Multi-state models (MSMs) are an extension of classical survival analysis, which allows adjustment to the prediction of survival duration of the patient in the course of time by incorporating new information regarding the progression of the medical history and to better understand how prognostic factors influence the different phases of the disease/recovery process. In recent years, a wide range of medical situations have been modelled using MSMs such as problems following lung transplantation, problems following heart transplantation, hepatic cancer, HIV infection and AIDS. Disease progression model is needed for understanding the progression of disease and important in retrospective cohort analyses. In this paper five states progression model is suggested. The suggested model is studied in the case of continuous time non-homogeneous multistate model based on non-homogeneous Markov processes. A parametric time-dependent multistate model are considered to fit a non-homogeneous Markov process where transitions are specified by the hazard of exponential and Weibull distribution. The parameters of the suggested models are estimated by ML method. An application using dataset containing histories of bronchiolitis obliterans syndrome (BOS) from lung transplant recipients is applied using the suggested models. The BOS data set is provided in the R package msm.