Computational Simulation of Epidemiological Models with Variable Rates on Complex Networks

• Ano de defesa: 2024
• Autor(a) principal: Castro, Marcus André Nunes
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Algoritmo de Gillespie; Epidemiologia; Epidemiology; Gillespie algorithm; Markov process; Modelo SIR; Modelo SIS; Monte Carlo cinético de caminho mais curto; Networks; Processos de Markov; Redes; Shortest-Path Kinetic Monte Carlo; SIR model; SIS model
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/100/100132/tde-17022025-113828/

The networks have been the focus of intensive study in recent years, because of their flexibility and applicability in a wide range of fields. This thesis delves into the basic understanding of networks, especially those described as complex, to examine their role in the context of epidemiology. The structure of contact networks and time dependence in recovery rates are often referred as aspects that alter the dynamics of infectious disease transmission, but classical epidemiological models assume homogeneous mixing and constant recovery rates, which idealize real-world processes. To overcome these limitations, we address the impact of complex network topologies and variable recovery rates on epidemic dynamics using two statistically exact algorithms: the Gillespie algorithm and the Shortest-Path Kinetic Monte Carlo (SPKMC) algorithm. These methods were applied to the classic Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Removed (SIR) epidemiological models to simulate the disease spread under different network structures and recovery rates close to realistic ones. The analysis described here highlights how these factors shape infectious disease time series, yielding deeper insights into the interplay between network topology and recovery time distributions.