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.Comment: Extended version of conference paper accepted at ECC 201

On imitation dynamics in potential population games

Imitation dynamics for population games are studied and their asymptotic properties analyzed. In the considered class of imitation dynamics - that encompass the replicator equation as well as other models previously considered in evolutionary biology - players have no global information about the game structure, and all they know is their own current utility and the one of fellow players contacted through pairwise interactions. For potential population games, global asymptotic stability of the set of Nash equilibria of the sub-game restricted to the support of the initial population configuration is proved. These results strengthen (from local to global asymptotic stability) existing ones and generalize them to a broader class of dynamics. The developed techniques highlight a certain structure of the problem and suggest possible generalizations from the fully mixed population case to imitation dynamics whereby agents interact on complex communication networks.Comment: 7 pages, 3 figures. Accepted at CDC 201

A multi-layer network model to assess school opening policies during a vaccination campaign:a case study on COVID-19 in France

We propose a multi-layer network model for the spread of an infectious disease that accounts for interactions within the family, between children in classes and schools, and casual contacts in the population. The proposed framework is designed to test several what-if scenarios on school openings during the vaccination campaigns, thereby assessing the safety of different policies, including testing practices in schools, diverse home-isolation policies, and targeted vaccination. We demonstrate the potentialities of our model by calibrating it on epidemiological and demographic data of the spring 2021 COVID-19 vaccination campaign in France. Specifically, we consider scenarios in which a fraction of the population is vaccinated, 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 transmission in schools may play a key role in the spreading of a disease. 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

On incentivizing innovation diffusion in a network of coordinating agents

Innovation diffusion is fundamental for societal growth and development, and understanding how to unlock it is key toward devising policies encouraging the adoption of new practices, e.g., sustainable innovations. Here, we propose a mathematical model to investigate such a problem. Specifically, we consider a coordination game —which is a standard game-theoretic model used to study innovation diffusion—and we embed it on an activity-driven network. Within this model, we integrate three policies to incentivize the adoption of the innovation: i) providing a direct advantage for adopting it, ii) making people sensitive to emerging trends at the population level, and iii) increasing the visibility of adopters of the innovation, respectively. We provide analytical insights to shed light on the effect of the joint use of these three policies on unlocking innovation diffusion, supported by numerical simulations

On modeling social diffusion under the impact of dynamic norms

We develop and analyze a collective decision-making model concerning the adoption and diffusion of a novel product, convention, or behavior within a population. Motivated by the growing social psychology literature on dynamic norms, under which an individual is influenced by changing trends in the population, we propose a stochastic model for the decision-making process encompassing two behavioral mechanisms. The first is social influence, which drives coordination among individuals. Consistent with the literature on social diffusion modeling, we capture such a mechanism through an evolutionary game-theoretic framework for a network of interacting individuals. The second, which is the main novelty of our model, represents the impact of dynamic norms, capturing the tendency of individuals to be attracted to products or behaviors with growing popularity. We analytically determine sufficient conditions under which a novel alternative spreads to the majority of the population. Our findings provide insights into the unique and nontrivial role of human sensitivity to dynamic norms in facilitating social diffusion

Modelling Behavioural Preferences in Epidemic Models for Sexually Transmitted Infections on Temporal Networks

In this paper, we propose a temporal model for the spreading of curable sexually transmitted infections (STIs). The model is developed within the framework of activity-driven networks, which allows to model the time-varying pattern of sexual encounters and the individuals’ heterogeneity in their proclivity to initiate them. Our model explicitly includes the delay between infectiousness and symptoms onset, and individuals’ behavioural preferences for the use of protection during encounters. Behavioural preferences evolve according to a nontrivial mechanism that accounts for the perceived risks, the cost of adopting protective measures, and the persuasive effect of interactions with individuals who have a different preference. In the limit of large-scale populations, we use a mean-field approach to derive the epidemic threshold and study the effect of two control measures on the spread of STIs: i) routine screening at STI clinics, and ii) condom (social) marketing campaigns. Our results reveal the important effect of routine screening for STIs, which has emerged as a key factor to favour stability of the disease-free equilibrium, while marketing campaigns can be very effective in mitigating endemic diseases

Fast Spread in Controlled Evolutionary Dynamics

We study a controlled evolutionary dynamics that models the spread of a novel state in a network where the exogenous control aims to quickly spread the novel state. We estimate the performance of the system by analytically establishing upper and lower bounds on the expected time needed for the novel state to replace the original one. Such bounds are expressed as functions of the control policy adopted and of the network structure, and establish fundamental limitations on the system's performance. Leveraging these results, we classify network structures depending on the possibility of achieving a fast spread of the novel state (i.e., complete replacement in a time growing logarithmically with the network size) using simple open-loop control policies. Finally, we propose a feedback control policy that using little knowledge of the network and of the system's evolution at a macroscopic level allows for a substantial speed up of the spreading process, guaranteeing fast spread on topologies where simple open-loop control policies are not sufficient. Examples and simulations corroborate our findings

The impact of deniers on epidemics: A temporal network model

We propose a novel network epidemic model to elucidate the impact of deniers on the spread of epidemic diseases. Specifically, we study the spread of a recurrent epidemic disease, whose progression is captured by a susceptible–infected–susceptible model, in a population partitioned into two groups: cautious individuals and deniers. Cautious individuals may adopt self-protective behaviors, possibly incentivized by information campaigns implemented by public authorities; on the contrary, deniers reject their adoption. Through a mean-field approach, we analytically derive the epidemic threshold for large-scale homogeneous networks, shedding light onto the role of deniers in shaping the course of an epidemic outbreak. Specifically, our analytical insight suggests that even a small minority of deniers may jeopardize the effort of public health authorities when the population is highly polarized. Numerical results extend our analytical findings to heterogeneous networks