arXiv subjects

Lorenzo Zino

Publications and source records attributed to Lorenzo Zino.

At least 37 records · Page 2Linked to original sources

arXiv2023

On Adaptive-Gain Control of Replicator Dynamics in Population Games

Controlling evolutionary game-theoretic dynamics is a problem of paramount importance for the systems and control community, with several applications spanning from social science to engineering. Here, we study a population of individuals who play a generic 2-action matrix game, and whose actions evolve according to a replicator equation -- a nonlinear ordinary differential equation that captures salient features of the collective behavior of the population. Our objective is to steer such a population to a specified equilibrium that represents a desired collective behavior -- e.g., to promote cooperation in the prisoner's dilemma. To this aim, we devise an adaptive-gain controller, which regulates the system dynamics by adaptively changing the entries of the payoff matrix of the game. The adaptive-gain controller is tailored according to distinctive features of the game, and conditions to guarantee global convergence to the desired equilibrium are established.

eess.SY↗

arXiv2023

Coevolutionary Dynamics of Actions and Opinions in Social Networks

Empirical studies suggest a deep intertwining between opinion formation and decision-making processes, but these have been treated as separate problems in the study of dynamical models for social networks. In this paper, we bridge the gap in the literature by proposing a novel coevolutionary model, in which each individual selects an action from a binary set and has an opinion on which action they prefer. Actions and opinions coevolve on a two-layer network. For homogeneous parameters, undirected networks, and under reasonable assumptions on the asynchronous updating mechanics, we prove that the coevolutionary dynamics is an ordinal potential game, enabling analysis via potential game theory. Specifically, we establish global convergence to the Nash equilibria of the game, proving that actions converge in a finite number of time steps, while opinions converge asymptotically. Next, we provide sufficient conditions for the existence of, and convergence to, polarized equilibria, whereby the population splits into two communities, each selecting and supporting one of the actions. Finally, we use simulations to examine the social psychological phenomenon of pluralistic ignorance.

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arXiv2022

Modeling the Co-evolution of Climate Impact and Population Behavior: A Mean-Field Analysis

Motivated by the climate crisis that is currently ravaging the planet, we propose and analyze a novel framework for the evolution of anthropogenic climate impact in which the evolution of human environmental behavior and environmental impact is coupled. Our framework includes a human decision-making process that captures social influence, government policy interventions, and the cost of environmentally-friendly behavior, modeled within a game-theoretic paradigm. By taking a mean-field approach in the limit of large populations, we derive the equilibria and their local stability characteristics. Subsequently, we study global convergence, whereby we show that the system converges to a periodic solution for almost all initial conditions. Numerical simulations confirm our findings and suggest that, before the system reaches such a periodic solution, the level of environmental impact might become dangerously high, calling for the design of optimal control strategies to influence the system trajectory.

math.DS↗

arXiv2022

A Polarized Temporal Network Model to Study the Spread of Recurrent Epidemic Diseases in a Partially Vaccinated Population

Motivated by massive outbreaks of COVID-19 that occurred even in populations with high vaccine uptake, we propose a novel multi-population temporal network model for the spread of recurrent epidemic diseases. We study the effect of human behavior, testing, and vaccination campaigns on the control of local outbreaks and infection prevalence. Our modeling framework decouples the vaccine effectiveness in protecting against transmission and the development of severe symptoms. Furthermore, the framework accounts for the polarizing effect of the decision to vaccinate and captures homophily, i.e., the tendency of people to interact with like-minded individuals. By means of a mean-field approach, we analytically derive the epidemic threshold. Our theoretical results suggest that, while vaccination campaigns reduce pressure on hospitals, they might facilitate resurgent outbreaks, highlighting the key role that testing campaigns may have in eradicating the disease. Numerical simulations are then employed to confirm and extend our theoretical findings to more realistic scenarios. Our numerical and analytical results agree that vaccination is not sufficient to achieve full eradication, without employing massive testing campaigns or relying on the population's responsibility. Furthermore, we show that homophily plays a critical role in the control of local outbreaks, highlighting the peril of a polarized network structure.

