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Numerical Algorithms for the Parametric Continuation of Stiff ODEs Deriving from the Modeling of Combustion with Detailed Chemical Mechanisms Read chapter Read first chapter

2020 | OriginalPaper | Chapter

Epidemic Spreading Curing Strategy Over Directed Networks

Authors : Clara Pizzuti, Annalisa Socievole

Published in: Numerical Computations: Theory and Algorithms

Publisher: Springer International Publishing

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Abstract

Epidemic processes on networks have been thoroughly investigated in different research fields including physics, biology, computer science and medicine. Within this research area, a challenge is the definition of curing strategies able to suppress the epidemic spreading while exploiting a minimal quantity of curing resources. In this paper, we model the network under analysis as a directed graph where a virus spreads from node to node with different spreading and curing rates. Specifically, we adopt an approximation of the Susceptible-Infected-Susceptible (SIS) epidemic model, the N-Intertwined Mean Field Approximation (NIMFA). In order to control the diffusion of the virus while limiting the total cost needed for curing the whole network, we formalize the problem of finding an Optimal Curing Policy (OCP) as a constrained optimization problem and propose a genetic algorithm (GA) to solve it. Differently from a previous work where we proposed a GA for solving the OCP problem on undirected networks, here we consider the formulation of the optimization problem for directed weighted networks and extend the GA method to deal with not symmetric adjacency matrices that are not diagonally symmetrizable.

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Footnotes
1
A matrix A is symmetrizable if there exists an invertible diagonal matrix D and symmetric matrix S such that \(A=DS\).
 
2
A semidefinite positive matrix \(A \in R^{N \times N}\) is a symmetric matrix such that \(x^TAx \ge 0 \) for all the \(x \in R^N\). Equivalently, all the eigenvalues of A are nonnegative.
 
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Metadata
Title
Epidemic Spreading Curing Strategy Over Directed Networks
Authors
Clara Pizzuti
Annalisa Socievole
Copyright Year
2020
Book
Numerical Computations: Theory and Algorithms

Print ISBN: 978-3-030-40615-8

Electronic ISBN: 978-3-030-40616-5

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-40616-5_14

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