Estimating the Final Epidemic Size for COVID-19 Outbreak using Improved Epidemiological Models

Rajesh Ranjan

Three epidemiological models-logistic, SIR and generalized SEIR models are used to make predictions for the final epidemic size of COVID-19. Both SIR and generalized SEIR models give similar predictions for regions with signs of flattening of COVID-19 curve, while the logistic model consistently gives lower estimates. Similar estimates with SIR and generalized SEIR models, which use very different parameters and initial values, indicate that the underlying data are reliable to give convergence of model parameters. Thus, the estimations with these models could be more reliable than early estimates in the literature that has used data only from the acceleration phase. However, symmetric distributions of the infection rate predicted by the models around the peak value are not realistic as the decay rate in infections is generally much slower than acceleration as seen from the recent data from Italy and other European countries. Hence, a correction based on the change in the variance of the normal distribution is introduced to account for this factor. This generally provides the upper limit of these estimates. Finally, these models are used to estimate the final epidemic size for key countries where the epidemic outbreak is severe. The epidemic size for a few states in the US are also reported. A good convergence for France, UK, Iran, and India could not be obtained due to recent outbreaks. However, it is hoped that these models give a reasonable estimate for range of final total infections and can be used with confidence for regions where decline or at least no increase in the infection rate is visible.