Kinetic Modelling of Epidemic Dynamics: Social Contacts, Control with Uncertain Data, and Multiscale Spatial Dynamics

Albi, Giacomo; Bertaglia, Giulia; Boscheri, Walter; Dimarco, Giacomo; Pareschi, Lorenzo; Toscani, Giuseppe; Zanella, Mattia

doi:10.1007/978-3-030-96562-4_3

Cited by 21 publications

(7 citation statements)

References 111 publications

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“…We highlight that, without having the intention to use real data for the calibration of the presented model, these values are coherent with several recent works for the COVID-19 pandemic (Albi et al. 2022 ; Buonomo and Della Marca 2020 ; Dimarco et al. 2022 ).…”

Section: Numerical Examplessupporting

confidence: 89%

“…Without attempting to revise the whole literature, we mention Albi et al. ( 2022 ), Bertaglia et al. ( 2021 ), Della Marca et al.…”

Section: Introductionmentioning

confidence: 99%

“…The transition rates between epidemiologically relevant states are furthermore influenced by several phenomena linked to the disease itself and to the social behaviour of individuals. Without attempting to revise the whole literature, we mention Albi et al (2022), Bertaglia et al (2021), Della Marca et al (2022a), Dimarco et al (2020Dimarco et al ( , 2021Dimarco et al ( , 2022, Loy and Tosin (2021) and the references therein for an introduction to the subject. Among them, contact dynamics are particularly relevant for contact-based disease transmissions.…”

Section: Introductionmentioning

confidence: 99%

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Kinetic Models for Epidemic Dynamics in the Presence of Opinion Polarization

Zanella

2023

Bull Math Biol

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Understanding the impact of collective social phenomena in epidemic dynamics is a crucial task to effectively contain the disease spread. In this work, we build a mathematical description for assessing the interplay between opinion polarization and the evolution of a disease. The proposed kinetic approach describes the evolution of aggregate quantities characterizing the agents belonging to epidemiologically relevant states and will show that the spread of the disease is closely related to consensus dynamics distribution in which opinion polarization may emerge. In the present modelling framework, microscopic consensus formation dynamics can be linked to macroscopic epidemic trends to trigger the collective adherence to protective measures. We conduct numerical investigations which confirm the ability of the model to describe different phenomena related to the spread of an epidemic.

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Section: Numerical Examplessupporting

confidence: 89%

“…Without attempting to revise the whole literature, we mention Albi et al. ( 2022 ), Bertaglia et al. ( 2021 ), Della Marca et al.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kinetic Models for Epidemic Dynamics in the Presence of Opinion Polarization

Zanella

2023

Bull Math Biol

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“…P2022JC95T, Data-driven discovery and control of multi-scale interacting artificial agent systems. This research was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/T024429/1 dynamics [4,32,38,21], interventions assessment in traffic management [78,49,75], and learning of opinion dynamics [5,8,45] However, the high dimensionality given by the state space and the large number of agents does not usually allow the synthesis of optimal feedback control by means of direct methods, see for example [24,13]. Hence, the development of novel efficient algorithms are key to handling real-time applications, which often stumble upon cumbersome software and hardware requirements.…”

Section: Introductionmentioning

confidence: 99%

Moment-Driven Predictive Control of Mean-Field Collective Dynamics

Albi¹,

Herty²,

Kalise³

et al. 2022

SIAM J. Control Optim.

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Feedback control synthesis for large-scale particle systems is reviewed in the framework of model predictive control (MPC). The high-dimensional character of collective dynamics hampers the performance of traditional MPC algorithms based on fast online dynamic optimization at every time step. Two alternatives to MPC are proposed. First, the use of supervised learning techniques for the offline approximation of optimal feedback laws is discussed. Then, a procedure based on sequential linearization of the dynamics based on macroscopic quantities of the particle ensemble is reviewed. Both approaches circumvent the online solution of optimal control problems enabling fast, real-time, feedback synthesis for large-scale particle systems. Numerical experiments assess the performance of the proposed algorithms.

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“…For a stochastic approach, we refer for instance also to Bertaglia et al (2022), while a fuzzy approach is in Al-Qaness et al ( 2020) and Regis et al (2021). On the basis of the epidemic evolution described by the present model, consequences at the social or economic levels can be described as in Albi et al (2021a) and Fabbri et al (2021), for instance, or (Bernardi et al 2022;Dimarco et al 2020) where a kinetic model of wealth exchange is proposed. A summary of the historical development of macroscopic models for virus diffusion and vaccination is in Groppi and Della Marca (2018).…”

Section: Introductionmentioning

confidence: 99%

Infectious Disease Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect

Colombo

Garavello

2022

Acta Biotheor

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We propose a framework for the description of the effects of vaccinations on the spreading of an epidemic disease. Different vaccines can be dosed, each providing different immunization times and immunization levels. Differences due to individuals’ ages are accounted for through the introduction of either a continuous age structure or a discrete set of age classes. Extensions to gender differences or to distinguish fragile individuals can also be considered. Within this setting, vaccination strategies can be simulated, tested and compared, as is explicitly described through numerical integrations.

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Kinetic Modelling of Epidemic Dynamics: Social Contacts, Control with Uncertain Data, and Multiscale Spatial Dynamics

Cited by 21 publications

References 111 publications

Kinetic Models for Epidemic Dynamics in the Presence of Opinion Polarization

Kinetic Models for Epidemic Dynamics in the Presence of Opinion Polarization

Moment-Driven Predictive Control of Mean-Field Collective Dynamics

Infectious Disease Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect

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