Coronavirus disease 19 (COVID-19) continues to challenge most scientists searching for an effective way to diminish global outbreaks. As a correlate, progress in our knowledge about the COVID-19 has occurred, and we are more acknowledged than the early stages of a pandemic. However, these efforts have not been enough to stop the viral transmission, and many questions remain unanswered. To this end, understanding the interaction between SARS-CoV-2 and target cells affected by this virus is mandatory. Along with studies in the field of the clinical setting and basic research, some achievements in the modeling and analysis of COVID-19 disease have been obtained in mathematics. Unfortunately, these models are not comprehensive to predict or approve of which occur inside the body after virus entry. Commensurate with these comments, models with more elaborate structures and minimum failure rate prediction are highly demanded. Here, we aimed to systematically construct the modeling of the interaction between the SARS-CoV-2 virus and innate immune system cells and especially analyze the invasion of the virus to epithelial cells.