Under What Conditions Can the SIR Model Approximate the SEIR Model?

Abstract

This study investigates the conditions under which the Susceptible–Infectious–Recovered (SIR)  model can provide an acceptable approximation of the Susceptible-Exposed–Infectious–Recovered (SEIR) model. Although SIR is simpler and requires fewer compartments, it assumes that individuals become infectious immediately after infection, whereas SEIR accounts for a latent period through an exposed compartment. The study compares the two models across different combinations of the basic reproduction number (R0), latent period, and infectious period. Their similarity is evaluated using infectious-population peak error and peak-time difference, with an approximation considered acceptable when the peak error is no greater than 10%, and the peak-time difference is no greater than 15 days. Across 20 tested parameter combinations, 3 were classified as acceptable. These cases occurred when the latent period was 1 day and the infectious period was 15 or 20 days, corresponding to latent-to-infectious ratios of approximately 0.050–0.067. As this ratio increased, the difference between the models became substantially larger, with the largest tested case producing a peak error of 302.98% and a peak-time difference of 90.85 days. The results indicate that SIR can serve as an approximation of SEIR when the latent period is very short relative to the infectious period, but SEIR becomes preferable when the latent stage has a substantial effect on epidemic dynamics. An interactive computational simulator was also developed to facilitate comparison of the two models and exploration of parameter effects.