Seminários de Equações Diferencias e Sistemas Dinâmicos (EDSD) – 12/09/2024 às 14h:00m
Seminários de Equações Diferencias e Sistemas Dinâmicos (EDSD)
Titulo: SIR models under random perturbations to investigate the spread of diseases
Palestrante: Alexandre N. Oliveira Sousa (MTM-UFSC)
Abstract: We investigate SIR models with vital dynamics, reinfection, and randomness at the transmission coefficient and recruitment rate. Initially, we conduct an extensive analysis of the autonomous scenario, covering aspects such as local and global well-posedness, the existence and internal structure of attractors, and the presence of gradient dynamics. Subsequently, we explore the implications of small nonautonomous random perturbations, establishing the continuity of attractors and ensuring their topological structural stability. Additionally, we study scenarios in which both the transmission coefficient and the recruitment rate exhibit time-dependent or random behavior. For each scenario, we establish the existence of attractors and delineate conditions that determine whether the disease is eradicated or reaches an endemic state.
Joint work with Javier López-de-la-Cruz (Universidad Politécnica de Madrid).
The work can be found in arxiv: https://arxiv.org/abs/2404.12776v1
Data: Quinta-feira, 12 de Setembro de 2024 às 14 horas
Local: Auditório Airton Silva, Departamento de Matemática – MTM /CFM