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On the Dynamic Behavior of the Network SIR Epidemic Model

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Title: On the Dynamic Behavior of the Network SIR Epidemic Model
Authors: Alutto, Martina, Cianfanelli, Leonardo, Como, Giacomo, Fagnani, Fabio
Contributors: Lund University, Faculty of Engineering, LTH, Departments at LTH, Department of Automatic Control, Lunds universitet, Lunds Tekniska Högskola, Institutioner vid LTH, Institutionen för reglerteknik, Originator, Lund University, Profile areas and other strong research environments, Strategic research areas (SRA), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Lunds universitet, Profilområden och andra starka forskningsmiljöer, Strategiska forskningsområden (SFO), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Originator, Lund University, Faculty of Engineering, LTH, LTH Profile areas, LTH Profile Area: AI and Digitalization, Lunds universitet, Lunds Tekniska Högskola, LTH profilområden, LTH profilområde: AI och digitalisering, Originator
Source: IEEE Transactions on Control of Network Systems. 12(1):177-189
Subject Terms: Natural Sciences, Mathematical Sciences, Probability Theory and Statistics, Naturvetenskap, Matematik, Sannolikhetsteori och statistik
Description: In this article, we study a susceptible–infected–recovered (SIR) epidemic model on a network of n interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the classical scalar epidemic SIR model, where the infection curve is known to be unimodal (either always decreasing over time, or initially increasing until reaching a peak and from then on monotonically decreasing and asymptotically vanishing), we show the possible occurrence of multimodal infection curves in the network SIR epidemic model with n ≥ 2 subpopulations. We then focus on the special case of rank-1 interaction matrices, modeling subpopulations of homogeneously mixing individuals with different activity rates, susceptibility to the disease, and infectivity levels. For this special case, we find n invariants of motion and provide an explicit expression for the limit equilibrium point. We also determine necessary and sufficient conditions for stability of theequilibrium points. We then establish an upper bound on the number of changes of monotonicity of the infection curve at the single node level and provide sufficient conditions for its multimodality. Finally, we present some numerical results revealing that in the case of interaction matrices with rank larger than 1, the single nodes' infection curves may display multiple peaks.
Access URL: https://doi.org/10.1109/TCNS.2024.3448136
Database: SwePub
Description
Abstract:In this article, we study a susceptible–infected–recovered (SIR) epidemic model on a network of n interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the classical scalar epidemic SIR model, where the infection curve is known to be unimodal (either always decreasing over time, or initially increasing until reaching a peak and from then on monotonically decreasing and asymptotically vanishing), we show the possible occurrence of multimodal infection curves in the network SIR epidemic model with n ≥ 2 subpopulations. We then focus on the special case of rank-1 interaction matrices, modeling subpopulations of homogeneously mixing individuals with different activity rates, susceptibility to the disease, and infectivity levels. For this special case, we find n invariants of motion and provide an explicit expression for the limit equilibrium point. We also determine necessary and sufficient conditions for stability of theequilibrium points. We then establish an upper bound on the number of changes of monotonicity of the infection curve at the single node level and provide sufficient conditions for its multimodality. Finally, we present some numerical results revealing that in the case of interaction matrices with rank larger than 1, the single nodes' infection curves may display multiple peaks.
ISSN:23255870
DOI:10.1109/TCNS.2024.3448136