Gaussian process prior to estimate the SIR epidemic model

In recent years, there has been significant activity in the development and application of efficient computational algorithms for estimating states and parameters in the stochastic SIR epidemic model. These models help us to understand reality because they quantify it. The populations under study are divided into states or categories. The transfer rates between states are mathematically expressed as derivatives with respect to time-based on the sizes of the states using systems of ordinary differential equations or stochastic differential equations. The main objective of this work is to model the dynamics of the spread of the 2019 coronavirus disease outbreak and estimate the trend curve of the effective reproductive number. Modeling the epidemic's spread facilitates statistical inference of the data and helps plan contingency strategies for population prevention. The methodology used to estimate the states and parameters of the stochastic SIR model involves applying the Euler-Maruyama algorithm, the Diffusion Bridge approximation, the Kalman filter, and the Gaussian process. We illustrate the methodology using simulated epidemic states and data collected by the Secretaría Nacional de Gestión de Riesgos y Emergencias. We show how unobserved processes or states can be inferred simultaneously with the underlying parameters. Among the main contributions of this work are proposing estimates for the number of infected, susceptible, and recovered individuals and providing a real-time monitoring tool for the number of cumulative cases.

• Autor principal: Velasco Ramírez, Byron Andrés (author)
• Format: bachelorThesis
• Idioma: eng
• Publicat: 2024
• Matèries: Modelo epidémico SIR; Proceso Gaussiano; Filtro de Kalman; SIR epidemic model; Gaussian process; Kalman filter
• Accés en línia: http://repositorio.yachaytech.edu.ec/handle/123456789/732