Final and peak epidemic sizes for SEIR models with quarantine and isolation - Z. Feng (Mathematical Biosciences and Engineering)
Two $SEIR$ models with quarantine and isolation are considered, inwhich the latent and infectious periods are assumed to have anexponential and gamma distribution, respectively. Previous studieshave suggested (based on numerical observations) that a gammadistribution model (GDM) tends to predict a larger epidemic peakvalue and shorter duration than an exponential distribution model(EDM). By deriving analytic formulas for the maximum and finalepidemic sizes of the two models, we demonstrate that either GDM orEDM may predict a larger epidemic peak or final epidemic size,depending on control measures. These formulas are helpful not onlyfor understanding how model assumptions may affect the predictions,but also for confirming that it is important to assume realisticdistributions of latent and infectious periods when the model isused for public health policy making.