One difficulty for real-time tracking of epidemics is related to reporting delay. The reporting delay may be due to laboratory confirmation, logistical problems, infrastructure difficulties, and so on. The ability to correct the available information as quickly as possible is crucial, in terms of decision making such as issuing warnings to the public and local authorities. A Bayesian hierarchical modelling approach is proposed as a flexible way of correcting the reporting delays and to quantify the associated uncertainty. Implementation of the model is fast due to the use of the integrated nested Laplace approximation. The approach is illustrated on dengue fever incidence data in Rio de Janeiro, and severe acute respiratory infection data in the state of Paraná, Brazil.