math.DS↗

arXiv2022

A mean-field analysis of a network behavioural-epidemic model

The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their real-world applicability. To address this gap, we propose and analyse a behavioural-epidemic model, in which a susceptible-infected-susceptible epidemic model and an evolutionary game-theoretic decision-making mechanism concerning the use of self-protective measures are coupled. Through a mean-field approach, we characterise the asymptotic behaviour of the system, deriving conditions for global convergence to a disease-free equilibrium and characterising the endemic equilibria of the system and their (local) stability. Interestingly, for a certain range of the model parameters, we prove global convergence to a limit cycle, characterised by periodic epidemic outbreaks.

math.DS↗

arXiv2022

Population games on dynamic community networks

In this letter, we deal with evolutionary game theoretic learning processes for population games on networks with dynamically evolving communities. Specifically, we propose a novel mathematical framework in which a deterministic, continuous-time replicator equation on a community network is coupled with a closed dynamic flow process between communities that is governed by an environmental feedback mechanism, resulting in co-evolutionary dynamics. Through a rigorous analysis of the system of differential equations obtained, we characterize the equilibria of the coupled dynamical system. Moreover, for a class of population games with two actions and symmetric rewards a Lyapunov argument is employed to establish an evolutionary folk theorem that guarantees convergence to the evolutionary stable states of the game. Numerical simulations are provided to illustrate and corroborate our findings.

cs.SI↗

arXiv2022

Predicting the effects of waning vaccine immunity against COVID-19 through high-resolution agent-based modeling

The potential waning of the vaccination immunity to COVID-19 could pose threats to public health, as it is tenable that the timing of such waning would synchronize with the near-complete restoration of normalcy. Should also testing be relaxed, we might witness a resurgent COVID-19 wave in winter 2021/2022. In response to this risk, an additional vaccine dose, the booster shot, is being administered worldwide. In a projected study with an outlook of six months, we explore the interplay between the rate at which boosters are distributed and the extent to which testing practices are implemented, using a highly granular agent-based model tuned on a medium-sized U.S. town. Theoretical projections indicate that the administration of boosters at the rate at which the vaccine is currently administered could yield a severe resurgence of the pandemic. Projections suggest that the peak levels of mid spring 2021 in the vaccination rate may prevent such a scenario to occur, although exact agreement between observations and projections should not be expected due to continuously evolving nature of the pandemics. Our study highlights the importance of testing, especially to detect asymptomatic individuals in the near future, as the release of the booster reaches full speed.

q-bio.PE↗

arXiv2021

Modelling the Effect of Vaccination and Human Behaviour on the Spread of Epidemic Diseases on Temporal Networks

Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination and relaxation of non-pharmaceutical interventions, we propose a mathematical model on time-varying networks for the spread of recurrent epidemic diseases in a partially vaccinated population. The model encapsulates several realistic features, such as the different effectiveness of the vaccine against transmission and development of severe symptoms, testing practices, the possible implementation of non-pharmaceutical interventions to reduce the transmission, isolation of detected individuals, and human behaviour. Using a mean-field approach, we analytically derive the epidemic threshold of the model and, if the system is above such a threshold, we compute the epidemic prevalence at the endemic equilibrium. These theoretical results show that precautious human behaviour and effective testing practices are key toward avoiding epidemic outbreaks. Interestingly, we found that, in many realistic scenarios, vaccination is successful in mitigating the outbreak by reducing the prevalence of seriously ill patients, but it could be a double-edged sword, whereby in some cases it might favour resurgent outbreaks, calling for higher testing rates, more cautiousness and responsibility among the population, or the reintroduction of non-pharmaceutical interventions to achieve complete eradication.

math.DS↗

arXiv2021

Optimal policy design to mitigate epidemics on networks using an SIS model

Understanding how to effectively control an epidemic spreading on a network is a problem of paramount importance for the scientific community. The ongoing COVID-19 pandemic has highlighted the need for policies that mitigate the spread, without relying on pharmaceutical interventions, that is, without the medical assurance of the recovery process. These policies typically entail lockdowns and mobility restrictions, having thus nonnegligible socio-economic consequences for the population. In this paper, we focus on the problem of finding the optimum policies that "flatten the epidemic curve" while limiting the negative consequences for the society, and formulate it as a nonlinear control problem over a finite prediction horizon. We utilize the model predictive control theory to design a strategy to effectively control the disease, balancing safety and normalcy. An explicit formalization of the control scheme is provided for the susceptible--infected--susceptible epidemic model over a network. Its performance and flexibility are demonstrated by means of numerical simulations.

