The Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model has been commonly used to analyze the spread of infectious diseases. This 4-compartment (S,E,IandR) model uses an approximation of temporal homogeneity of individuals in these compartments to calculate the transfer rates of the individuals from compartmentEtoItoR. Although thisSEIRmodel has been generally adopted, the calculation errors caused by temporal homogeneity approximation have not been quantitatively examined. In this study, a 4-compartmentl-i SEIRmodel considering temporal heterogeneity was developed from a previous epidemic model (Liu X., Results Phys. 2021; 20:103712), and a closed-form solution of thel-i SEIRmodel was derived. Here,lrepresents the latent period andirepresents the infectious period. Comparingl-i SEIRmodel with the conventionalSEIRmodel, we are able to examine how individuals move through each corresponding compartment in the twoSEIRmodels to find what information may be missed by the conventionalSEIRmodel and what calculation errors may be introduced by using the temporal homogeneity approximation. Simulations showed thatl-i SEIRmodel could generate propagated curves of infectious cases under the condition ofl>i. Similar propagated epidemic curves were reported in literature, but the conventionalSEIRmodel could not generate propagated curves under the same conditions. The theoretical analysis showed that the conventionalSEIRmodel overestimates or underestimates the rate at which individuals move from compartmentEtoItoRin the rising or falling phase of the number of infectious individuals, respectively. Increasing the rate of change in the number of infectious individuals leads to larger calculation errors in the conventionalSEIRmodel. Simulations from the twoSEIRmodels with assumed parameters or with reported daily COVID-19 cases in the United States and in New York further confirmed the conclusions of the theoretical analysis.