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

Rajesh Ranjan

Predictions for the US are shown in Fig. 6 . Both SIR and SEIQRDP models both give very close predictions of the final epidemic size of around 0.85 million, indicating good convergence of model parameters. As expected, the predicted size from the logistic model is much smaller than this value. Further, flattening of the curve begins in the third week of April. The corrections due to adjustment of deceleration gives the final estimate about 1.09 million. The final epidemic size for all the regions discussed in this paper is given in Table 3 . Figure 6 (b) also shows predictions for deaths using SEIQRDP. It is estimated that total deaths by the end of the epidemic could be around 33000, which is around 4% of total estimated cases. This is a very optimistic case as countries like Italy and France, have respectively reported 13% and 11% deaths per total infections. Fig. 7 shows the infection rate with the SIR model. Though the estimated decline begins on April 6, the curve shows a very long tail (even without correction) till the middle of May for zero new infection. As shown in Table 2 , there is a great disparity in the number of cases in different states in the US. New York alone accounts for 30% of the total cases in the US. Thus, we show predictions for some key states in the US in Fig. 8 . It is estimated that the number of cases in New York could rise to around 0.4 million at the end of epidemic. Estimations for New Jersey, California, Washington, Michigan, and Ohio are also shown and are also tabulated in Table 3 . For some of the states, such as New Jersey, California and Michigan, SIR and SEIQRDP models give slightly different estimates. However, as shown in table 2, these estimates are not very far from each other, and give a range of expected final size. The total number of cases in Ohio may limit to 10945 according to predictions. This may be due to early action of social distancing measures compare to a few other states (see Table 2 . Of course, these predictions depend on the compliance level of the social distancing measures so that governing parameters in the model do not change significantly.