# SEIRD COVID-19 Formal Characterization and Model Comparison Validation
## 7 Discussion  
With the SEIRD approach, we have not been able to fit the active and cumulative case curves simultaneously. To achieve this, it will be necessary to extend the model to a SEIHRD type by adding the hospitalized compartment as shown in Figure 14. This is due to the high heterogeneity in the prognosis of the disease, in which approximately 80% of those affected have mild or moderate symptoms and the remaining 20% are severe, sometimes fatal [32]. This disparity in prognosis means that the recovery time for the latter is much longer than for the former. In the basic SEIR model, recovery time is equal to the infectious period, but this is not the case for hospitalized patients. Moreover, it is precisely expected that in confirmed cases they should present a strong bias in favor of severe cases, making the basic SEIR model insufficient. All of the process presented allows us to define credible models that can be expanded and validated. With this premise, we can add containment measures that affect two parameters, the Susceptible population, and the rate of infection. The initial parametrization is based on the suggested current data. The containment measures, if this model is true, must be reinforced to contain the propagation of the pandemic due to the high possibility of asymptomatic cases; once the curve flattens, extensive testing will be needed to ensure that, after 15 days, no one is still infected. With all this process we will able to find an initial set of parameters for our models, which are summarized in Table 2 for the Korea case. Notice that this is an initial result that must be contrasted continuously with new datasets and with the new models that increase the capabilities to represent the reality. While the purpose of this article is not to delve into the parameterization of the epidemic, it is clear that a more exhaustive analysis, considering more countries and with a deeper and more robust exploration of the parameter space, could allow us to better infer the values of the model from comparative studies. One thing is clear; the hypothesis of higher R\({}_{0}\) in the range 5 to 6 and lower IFR of 0.3 to 0.7 seems increasingly feasible. If this were the case, the deconfinement strategy should take \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameter** & **Notation** & **Model 1** & **Model 2** & **Remark** \\ \hline Initial susceptible population & S\({}_{0}\) & 51.6 million & 51.6 million & S. Korea population \\ Transmission rate & \(\beta\) & 0.952 & 0.957 & Fitted parameter \\ Contention factor & \(\rho\) & 0.1372 & [0.1834, 0.1295] & Fitted stepwise function \\ Contention start dates * & t (\(\rho\)) & 41.56 days & [40.19, 52.26] & Fitted intervals \\ Mean incubation period & \(\alpha^{-1}\) & 5 days & 5 days & [[PERSON] et al.2020] \\ Mean infectious period & \(\gamma^{-1}\) & 5.4 days & 5.4 days & Fitted in model 1 \\ Infectious fatality rate & \(\mu\) & 0.48\% & [0.40, 0.57] & Fitted stepwise function \\ Basic reproduction number & R\({}_{0}=\beta/\gamma\) & 5.16 & 5.19 & Calculated \\ \hline \end{tabular}
\end{table} 
Table 2: Model 1 corresponds to a one change point scenario, and model 2 to a two change points scenario. To each change point corresponds a contention factor and a contention date, representing the intensity and the timing of each change, (*) days after 22 January 2020. Figure 14: SEIHRD compartment model diagram; it is a SEIRD model adding the hospitalized compartment. this into account. We notice also that the parameters of the model will be affected by the containment measures, hence they will change during the pandemic process. The hidden reasons for this can be analyzed with more detailed models, where MAS techniques can become a key ingredient to glimpse the causality that rules the behavior of citizens in a confinement process.