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Graph, Spectra, Control and Epidemics: An Example with a SEIR Model

Author

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  • Giacomo Aletti

    (Environmental Science and Policy Department, Università degli Studi di Milano, 20133 Milan, Italy
    The three authors are members of the Italian Group GNCS of the Italian Institute “Istituto Nazionale di Alta Matematica”, and of the ADAMSS Center of the Università degli Studi di Milano (Italy).)

  • Alessandro Benfenati

    (Environmental Science and Policy Department, Università degli Studi di Milano, 20133 Milan, Italy
    The three authors are members of the Italian Group GNCS of the Italian Institute “Istituto Nazionale di Alta Matematica”, and of the ADAMSS Center of the Università degli Studi di Milano (Italy).)

  • Giovanni Naldi

    (Environmental Science and Policy Department, Università degli Studi di Milano, 20133 Milan, Italy
    The three authors are members of the Italian Group GNCS of the Italian Institute “Istituto Nazionale di Alta Matematica”, and of the ADAMSS Center of the Università degli Studi di Milano (Italy).)

Abstract

Networks and graphs offer a suitable and powerful framework for studying the spread of infection in human and animal populations. In the case of a heterogeneous population, the social contact network has a pivotal role in the analysis of directly transmitted infectious diseases. The literature presents several works where network-based models encompass realistic features (such as contacts networks or host–pathogen biological data), but analytical results are nonetheless scarce. As a significant example, in this paper, we develop a multi-group version of the epidemiological SEIR population-based model. Each group can represent a social subpopulation with the same habits or a group of geographically localized people. We consider also heterogeneity in the weighting of contacts between two groups. As a simple application, we propose a simple control algorithm in which we optimize the connection weights in order to minimize the combination between an economic cost and a social cost. Some numerical simulations are also provided.

Suggested Citation

  • Giacomo Aletti & Alessandro Benfenati & Giovanni Naldi, 2021. "Graph, Spectra, Control and Epidemics: An Example with a SEIR Model," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2987-:d:685376
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    References listed on IDEAS

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    1. Eva Kaslik & Mihaela Neamţu & Anca Rădulescu, 2022. "Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”," Mathematics, MDPI, vol. 10(19), pages 1-3, September.

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