Stochastic modeling for uncertainty quantification in COVID-19 dynamics using Euler Maruyama approximation

We propose a stochastic extension of a compartmental epidemiological model for COVID-19 to describe the transmission dynamics in Bogotá, Colombia. To account for intrinsic variability in infection, incubation, recovery, and vaccination processes, random perturbations are incorporated into key model parameters. The resulting system of stochastic differential equations is approximated using the Euler-Maruyama method, enabling likelihood-based parameter estimation. We derive an extended basic reproduction number, along with its associated uncertainty, providing a statistically grounded measure of epidemic potential under varying conditions. Simulation results demonstrate that the proposed framework successfully captures the variability observed in the epidemiological data and highlights the importance of accounting for parameter uncertainty in public health decision-making. The model is statistically tractable, computationally efficient, and adaptable to other infectious diseases and urban settings. Possible extensions include incorporating reinfection dynamics, integrating additional data sources, and using Bayesian inference to enhance uncertainty quantification.