Modelling of infectious diseases has been increasingly used to evaluate the potential impact of different control measures and to guide public health policy decisions. In recent years, individual-level models (ILMs) have been effectively used to model infectious disease transmission. These models are well developed but assume the probability of disease transmission between two individuals depends only on their spatial (or network-based) separation. Consequently, we extend ILMs to a geographically-dependent ILMs (GD-ILMs) that allow the evaluation of the effect of spatially varying risk factors (e.g., education, social deprivation), environmental factors (such as temperature, air quality, rainfall, and humidity), as well as unobserved spatial structure, upon the transmission of infectious disease. In this study, we modeled the spread of infectious diseases on real/continuous-time scale based on GD-ILMs while infectious period and infection times are treated as unknown nuisance parameters. These nuisance parameters of latent variables are estimated using data augmentation techniques. The Bayesian framework is then adopted for inference and fitting of such models along with the computational tool Markov Chain Monte Carlo (MCMC) methods. The reliability of these models is investigated on a combination of simulated epidemic data and real data.