Banca de DEFESA: LUCIANO SOARES MENDES JUNIOR

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : LUCIANO SOARES MENDES JUNIOR
DATE: 29/08/2022
TIME: 15:30
LOCAL: Remoto
TITLE:

Study of the correlation between adjacent neighbors in transmission models defined in finite graphs

KEY WORDS:

epidemic model; rumor model; stochastic process; correlations; information
transmission.

PAGES: 79
BIG AREA: Ciências Exatas e da Terra
AREA: Probabilidade e Estatística
SUMMARY:

This paper is a theoretical and numerical study of the correlation behavior involved in the
SIS, SIR, and MT models. Initially, were developed studies about recent arguments in
the literature. In this step was applied the FKG inequality to show that the variables of
interest have a non-negative correlation. Subsequently, another argument was analyzed
with a counterexample and consequently showed that the arguments previously studied
are not valid for the SIR model. Then, Monte Carlo simulation methods were developed
to verify the behavior of the correlations in the mentioned models.The first method
developed estimates the average correlation along the process in a pair of neighboring
vertices. The second method, in turn, estimates the average correlation in each unit of
process time. The developed methods were applied in two types of graphs: a k-regular
graph and another graph formed by two stars with n vertices connected by their respective
central vertices.We verified that in the SIR and MT models defined in the k-regular
graph, the correlations present a non-negative behavior. On the other hand, this behavior
is not repeated by the same models defined in the graph formed by two stars connected
by their respective central vertices.

BANKING MEMBERS:
Externo à Instituição - ANGÉLICA YOHANA PACHÓN PINZÓN
Externo à Instituição - LEON ALEXANDER VALENCIA HENAO
Presidente - 3100567 - PABLO MARTIN RODRIGUEZ
Externo à Instituição - ÉLCIO LEBENSZTAYN - UNICAMP