Analytical Solution of a New SEIR Model Based on Latent Period-Infectious Period Chronological Order

ABSTRACT The Susceptible-Infectious-Recovered ( SIR ) and SIR derived epidemic models have been commonly used to analyze the spread of infectious diseases. The underlying assumption in these models, such as Susceptible-Exposed-Infectious-Recovered ( SEIR ) model, is that the change in variables E, I or R at time t is dependent on a fraction of E and I at time t . This means that after exposed on a day, this individual may become contagious or even recover on the same day. However, the real situation is different: an exposed individual will become infectious after a latent period ( l ) and then recover after an infectious period ( i ). In this study, we proposed a new SEIR model based on the latent period-infectious period chronological order (Liu X., Results Phys. 2021; 20:103712). An analytical solution to equations of this new SEIR model was derived. From this new SEIR model, we obtained a propagated curve of infectious cases under conditions l > i . Similar propagated epidemic curves were reported in literature. However, the conventional SEIR model failed to simulate the propagated epidemic curves under the same conditions. For l < i , the new SEIR models generated bell-shaped curves for infectious cases, and the curve is near symmetrical to the vertical line passing the curve peak. This characteristic can be found in many epidemic curves of daily COVID-19 cases reported from different countries. However, the curve generated from the conventional SEIR model is a right-skewed bell-shaped curve. An example for applying the analytical solution of the new SEIR model equations to simulate the reported daily COVID-19 cases was also given in this paper.