The paper presents the DEF-AI-MIA COV19D Competition, which is organized in the framework of the 'Domain adaptation, Explainability, Fairness in AI for Medical Image Analysis (DEF-AI-MIA)' Workshop of the 2024 Computer Vision and Pattern Recognition (CVPR) Conference. The Competition is the 4th in the series, following the first three Competitions held in the framework of ICCV 2021, ECCV 2022 and ICASSP 2023 International Conferences respectively. It includes two Challenges on: i) Covid-19 Detection and ii) Covid-19 Domain Adaptation. The Competition use data from COV19-CT-DB database, which is described in the paper and includes a large number of chest CT scan series. Each chest CT scan series consists of a sequence of 2-D CT slices, the number of which is between 50 and 700. Training, validation and test datasets have been extracted from COV19-CT-DB and provided to the participants in both Challenges. The paper presents the baseline models used in the Challenges and the performance which was obtained respectively.