A compartmental model considering the temporal heterogeneity of infected individuals

What is it about?

The Susceptible-Exposed-Infectious-Recovered (SEIR) epidemic model has been frequently used to analyze the spread of infectious diseases. This 4-compartment (S, E, I and R) model uses an approximation of temporal homogeneity of individuals in these compartments to calculate the transfer rates of the individuals from compartment E (exposed status) to I (infectious status) to R (recovered status). Although this SEIR model has been broadly adopted, the calculation errors caused by temporal homogeneity approximation have not been quantitatively examined. In this study, a 4-compartment l-i SEIR model considering temporal heterogeneity of infected individuals was developed. Simulations showed that l-i SEIR model could generate propagated curves of infectious cases, which usually consist of a series of waves with successively larger peaks, under the condition of l>i. Similar propagated epidemic curves were reported in literature, but the conventional SEIR model could not generate propagated curves under the same conditions. The theoretical analysis showed that the conventional SEIR model overestimates or underestimates the rate at which individuals move from compartment E (exposed status) to I (infectious status) to R (recovered status) in 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 conventional SEIR model. Simulations from the two SEIR models 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.

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Why is it important?

Epidemic compartmental models played an important role in formulating the proper social interventions to slow down the spread of COVID-19. Accurately forecasting the trajectory of COVID-19 transmission curve is a big challenge to researchers in the field of epidemic modeling. This challenge is not only due to the existence of multiple factors (such as social distancing, vaccinations, public health interventions, and new COVID-19 variants) that can affect the trajectory of transmission of infectious diseases, but also because of the inclusion of the possible calculation errors that are induced from the approximation of temporal homogeneity in the compartmental epidemic models. This study presented a new SEIR epidemic model taking into account of the temporal heterogeneity of infected individuals, and finding that the calculation errors caused by the approximation of temporal homogeneity in conventional compartment models linearly increase with the relative rising rate of infection cases, suggesting that one needs to use the conventional SEIR model with caution when simulating an epidemic curve with a fast rising rate, such as a highly transmissible infectious disease outbreak without stringent interventions to slow the spread.