Kinetic models for epidemic dynamics with social heterogeneity

Dimarco, Giacomo; Perthame, Benôıt; Toscani, Giuseppe; Zanella, Mattia

doi:10.1007/s00285-021-01630-1

Cited by 55 publications

(86 citation statements)

References 49 publications

(83 reference statements)

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“…Extensions of the presented methodology are possible to include disease-related mortality and redistribution operators. Moreover, since a direct comparison of the results of similar compartmental kinetic models—in the case of social aspects related to the transience of the epidemic—outlined a good agreement with the actual data [ 8 , 38 , 39 ], we can assume that the present approach is able to follow the real evolution of the economic parameters of a country over a sufficiently long period of time. Indeed, even though the model introduced here necessarily represents a strong simplification of an extremely complex phenomenon, its qualitative behavior is capable of describing the essential features of the pandemic’s impact on individuals’ wealth.…”

Section: Discussionmentioning

confidence: 61%

“…Depending on the specific choice of β and using the knowledge on the equilibrium states discussed in Section 3.1 it is possible, through the classical hydrodynamic closure of kinetic theory, to derive epidemic models where the dynamics, instead of being homogeneous as in classical compartmental modeling, is influenced by the heterogeneous wealth status of individuals. We refer to [ 8 , 38 ] for examples in this direction.…”

Section: Wealth Dynamics In Epidemic Phenomenamentioning

confidence: 99%

“…The interplay between epidemic spread and the social economic background is described here as the result of interactions among a large number of individuals, each of which is characterized by the variable

, measuring the amount of wealth of a single agent. In this regard, as shown in [ 1 , 8 , 38 , 39 ], the fundamental tools of statistical physics allow the understanding of epidemiological dynamics by linking classical compartmental approaches with a statistical description of economic aspects. Indeed, the multiscale nature of kinetic theory allows for the determination of the macroscopic (or aggregate) and measurable features of disease evolution [ 27 , 40 , 41 ].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models

Bernardi

Pareschi

Toscani

et al. 2022

Entropy

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The spread of the COVID-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modeling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated, resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth distribution based on binary wealth exchanges. The interplay between wealth exchanges and the progress of the infectious disease is realized by assuming, on the one hand, that individuals in different compartments act differently in the economic process and, on the other hand, that the epidemic affects risk in economic transactions. Using the mathematical tools of kinetic theory, it is possible to identify the equilibrium states of the system and the formation of inequalities due to the pandemic in the wealth distribution of the population. Numerical experiments highlight the importance of the vaccination campaign and its positive effects in reducing economic inequalities in the multi-agent society.

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Section: Discussionmentioning

confidence: 61%

Section: Wealth Dynamics In Epidemic Phenomenamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models

Bernardi

Pareschi

Toscani

et al. 2022

Entropy

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“…The advantage of these methods relies on an arbitrarily accurate description of the steady state distribution of the Fokker-Planck model of interest. Similar approaches have been investigated in a different context also in [12,13].…”

Section: Examples and Applicationsmentioning

confidence: 88%

“…Previously, kinetic models that include the role of competence or knowledge had been proposed in [5,29,31]. The behavior of a social system composed by a large number of interacting agents has been studied in the case of opinion formation [3,9,14,15,34] and more recently epidemiological dynamics [1,2,12]. We refer to [28] for an introduction to the subject.…”

Section: Introductionmentioning

confidence: 99%

From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications

Franceschi¹,

Pareschi²,

Zanella³

2022

Preprint

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Fake news spreading, with the aim of manipulating individuals' perceptions of facts, is now recognized as a major problem in many democratic societies. Yet, to date, little has been understood about how fake news spreads on social networks, what the influence of the education level of individuals is, when fake news is effective in influencing public opinion, and what interventions might be successful in mitigating their effect. In this paper, starting from the recently introduced kinetic multi-agent model with competence by the first two authors, we propose to derive reducedorder models through the notion of social closure in the mean-field approximation that has its roots in the classical hydrodynamic closure of kinetic theory. This approach allows to obtain simplified models in which the competence and learning of the agents maintain their role in the dynamics and, at the same time, the structure of such models is more suitable to be interfaced with data-driven applications. Examples of different Twitter-based test cases are described and discussed.

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On the optimal control of kinetic epidemic models with uncertain social features

Franceschi

Medaglia

Zanella

2023

Optim Control Appl Methods

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It is recognized that social heterogeneities in terms of the contact distribution have a strong influence on the spread of infectious diseases. Nevertheless, few data are available on the group composition of social contacts, and their statistical description does not possess universal patterns and may vary spatially and temporally. It is therefore essential to design robust control strategies, mimicking the effects of non‐pharmaceutical interventions, to limit efficiently the number of infected cases. In this work, starting from a recently introduced kinetic model for epidemiological dynamics that takes into account the impact of social contacts of individuals, we consider an uncertain contact formation dynamics leading to slim‐tailed as well as fat‐tailed distributions of contacts. Hence, we analyse the effects of an optimally robust control strategy of the system of agents. Thanks to classical methods of kinetic theory, we couple uncertainty quantification methods with the introduced mathematical model to assess the effects of social limitations. Finally, using the proposed modeling approach and starting from available data, we show the effectiveness of the proposed selective measures to dampen uncertainties together with the epidemic trends.

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Kinetic models for epidemic dynamics with social heterogeneity

Cited by 55 publications

References 49 publications

Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models

Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models

From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications

On the optimal control of kinetic epidemic models with uncertain social features

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