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

Giacomo Aletti, Alessandro Benfenati and Giovanni Naldi
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Giacomo Aletti: Environmental Science and Policy Department, Università degli Studi di Milano, 20133 Milan, Italy
Alessandro Benfenati: Environmental Science and Policy Department, Università degli Studi di Milano, 20133 Milan, Italy
Giovanni Naldi: Environmental Science and Policy Department, Università degli Studi di Milano, 20133 Milan, Italy

Mathematics, 2021, vol. 9, issue 22, 1-13

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.

Keywords: epidemic spread; multi-group models; network based model; control of spread dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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