By applying AI techniques to a variety of pandemic-relevant data, artificial intelligence (AI) has substantially supported the control of the spread of the SARS-CoV-2 virus. Along with this, epidemiological machine learning studies of SARS-CoV-2 have been frequently published. While these models can be perceived as precise and policy-relevant to guide governments towards optimal containment policies, their black box nature can hamper building trust and relying confidently on the prescriptions proposed. This paper focuses on interpretable AI-based epidemiological models in the context of the recent SARS-CoV-2 pandemic. We systematically review existing studies, which jointly incorporate AI, SARS-CoV-2 epidemiology, and explainable AI approaches (XAI). First, we propose a conceptual framework by synthesizing the main methodological features of the existing AI pipelines of SARS-CoV-2. Upon the proposed conceptual framework and by analyzing the selected epidemiological studies, we reflect on current research gaps in epidemiological AI toolboxes and how to fill these gaps to generate enhanced policy support in the next potential pandemic.