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.

Graph, Spectra, Control and Epidemics: An Example with a SEIR Model / G. Aletti, A. Benfenati, G. Naldi. - In: MATHEMATICS. - ISSN 2227-7390. - 9:22(2021 Nov), pp. 2987.1-2987.13. [10.3390/math9222987]

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

G. Aletti
Primo
;
A. Benfenati
Secondo
;
G. Naldi
Ultimo
2021

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.
epidemic spread; multi-group models; network based model; control of spread dynamics;
Settore MAT/08 - Analisi Numerica
Settore MAT/03 - Geometria
Settore MAT/05 - Analisi Matematica
   Progetto PRECISION
   UNIVERSITA' DEGLI STUDI DI MILANO
nov-2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/887426
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