Spreading processes on complex networks: theory, simulations and applications

• Autor(a) principal: Costa, Guilherme Henrique da Silva
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: https://locus.ufv.br//handle/123456789/31092; https://doi.org/10.47328/ufvbbt.2022.508
• topic: Física estatística; Espalhamento (Física); Epidemiologia - Métodos estatísticos; Física Estatística e Termodinâmica

The use of complex networks as a substrate for the study of dynamic processes is a rich interdisciplinary area with several applications in real problems. In particular, the study of spreading processes in this framework are foundational for several models in biology, physics, and sociology. In this thesis, we develop studies on fundamental and theoretical aspects of dynamical processes, which have a connection with non- equilibrium statistical mechanics, as well as direct and practical applications for the study of real infectious diseases. We developed a quasi-stationary simulation method, one way to analyze systems with absorbing states, aiming at joining the best of ex- isting methods: computational simplicity with precision in the characterization of lo- calized transitions. After extensive simulations of the susceptible-infected-susceptible model in several types of complex networks, we were able to validate the method. Furthermore, we developed an heterogeneous mean-field theory for the symbiotic contact process with two species. Numerical integrations of the equations indicates the existence of a biestability region that depends on the heterogeneity of the com- plex network in addition to non-trivial finite size behaviors. Computer simulations in complex networks validated the theory and complemented the results. Finally, we de- veloped works with applications for the spreading of COVID-19. In the beginning of the pandemic, we built a data-driven compartmental epidemic model with metapop- ulations to investigate how Sars-Cov-2 would spread in Brazil in a municipality level. We were able to compare several mitigation scenarios and verify the desynchroniza- tion of the epidemic outbreaks in Brazil, a result confirmed a posteriori. In addition, we developed a method to estimate the underreporting of documented COVID-19 cases in different locations in Brazil using a compartmental model. These contribu- tions show the vast applications of dynamic process toolbox in complex networks, in addition to its importance for real situations. Keywords: Dynamical processes. Theoretical epidemiology. Complex networks.