Prediction of daily new COVID-19 cases - Difficulties and possible solutions.

Epidemiological compartmental models, such as SEIR (Susceptible, Exposed, Infectious, and Recovered) models, have been generally used in analyzing epidemiological data and forecasting the trajectory of transmission of infectious diseases such as COVID-19. Experience shows that accurately forecasting the trajectory of COVID-19 transmission curve is a big challenge for researchers in the field of epidemiological modeling because multiple unquantified factors can affect the trajectory of COVID-19 transmission. In the past years, we used a new compartmental model, l-i SEIR model, to analyze the COVID-19 transmission trend in the United States. Unlike the conventional SEIR model and the delayed SEIR model that use or partially use the approximation of temporal homogeneity, the l-i SEIR model takes into account chronological order of infected individuals in both latent (l) period and infectious (i) period, and thus improves the accuracy in forecasting the trajectory of transmission of infectious diseases, especially during periods of rapid rise or fall in the number of infections. This paper describes (1) how to use the new SEIR model (a mechanistic model) combined with fitting methods to simulate or predict trajectory of COVID-19 transmission, (2) how social interventions and new variants of COVID-19 significantly change COVID-19 transmission trends by changing transmission rate coefficient βn, the fraction of susceptible people (Sn/N), and the reinfection rate, (3) why accurately forecasting COVID-19 transmission trends is difficult, (4) what are the strategies that we have used to improve the forecast outcome and (5) what are some successful examples that we have obtained.