Health sciences research often involves analyses of repeated measurement or longitudinal count data analyses that exhibit excess zeros. Overdispersion occurs when count data measurements have greater variability than allowed. This phenomenon can be carried over to zero-inflated count data modeling. Referred to as zero-inflation, the Zero-Inflated Poisson (ZIP) model can be used to model such data. The Zero-Inflated Negative Binomial (ZINB) model is used to account for overdispersion detected in count data. The ZINB model is considered as an alternative for the Zero-Inflated Generalized Poisson (ZIGP) model for zero-inflated overdispersed count data. Consequently, zero-inflated models have been proposed for the situations where the data generating process results are overdispersed. This study considers modeling and handling overdispersion data among children with Thalassemia disease using the ZIP, ZINB and ZIGP models.