Most studies modelling population mobility and the spread of infectious diseases, particularly using meta-population-multi-patched models, tend to focus on theoretical properties and numerical simulations of such models. There is relatively scanty literature published on fit, inference and uncertainty quantification on epidemic models with population mobility. In this research, we have used three estimation techniques to solve an inverse problem and quantify its uncertainty on a human mobility-based multi-patched epidemic model, using mobile phone sensing data and COVID-19 confirmed positive cases in Hermosillo, Mexico. First, we have utilized a Brownian bridge model using mobile phone GPS data to estimate residence and mobility parameters of the epidemic model. In the second step, we have estimated the optimal model epidemiological parameters by deterministically inverting the model using genetic algorithm (GA). The third part of the analysis involves performing inference and uncertainty quantification on the epidemic model using two Bayesian Monte Carlo sampling methods: t-walk and Hamiltonian Monte Carlo (HMC). The results show that the estimated model parameters and incidence adequately fit the observed daily COVID-19 incidence in Hermosillo. Moreover, the estimated parameters from HMC result into large credible intervals, improving their coverage for the observed and predicted daily incidences. We also observe improved predictions when using multi-patch model with mobility against the single-patch model.