This study proposes Hurdle-INGARCHX(1,1) models to address common challenges in count time series, such as zero inflation and overdispersion. The models integrate Poisson and Generalized Poisson hurdle with INGARCHX to allow the inclusion of exogenous variables with delay parameters to account for external influences. We employ Bayesian Markov Chain Monte Carlo (MCMC) methods to estimate the unknown parameters of the proposed models. The proposed models are applied to dengue incidence in Bislig City, Butuan City, and Bayugan City in the Caraga region, Philippines, with rainfall and average temperature serving as the exogenous variables to evaluate the effectiveness of the methods. Simulation outcomes reveal that the MCMC method is sufficient and provides reasonable estimates. Model performance is evaluated using the Deviance Information Criterion (DIC), and the Generalized Poisson hurdle-INGARCHX model demonstrates better performance than its Poisson counterpart. The in-sample prediction results strongly align with observed data, and diagnostic checks indicate no significant residual autocorrelation.