The illness-death model with three states (the health state, the illness state, and the death state) is a special case of multistate models. This model is important in several applications such as medical applications and research to analyze disease evolution or mortality. The transition probabilities are derived as functions of the hazard rates. This paper introduces a trial to obtain explicit mathematical expressions for the hazard rates of the illness-death model using data of Egypt in 2019. The hazard rates are derived using the Pearson distributions system.