Severe respiratory syndrome COVID-19 (SARS-CoV-2) outbreak has became the most important global health issue, and simultaneous efforts to fast and low-cost diagnosis of this virus were performed by researchers. One of the most usual tests was colorimetric methods based on the change of color of gold nanoparticles in the presence of viral antibodies, antigens, and other biological agents. This spectral change can be due to the aggregation of the particles or the shift of localized surface plasmon resonance due to the electrical interactions of surface agents. It is known that surface agents could easily shift the absorption peak of metallic nanocolloids which is attributed to the localized surface plasmon resonance. Experimental diagnosis assays for colorimetric detection of SARS-CoV-2 using Au NPs were reviewed, and the shift of absorption peak was studied from the viewpoint of numerical analysis. Using the numerical method, the refractive index and real and imaginary parts of the effective relative permittivity of the viral biological shell around Au NPs were obtained. This model gives a quantitative description of colorimetric assays of the detection of SARS-CoV-2 using Au NPs.