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A Modified SEIR Model: Stiffness Analysis and Application to the Diffusion of Fake News

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Computational Science and Its Applications – ICCSA 2022 (ICCSA 2022)

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Abstract

In this work we propose a novel and alternative interpretation of the SEIR model, typically used in epidemiology to describe the spread of a disease in a given population, to describe the diffusion of fake information on the web and the consequent truth re-affirmation. We describe the corresponding system of ordinary differential equations, giving a proper definition of the involved parameters and, through a local linearization of the system, we calculate the so-called stiffness ratio, i.e. the ratio between the real parts of the largest and smallest eigenvalues of the Jacobian matrix of the linearized problem. A large gap in the spectrum of such a Jacobian matrix (i.e., a large stiffness ratio) makes the underlying differential problem stiff. So, we study and analyze the stiffness index of the SEIR model and, through selected numerical examples on real datasets, we show that the more the model is stiff, the faster is the transit of fake information in a given population.

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Acknowledgements

The authors are members of the GNCS group. This work was supported by GNCS-INDAM project, and by the Italian Ministry of University and Research (MUR) through the PRIN 2020 project (No. 2020JLWP23) “Integrated Mathematical Approaches to Socio-Epidemiological Dynamics” (CUP: E15F21005420006) and through the PRIN 2017 project (No. 2017JYCLSF) “Structure preserving approximation of evolutionary problems”. Patricia Díaz de Alba gratefully acknowledges Fondo Sociale Europeo REACT EU - Programma Operativo Nazionale Ricerca e Innovazione 2014–2020 and Ministero dell’Università e della Ricerca for the financial support.

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Authors and Affiliations

  1. Università degli Studi di Salerno, 84084, Fisciano, Italy

    Patricia Díaz de Alba, Giuseppe Giordano & Beatrice Paternoster

  2. Università degli Studi dell’Aquila, 67100, L’Aquila, Italy

    Raffaele D’Ambrosio

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  1. Raffaele D’Ambrosio
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  2. Patricia Díaz de Alba
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  3. Giuseppe Giordano
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  4. Beatrice Paternoster
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Correspondence to Patricia Díaz de Alba .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Universidad de Málaga, Malaga, Spain

    Eligius M. T. Hendrix

  4. Monash University, Clayton, VIC, Australia

    David Taniar

  5. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

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D’Ambrosio, R., Díaz de Alba, P., Giordano, G., Paternoster, B. (2022). A Modified SEIR Model: Stiffness Analysis and Application to the Diffusion of Fake News. In: Gervasi, O., Murgante, B., Hendrix, E.M.T., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications – ICCSA 2022. ICCSA 2022. Lecture Notes in Computer Science, vol 13375. Springer, Cham. https://doi.org/10.1007/978-3-031-10522-7_7

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