In this study, a count times series model is used to estimate the weekly dengue cases in Surigao del Norte, Philippines, with weekly average temperature and cumulative rainfall as meteorological variables. We employ recent integer-valued time series models that can describe overdispersion, zero-inflation and influences from exogenous variables. Furthermore, we employ adaptive Markov Chain Monte Carlo method for the estimation and prediction of dengue cases. We determine the best model based on the lowest value of the Deviance Information Criterion (DIC) and calculate standardized Pearson residual for diagnostic checking of the best model. Empirical results show that zero-inflated transfer function models perform well and that the system exhibits a delay of one week in its responses to changes in rainfall and a three-week delay for changes in the temperature. Lastly, the integer-valued transfer function models in the Bayesian framework are shown to be adequate and describe well the dengue cases in Surigao del Norte.