) epidemic model in which the interaction matrix describing the infection rates across subpopulations depends in feedback on the current epidemic state. This model captures both heterogeneities in individuals mixing, contact frequency, aptitude to contract and spread the infection, and endogenous behavioral responses such as voluntary social distancing and the adoption of self-protective measures. We study the stability of the equilibria and illustrate through several examples how the shape of the stability region depends on the structure of the interaction matrix, providing insights for the design of effective control strategies. We then analyze the transient behavior of the dynamics, showing that, for a special class of rank-1 interaction matrices, there always exists an aggregate infection curve that exhibits a unimodal behavior, expanding the results on the unimodality of infection curve known in the literature of epidemic models and paving the way for future control applications.

math.DS↗

arXiv2026

On Leadership Emergence in Opinion Dynamics on Social Networks

Leadership in social groups emerges dynamically through interaction and opinion exchange. Empirical evidence indicates that individuals expressing strong opinions tend to gain influence, while sustained leadership critically depends on maintaining alignment with the surrounding social context. Motivated by these observations, we introduce a coupled dynamical model describing the simultaneous evolution of opinions and leadership in a networked population. Extending the Friedkin-Johnsen framework, we represent leadership as a time-varying susceptibility to social influence, which evolves according to a game-theoretic mechanism, consistent with social psychology evidence. Within this setting, agents strengthen their leadership by expressing decisive yet socially coherent opinions, whereas misalignment with the collective state results in a loss of influence. We analyze the coupled dynamics and establish sufficient conditions to identify which agents necessarily emerge as leaders and which act as followers in the social network.

physics.soc-ph↗

arXiv2026

On a Co-evolving Opinion-Leadership Model in Social Networks

Leadership in social groups is often a dynamic characteristic that emerges from interactions and opinion exchange. Empirical evidence suggests that individuals with strong opinions tend to gain influence, at the same time maintaining alignment with the social context is crucial for sustained leadership. Motivated by the social psychology literature that supports these empirical observations, we propose a novel dynamical system in which opinions and leadership co-evolve within a social network. Our model extends the Friedkin-Johnsen framework by making susceptibility to peer influence time-dependent, turning it into the leadership variable. Leadership strengthens when an agent holds strong yet socially aligned opinions, and declines when such alignment is lost, capturing the trade-off between conviction and social acceptance. After illustrating the emergent behavior of this complex system, we formally analyze the coupled dynamics, establishing sufficient conditions for convergence to a non-trivial equilibrium, and examining two time-scale separation regimes reflecting scenarios where opinion and leadership evolve at different speeds.

physics.soc-ph↗

arXiv2026

Optimal Control of Behavioral-Feedback SIR Epidemic Model

We consider a behavioral-feedback SIR epidemic model, in which the infection rate depends in feedback on the fractions of susceptible and infected agents, respectively. The considered model allows one to account for endogenous adaptation mechanisms of the agents in response to the epidemics, such as voluntary social distancing, or the adoption of face masks. For this model, we formulate an optimal control problem for a social planner that has the ability to reduce the infection rate to keep the infection curve below a certain threshold within an infinite time horizon, while minimizing the intervention cost. Based on the dynamic properties of the model, we prove that, under quite general conditions on the infection rate, the filling the box strategy is the optimal control. This strategy consists in letting the epidemics spread without intervention until the threshold is reached, then applying the minimum control that leaves the fraction of infected individuals constantly at the threshold until the reproduction number becomes less than one and the infection naturally fades out. Our result generalizes one available in the literature for the equivalent problem formulated for the classical SIR model, which can be recovered as a special case of our model when the infection rate is constant. Our contribution enhances the understanding of epidemic management with adaptive human behavior, offering insights for robust containment strategies.

eess.SY↗

arXiv2026

On a Coupled Adoption-Opinion Framework for Competing Innovations

In this paper, we propose a two-layer adoption-opinion model to study the diffusion of two competing technologies within a population whose opinions evolve under social influence and adoption-driven feedback. After adopting one technology, individuals may become dissatisfied and switch to the alternative. We prove the existence and uniqueness of the adoption-diffused equilibrium, showing that both technologies coexist and that neither partial-adoption nor monopoly can arise. Numerical simulations show that while opinions shape the equilibrium adoption levels, the relative market share between the two technologies depends solely on their user-experience. As a consequence, interventions that symmetrically boost opinions or adoption can disproportionately favor the higher-quality technology, illustrating how symmetric control actions may generate asymmetric outcomes.

eess.SY↗

arXiv2026

Model Predictive Control for Coupled Adoption-Opinion Dynamics

This paper investigates an optimal control problem for an adoption-opinion model that couples opinion dynamics with a compartmental adoption framework on a multilayer network to study the diffusion of sustainable behaviors. Adoption evolves through social contagion and perceived benefits, while opinions are shaped by social interactions and feedback from adoption levels. Individuals may also stop adopting virtuous behavior due to external constraints or shifting perceptions, affecting overall diffusion. After the stability analysis of equilibria, both in the presence and absence of adopters, we introduce a Model Predictive Control (MPC) framework that optimizes interventions by shaping opinions rather than directly enforcing adoption. This nudge-based control strategy allows policymakers to influence diffusion indirectly, making interventions more effective and scalable. Numerical simulations demonstrate that, in the absence of control, adoption stagnates, whereas MPC-driven interventions sustain and enhance adoption across communities.

