Mathematical and computational modeling of entry into host cells by the SARS-CoV-2 virus. The modeling is at the molecular level, aiming to understand how membrane fusion is accomplished by the viral spike protein S. This is a complex process, and its modeling relies on recently available (but as yet incomplete) information about the structure and conformation of the spike protein and how it interacts with ACE2 receptors in target cells. On binding receptors a process of cleavage (S into S1 and S2) is followed by unfolding of the fusion protein S2 into an extended state, penetration into the target membrane, refolding of S2, and then fusion of the viral and host membranes which accomplishes viral entry and insertion of the viral genetic material into the host cell. All of these processes are poorly understood. We have considerable experience in studying influenza, and related processes of exocytosis where fusion is accomplished by SNARE proteins (and many auxiliaries).