q-bio.PE↗

arXiv2021

Game-theoretic modeling of collective decision-making during epidemics

The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a parsimonious game-theoretic behavioral--epidemic model, in which an interplay of realistic factors shapes the co-evolution of individual decision-making and epidemics on a network. Although such a co-evolution is deeply intertwined in the real-world, existing models schematize population behavior as instantaneously reactive, thus being unable to capture human behavior in the long term. Our model offers a unified framework to model and predict complex emergent phenomena, including successful collective responses, periodic oscillations, and resurgent epidemic outbreaks. The framework also allows to assess the effectiveness of different policy interventions on ensuring a collective response that successfully eradicates the outbreak. Two case studies, inspired by real-world diseases, are presented to illustrate the potentialities of the proposed model.

q-bio.PE↗

arXiv2021

A multi-layer network model to assess school opening policies during the COVID-19 vaccination campaign

We propose a multi-layer network model for the spread of COVID-19 that accounts for interactions within the family, between schoolmates, and casual contacts in the population. We utilize the proposed model-calibrated on epidemiological and demographic data-to investigate current questions concerning the implementation of non-pharmaceutical interventions (NPIs) during the vaccination campaign. Specifically, we consider scenarios in which the most fragile population has already received the vaccine, and we focus our analysis on the role of schools as drivers of the contagions and on the implementation of targeted intervention policies oriented to children and their families. We perform our analysis by means of a campaign of Monte Carlo simulations. Our findings suggest that, in a phase with NPIs enacted but in-person education, children play a key role in the spreading of COVID-19. Interestingly, we show that children's testing might be an important tool to flatten the epidemic curve, in particular when combined with enacting temporary online education for classes in which infected students are detected. Finally, we test a vaccination strategy that prioritizes the members of large families and we demonstrate its good performance. We believe that our modeling framework and our findings could be of help for public health authorities for planning their current and future interventions, as well as to increase preparedness for future epidemic outbreaks.

physics.soc-ph↗

arXiv2021

Analysis, Prediction, and Control of Epidemics: A Survey from Scalar to Dynamic Network Models

During the ongoing COVID-19 pandemic, mathematical models of epidemic spreading have emerged as powerful tools to produce valuable predictions of the evolution of the pandemic, helping public health authorities decide which intervention policies should be implemented. The study of these models -- grounded in the systems theory and often analyzed using control-theoretic tools -- is an extremely important research area for many researchers from different fields, including epidemiology, engineering, physics, mathematics, computer science, sociology, economics, and management. In this survey, we review the history and present the state of the art in the modeling, analysis, and control of epidemic dynamics. We discuss different approaches to epidemic modeling, either deterministic or stochastic, ranging from the first implementations of scalar systems of differential equations to describing the epidemic spreading at the population level, and to more recent models on dynamic networks, which capture the spatial spread and the time-varying nature of human interactions.

math.DS↗

arXiv2021

A two-layer model for coevolving opinion dynamics and collective decision-making in complex social systems

Motivated by the literature on opinion dynamics and evolutionary game theory, we propose a novel mathematical framework to model the intertwined coevolution of opinions and decision-making in a complex social system. In the proposed framework, the members of a social community update their opinions and revise their actions as they learn of others' opinions shared on a communication channel, and observe of others' actions through an influence channel; these interactions determine a two-layer network structure. We offer an application of the proposed framework by tailoring it to study the adoption of a novel social norm, demonstrating that the model is able to capture the emergence of several real-world collective phenomena such as paradigm shifts and unpopular norms. Through the establishment of analytical conditions and Monte Carlo numerical simulations, we shed light on the role of the coupling between opinion dynamics and decision-making, and of the network structure, in shaping the emergence of complex collective behavior in social systems.