eess.SY↗

arXiv2025

Modeling and Control of Sustainable Transitions through Opinion-Behavior Coupling in Heterogeneous Networks

Understanding how sustainable behaviors spread within heterogeneous societies requires the integration of behavioral data, social influence mechanisms, and structured approaches to control. In this paper, we propose a data-driven computational framework for coupled opinion-adoption dynamics in social systems. Each node in the multilayer network represents a community characterized by a specific age group and mobility level, derived from large-scale survey data on the predisposition to adopt electric vehicles in Northern Europe. The proposed model captures three mechanisms: behavioral contagion through social and informational diffusion, abandonment driven by dissatisfaction, and feedback between opinions and adoption levels through social influence. Analyzing the equilibrium points of the coupled system allows us to derive the conditions that enable large-scale adoption. We empirically calibrate the model using data to construct synthetic populations and social similarity networks, which we use to explore targeted interventions that promote sustainable transitions. Specifically, the analysis focuses on two types of control strategies: opinion-based policies, which act on the social network layer, and policies that aim to improve experience and reduce dissatisfaction. Simulation results show that the latter ensure more stable and long-term adoption, offering concrete insights for designing effective interventions in sociotechnical transitions toward sustainability.

cs.SI↗

arXiv2025

Predictive Control Strategies for Sustaining Innovation Adoption on Multilayer Social Networks

This paper studies an optimal control problem for an adoption-opinion model that couples innovation adoption with opinion formation on a multilayer network. Adoption spreads through social contagion and perceived benefits, while opinions evolve via social interactions and feedback from adoption levels. Individuals may abandon adoption due to dissatisfaction or external constraints, potentially hindering diffusion. We analyze system equilibria and their stability, identifying conditions under which adoption persists. We introduce a Model Predictive Control (MPC) strategy that dynamically adapts interventions to the predicted system evolution. Three types of control are compared: shaping opinions, acting on the adoption rate, and reducing dissatisfaction. Overall, MPC interventions outperform static constant control, achieving higher adoption at comparable or lower cost. These results highlight the potential of predictive, adaptive strategies to support sustainable behavior diffusion, offering policymakers scalable tools for effective interventions.

math.OC↗

arXiv2025

Behavioral-feedback SIR epidemic model: analysis and control

This paper investigates a behavioral-feedback SIR model in which the infection rate adapts dynamically based on the fractions of susceptible and infected individuals. We introduce an invariant of motion and we characterize the peak of infection. We further examine the system under a threshold constraint on the infection level. Based on this analysis, we formulate an optimal control problem to keep the infection curve below a healthcare capacity threshold while minimizing the economic cost. For this problem, we study a feasible strategy that involves applying the minimal necessary restrictions to meet the capacity constraint and characterize the corresponding cost.

q-bio.PE↗

arXiv2024

On the dynamic behavior of the network SIR epidemic model

We study a susceptible-infected-recovered (SIR) epidemic model on a network of $n$ interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the classical scalar epidemic SIR model, where the infection curve is known to be unimodal (either always decreasing over time, or initially increasing until reaching a peak and from then on monotonically decreasing and asymptotically vanishing), we show the possible occurrence of multimodal infection curves in the network SIR epidemic model with $n\ge2$ subpopulations. We then focus on the special case of rank-$1$ interaction matrices, modeling subpopulations of homogeneously mixing individuals with different activity rates, susceptibility to the disease, and infectivity levels. For this special case, we find $n$ invariants of motion and provide an explicit expression for the limit equilibrium point. We also determine necessary and sufficient conditions for stability of the equilibrium points. We then establish an upper bound on the number of changes of monotonicity of the infection curve at the single node level and provide sufficient conditions for its multimodality. Finally, we present some numerical results revealing that, in the case of interaction matrices with rank larger than $1$, the single nodes' infection curves may display multiple peaks.

math.DS↗

arXiv2021

On SIR epidemic models with feedback-controlled interactions and network effects

We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and infected individuals. This allows one to model either the reaction of individuals to the information about the spread of the disease or the result of government restriction measures, imposed to limit social interactions and contain contagion. We study the effect of both smooth dependancies of the contact rate for which we prove the existence of a threshold phenomenon that generalizes the well-known dichotomy associated to the reproduction rate parameter in the classical SIR model, and discontinuous feedback terms, which can be studied using tools from sliding mode control. Finally, we consider network SIR models involving different subpopulations that interact on a contact graph and present some preliminary simulations of modified versions of the classic SIR network.

math.DS↗