Modelling factors that influence under-5 morbidity counts examines salient factors affecting morbidity cases among children below five years.Diseases such as measles , pneumonia, malaria, diarrhea etc were examined. It also highlights methods of modelling counts and also handling issues of over dispersion in count data. The poisson regression model is considered while Negative-binomial and quasi-poisson models are adopted in dealing with over dispersed data.