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Master's Dissertation
DOI
10.11606/D.100.2019.tde-16012019-173906
Document
Author
Full name
Cristiane Dias de Souza Martorello
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Hase, Masayuki Oka (President)
Pereira, Marcone Corrêa
Rodrigues Neto, Camilo
Vannucchi, Fabio Stucchi
Title in English
Epidemiology in complex networks - modified heterogeneous mean-field model
Keywords in English
Networks
Scale-free network
SIS model
Abstract in English
The study of complex networks presented a huge development in last decades. In this dissertation we want to analyze the epidemic spread in scale-free networks through the Susceptible - Infected - Susceptible (SIS) model. We review the fundamental concepts to describe complex networks and the classical epidemiological models. We implement an algorithm that produces a scale-free network and explore the Quenched Mean-Field (QMF) dynamics in a scale-free network. Moreover, we simulate a change on the topology of the network according to the states of the nodes, and it generates a positive epidemic threshold. We show analytically that the fraction of infected vertices follows a power-law distribution in the vicinity of this critical point
Title in Portuguese
Epidemiologia em redes complexas - modelo de campo médio heterogêneo modificado
Keywords in Portuguese
Modelo SIS
Rede livre de escala
Redes
Abstract in Portuguese
O estudo de redes complexas tem se desenvolvido muito nos últimos anos. Nesta dissertação queremos analisar o processo de propagação de epidemia em redes livres de escala através do modelo Suscetível - Infectado - Suscetível (SIS). Apresentamos uma revisão de redes e as principais características dos modelos epidemiológicos clássicos. Implementamos um algoritmo que produz uma rede livre de escala dado um expoente e exploramos a dinâmica do modelo Quenched Mean-Field (QMF) inserido em uma rede livre de escala. Além disso, foi simulada uma possível alteração na topologia da rede, devido aos estados dos vértices infectados, que gerou um limiar epidêmico positivo no modelo e a probabilidade de vértices infectados seguiu uma lei de potência na vizinhança desse ponto crítico
 
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Dissertacao_16jan.pdf (1,017.89 Kbytes)
Publishing Date
2019-02-06
 
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