The main focus of this project is modelling the behaviour of the Covid-19 disease in order to carry out estimations and predictions. A deterministic model has been created for modelling purposes. An estimation algorithm as the Extended Kalman Filter has been used in order to cope with the non-linearities of the model, estimating its states based on measurement´s data extracted from the Danish Health Authorities. A long-term and a short-term estimation have been carried out in order to prove the adaptation of the model to different time frames. An estimation of the behaviour of the Covid-19 disease during the pandemic have been made for each of the Danish regions. A 40-days prediction for the hospitalized state in the region of Hovedstaden has been carried out in order to show the behaviour of the model when no measurement´s data is added after the EKF prediction step. The results shown in this report have proven that the model developed in this thesis shows a good estimation of how the Covid-19 disease performs in Danish society, although certain aspects of the modelling rely on assumptions that can be subject to further investigations.