Many time-series models for disease counts utilise information from environmental variables. We focus on weekly dengue fever (DF) incidence rates in Singapore and demonstrate the strong negative correlation between an appropriately time-lagged total weekly rainfall and DF incidence. A Bayesian neural network time-series model for predicting DF incidence which utilizes rainfall data is introduced. A comparison is made between this neural network model and a time-series model which does not use any covariate information. An easily implementable method for choosing between the models which optimizes future prediction accuracy is suggested as well. We note that our proposed comparison method is applicable to any competing time-series models. This algorithm is demonstrated through examples of comparisons between pairs of different time-series models.