Fig 1.
Comparison of difference between the l-i SEIR model and the conventional SEIR model in finding vE_out, the number of people who leave compartment E and enter compartment I per unit time.
Fig 2.
Comparison of the number of infectious individuals (In) calculated from the l-i SEIR model with the number of infectious individuals (I(t)) calculated from the conventional SEIR model when l>i.
Assuming that the latent period l = 1/σ = 8 days, the infectious period i = 1/γ = 2 days, βn = β(t) = 1 and N = 3.3x108, the l-i SEIR model generated a propagated epidemic curve for In (solid line in A), but the conventional SEIR model generated an epidemic curve for I(t), which increased in a near-exponential form (dashed line in A). Daily measles cases (an example of propagated epidemic curves) were reported in Aberdeen, South Dakota, USA from October 15, 1970 to January 16, 1971 (B).
Fig 3.
Examination of differences between curves S(t), E(t), I(t) and R(t) of the conventional SEIR model and their corresponding curves Sn, En, In and Rn of the l-i SEIR model at different rates of change in the number of infection cases.
Simulations in (A)-(D) were performed by assuming parameters βn = β(t) = 1 and N = 3.3x108, and (A) l = 1/σ = 2, i = 1/γ = 8, (B) l = 1/σ = 3, i = 1/γ = 7, (C) parameters same as those in (B), but the initial date (the day on which the first person was infected) in the conventional SEIR model was postponed by 3 days, and (D) l = 1/σ = 4, i = 1/γ = 5, the initial date in the conventional SEIR model was postponed by 6 days. (E) Simulations were performed by assuming parameters N = 3.3x108, l = 1/σ = 3, i = 1/γ = 7, and downregulating both βn and β(t) to slow down I(t) and matching I(t) and In to each other. (F) Parameters are the same as those used in (E), but I(t) and In were further slowed down by reducing βn and β(t).
Table 1.
The relative rising rate of I(t) and the normalized maximal calculation errors of R(t).
Fig 4.
Comparisons of l-i SEIR model with conventional SEIR model in simulations of COVID-19 epidemic data in the US and in NY.
(A) Fitting the numbers of daily new COVID-19 cases (yn and y(t)) calculated from the two SEIR models to the numbers (red dots) of daily new COVID-19 cases reported in the United States. (B) The calculated S, E, I and R curves from the two SEIR models after the fitting process in (A) was completed. (C) and (D) are the same as (A) and (B) except that the numbers of daily new COVID-19 cases
were reported in NY.
Fig 5.
Plot of the normalized maximal calculation errors of R(t) vs. the relative rising rate of I(t) with data from Table 1.