## 3 Results
### Epidemiological Model Predictions  
The Richards, generalized logistic, Gompertz, and SIR models were used to estimate the cumulative number and the daily number of cases of infection from 31 March 2020 to 21 July 2020 with a 95% confidence interval (CI) (Figure 4). The results of the four models showed good agreement between the fitted and the observed values (Figure 4A,C,E,G).  
Furthermore, the final number of cases of infection and the end dates of the pandemic were predicted using each model, as summarized in Table 1. The SIR model revealed the lowest final cumulative number of cases of COVID-19 infection, with an end date on 7 September 2020, compared to the growth models. Conversely, a higher cumulative number of cases of infection was estimated by the Gompertz model, with an end date on 20 December 2020. Correspondingly, the Richards and generalized logistic models predicted the end date of this pandemic to be in October 2020, with approximately 404,853 and 420,593 as final number of cases, respectively.  
Figure 5 shows the cumulative and daily number of cases of infection for all models used in this study overlaid with the observed cases. It can be clearly seen from Figure 5A that the maximum final cumulative number of cases of infection was predicted by the Gompertz model. Conversely, the SIR model estimated the minimum number of final infection cases, which was 26% lower that that predicted by the Gompertz model. Subsequently, the SIR model showed an earlier end date in Saudi Arabia compared to the other models (as shown in Figure 5B and Table 1). The Gompertz growth model revealed that new cases of infection would last until 20 December 2020, as shown in Table 1. In Figure 5, the area shaded in yellow illustrates the period of lockdown, while the unshaded area refers to the period after 30 May 2020, where most restrictions were lifted in Saudi Arabia, except in Makkah Al-Mukarramah.  
Figure 3: The rates of infection (**A**), mortality (**B**), and recovery (**C**) of COVID-19 calculated from the reported cases in Saudi Arabia at different weekly intervals.  
Figure 4: Model predictions of the cumulative and daily number of cases of COVID-19 infection in Saudi Arabia, from 31 March 2020 until 21 July 2020. (**A,C,E,G**) The predicated cumulative cases with the 95% confidence interval (CI) of each model (line plot) overlaid by the reported data (blue cross). (**B,D,F,H**) Simulations of the number of daily cases (line plot) and the actual number of daily cases (bar plot).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Final Number \(\pm\) 95\% CI (cases \(\times\) 10\({}^{3}\))** & **End Date \(\pm\) 95\% CI** \\ \hline Richards & 404,853 \(\pm\) 27,024 & 24 October 2020 \(\pm\) 36 days \\ \hline Generalized logistic & 420,593 \(\pm\) 27,356 & 21 October 2020 \(\pm\) 36 days \\ \hline Gompertz & 488,318 \(\pm\) 27,659 & 20 December 2020 \(\pm\) 44 days \\ \hline SIR & 359,794 \(\pm\) 26,626 & 7 September 2020 \(\pm\) 25 days \\ \hline \hline \end{tabular}
\end{table}
Table 1: The final number of cases of infection and the end date of COVID-19 in Saudi Arabia, as predicted by the four models.  
Figure 5: Predictions of (**A**) the cumulative number of cases of COVID-19 infection, as well as the (**B**) daily number of cases of infection in Saudi Arabia from the SIR, Richards, generalized logistics, and Gompertz models based on the aggregated data from 31 March 2020 until 21 July 2020. The area shaded in yellow illustrates the period of lockdown.  
Table 2 presents the four statistical measures (RMSE, R\({}^{2}\), R\({}^{2}_{\rm adj}\), and AIC) for each model. Lower values of the RMSE and AIC and higher values of R\({}^{2}\) and R\({}^{2}_{\rm adj}\) represent better goodness of fit of the models. Hence, the results of these four statistical measures (RMSE = 2790.69, R\({}^{2}\) = 99.88%, R\({}^{2}_{\rm adj}\) = 99.88% and AIC = 1796.05) for the SIR model indicated that it was the best model compared to the [PERSON], generalized logistic, and Gompertz models (Table 2).