A reliable interval estimation of the latent mean incidence rate is important but challenging in infectious disease surveillance because count data are often zero-inflated and overdispersed. This study compared frequentist (normal approximation (NA), bootstrap percentile (BP), and bootstrap-t (BT)) and Bayesian (equal-tailed interval (ETI) and highest density interval (HDI)) intervals under the zero-inflated negative binomial (ZINB) model. A Monte Carlo simulation study varied levels of zero inflation, dispersion, and the observation period, evaluating conditional and unconditional coverage and average interval length. NA and BP showed undercoverage throughout the evaluated scenarios. BT improved conditional coverage over BP in 47 of 54 scenarios but generally produced wider intervals. Bayesian intervals often had higher coverage, although overcoverage and diagnostic failures prevented a uniform advantage. HDI was shorter than ETI in every scenario. An empirical application to dengue surveillance data from Phayao Province, Thailand, illustrated the five interval procedures under a fitted ZINB model; however, the NB model had lower AIC/BIC values. Temporal diagnostics and block bootstrap results indicated sensitivity to dependence assumptions. Overall, interval performance depended on the scenario, prior specification, and successful interval construction; no method uniformly achieved nominal coverage.