cs.SI↗

arXiv2021

High-resolution agent-based modeling of COVID-19 spreading in a small town

Amid the ongoing COVID-19 pandemic, public health authorities and the general population are striving to achieve a balance between safety and normalcy. Ever changing conditions call for the development of theory and simulation tools to finely describe multiple strata of society while supporting the evaluation of "what-if" scenarios. Particularly important is to assess the effectiveness of potential testing approaches and vaccination strategies. Here, an agent-based modeling platform is proposed to simulate the spreading of COVID-19 in small towns and cities, with a single-individual resolution. The platform is validated on real data from New Rochelle, NY -- one of the first outbreaks registered in the United States. Supported by expert knowledge and informed by reported data, the model incorporates detailed elements of the spreading within a statistically realistic population. Along with pertinent functionality such as testing, treatment, and vaccination options, the model accounts for the burden of other illnesses with symptoms similar to COVID-19. Unique to the model is the possibility to explore different testing approaches -- in hospitals or drive-through facilities -- and vaccination strategies that could prioritize vulnerable groups. Decision making by public authorities could benefit from the model, for its fine-grain resolution, open-source nature, and wide range of features.

q-bio.PE↗

arXiv2020

Modelling and predicting the effect of social distancing and travel restrictions on COVID-19 spreading

To date, the only effective means to respond to the spreading of COVID-19 pandemic are non-pharmaceutical interventions (NPIs), which entail policies to reduce social activity and mobility restrictions. Quantifying their effect is difficult, but it is key to reduce their social and economical consequences. Here, we introduce a meta-population model based on temporal networks, calibrated on the COVID-19 outbreak data in Italy and apt to evaluate the outcomes of these two types of NPIs. Our approach combines the advantages of granular spatial modelling of meta-population models with the ability to realistically describe social contacts via activity-driven networks. We provide a valuable framework to assess the viability of different NPIs, varying with respect to their timing and severity. Results suggest that the effects of mobility restrictions largely depend on the possibility to implement timely NPIs in the early phases of the outbreak, whereas activity reduction policies should be prioritised afterwards.

physics.soc-ph↗

arXiv2020

Imitation dynamics in population games on community networks

We study the asymptotic behavior of deterministic, continuous-time imitation dynamics for population games over networks. The basic assumption of this learning mechanism -- encompassing the replicator dynamics -- is that players belonging to a single population exchange information through pairwise interactions, whereby they get aware of the actions played by the other players and the corresponding rewards. Using this information, they can revise their current action, imitating the one of the players they interact with. The pattern of interactions regulating the learning process is determined by a community structure. First, the set of equilibrium points of such network imitation dynamics is characterized. Second, for the class of potential games and for undirected and connected community networks, global asymptotic convergence is proved. In particular, our results guarantee convergence to a Nash equilibrium from every fully supported initial population state in the special case when the Nash equilibria are isolated and fully supported. Examples and numerical simulations are offered to validate the theoretical results and counterexamples are discussed for scenarios when the assumptions on the community structure are not verified.

eess.SY↗

arXiv2020

Fast Spread in Controlled Evolutionary Dynamics

We study the spread of a novel state in a network, in the presence of an exogenous control. The considered controlled evolutionary dynamics is a non-homogeneous Markov process that describes the evolution of the states of all nodes in the network. Through a rigorous analysis, we estimate the performance of the system by establishing upper and lower bounds on the expected time needed for the novel state to replace the original one. Such bounds are expressed in terms of the support and intensity of the control policy (specifically, the set of nodes that can be controlled and its energy) and of the network topology and establish fundamental limitations on the system's performance. Leveraging these results, we are able to classify network structures depending on the possibility to control the system using simple open-loop control policies. Finally, we propose a feedback control policy that, using little knowledge of the network topology and of the system's evolution at a macroscopic level, allows for a substantial speed up of the spreading process with respect to simple open-loop control policies. All these theoretical results are presented together with explanatory examples, for which Monte Carlo simulations corroborate our analytical findings.

eess.SY↗

arXiv2018

On stochastic imitation dynamics in large-scale networks

We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game structure: they only know their own current utility and the one of neighbor players contacted through pairwise interactions in a network. In response to this information, players update their state according to some stochastic rules. For potential population games and complete interaction networks, we prove convergence and long-lasting permanence close to the evolutionary stable strategies of the game. These results refine and extend the ones known for deterministic imitation dynamics as they account for new emerging behaviors including meta-stability of the equilibria. Finally, we discuss extensions of our results beyond the fully mixed case, studying imitation dynamics where agents interact on complex communication networks.

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