Two $SEIR$ models with quarantine and isolation are considered, in
which the latent and infectious periods are assumed to have an
exponential and gamma distribution, respectively. Previous studies
have suggested (based on numerical observations) that a gamma
distribution model (GDM) tends to predict a larger epidemic peak
value and shorter duration than an exponential distribution model
(EDM). By deriving analytic formulas for the maximum and final
epidemic sizes of the two models, we demonstrate that either GDM or
EDM may predict a larger epidemic peak or final epidemic size,
depending on control measures. These formulas are helpful not only
for understanding how model assumptions may affect the predictions,
but also for confirming that it is important to assume realistic
distributions of latent and infectious periods when the model is
used for public health policy making.
Citation: Z. Feng. Final and peak epidemic sizes for SEIR models with quarantine and isolation[J]. Mathematical Biosciences and Engineering, 2007, 4(4): 675-686. doi: 10.3934/mbe.2007.4.675
Abstract
Two $SEIR$ models with quarantine and isolation are considered, in
which the latent and infectious periods are assumed to have an
exponential and gamma distribution, respectively. Previous studies
have suggested (based on numerical observations) that a gamma
distribution model (GDM) tends to predict a larger epidemic peak
value and shorter duration than an exponential distribution model
(EDM). By deriving analytic formulas for the maximum and final
epidemic sizes of the two models, we demonstrate that either GDM or
EDM may predict a larger epidemic peak or final epidemic size,
depending on control measures. These formulas are helpful not only
for understanding how model assumptions may affect the predictions,
but also for confirming that it is important to assume realistic
distributions of latent and infectious periods when the model is
used for public health policy making.