For around ten years, M. Rera and his team have been studying the biological mechanisms of ageing using a phenotype that predicts the onset of natural death in Drosophila and other model organisms :  the Smurf phenotype.  In this work, we propose a stochastic mathematical model of the two-phase ageing framework where the life of each individual is defined by the rate at which it turns Smurf and the rate at which it dies once Smurf. We use both non-parametric and parametric estimations of these rates on in-vitro data to determine the dynamics of the model, investigate the potential dependence between time spent non-Smurf and Smurf and assess the relevance of modeling ageing as a two phase process. The non-parametric estimations are performed with kernel estimators. As the most commonly used kernels suffer from boundary bias near 0 when estimating hazard rates, we work with non-classical kernels for which we also present convergence results.