Receptor diffusion on cell membrane is usually believed as a major factor that controls how fast a virus can enter into host cell via endocytosis.However,when receptors are densely distributed around the binding site so that receptor recruiting through diffusion is no longer energetically favorable,we thus hypothesize that another effect,the creep deformation of cytoskeleton,might turn to play the dominant role in relaxing the engulfing process.In order to deeply understand this mechanism,we propose a viscoelastic model to investigate the dynamic process of virus engulfment retarded by the creep deformation of cytoskeleton and driven by the binding of ligand-receptor bonds after overcoming resistance from elastic deformation of lipid membrane and cytoskeleton.Based on this new model,we predict the lower bound of the ligand density and the range of virus size that allows the complete engulfment,and an optimal virus size corresponding to the smallest wrapping time.Surprisingly,these predictions can be reduced to the previous predictions based on simplified membrane models by taking into account statistical thermodynamic effects.The results presented in this study may be of interest to toxicologists,nanotechnologists,and virologists. Receptor diffusion on cell membrane is usually believed as a major factor that controls how fast a virus can enter into host cell via endocytosis. Despite, when receptors are densely distributed around the binding site so that receptor recruiting through diffusion is no longer energetically favorable, we thus hypothesize that another effect, the creep deformation of cytoskeleton, might turn to play the dominant role in relaxing the engulfing process.In order to deeply understand this mechanism, we propose a viscoelastic model to investigate the dynamic process of virus engulfment retarded by the creep deformation of cytoskeleton and driven by the binding of ligand-receptor bonds after overcoming resistance from elastic deformation of lipid membrane and cytoskeleton. based on this new model, we predict the lower bound of the ligand density and the range of virus size that allows the complete engulfment, and an optimal virus size corresponding to the smallest wrapping time. Surprisingly, these pred ictions can be reduced to the previous predictions based on simplified membrane models by taking into account statistical thermodynamic effects. the results presented in this study may be of interest to toxicologists, nanotechnologists, and virologists.