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We analyze the endocytosis process of COVID-19 (coronavirus disease 2019) virus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) using a mechanical-thermodynamic model. The virus particle is designed to interface with the cell membrane as a hard sphere. The role of cytoplasmic BAR (Bin/Amphiphysin/RVs) proteins is considered in the endocytosis. Interestingly, the Endophilin N-BAR cytoplasmic proteins show resistance in participating endocytosis, whereas F-BAR, Arfaptin BAR, Amphiphysin N-BAR, and PX-BAR proteins participate in endocytosis. The increase in membrane tension, concentrated force between the cell membrane receptor, and spike glycoprotein present on the surface of virus particle promote the endocytosis. Also, the increase in the bending modulus of membrane leads to the two-phase solution of BAR protein concentration on the interior of cell membrane surface. We observe an unstable region of protein concentration, which may help one to retard the endocytosis process and thus the viral infection. Though the present study is focused on SARS-CoV-2, it can be extended to understand any other viral infections, involving endocytosis process.