# SEIRD COVID-19 Formal Characterization and Model Comparison Validation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{0}, however, the estimation of this parameter, based on the data we obtain from the observations is not a simple task, due to the complexity to cope with a new phenomenon, and the time-lapse we use to analyze this information.

## 2. System Dynamics Model

## 3. SDL Conceptual Model

## 4. Python Codification and Parameter Fitting

- 1.
- The time lag in the publication of the data.
- 2.
- The degree of underreporting in the numbers of newly infected.
- 3.
- The timing of the adoption of containment and confinement policies.
- 4.
- The containment factor (ρ) that quantifies the power of these measures.

## 5. Comparison with Other Models’ Validation

## 6. Parameters Validation

#### 6.1. South Korea Case

_{0}value than initially estimated (2.2–2.7). The Imperial College raised it in its March 30 report [29] to 3.87 [3.01–4.66] and the CDC published, on April 7 [30], an even more dramatic update raising R

_{0}to 5.7 [3.8–8.9]. The latter values are in line with those obtained in our fits. Of course, there is still a lot of uncertainty around these values but a relatively high value of R

_{0}is already a reasonable hypothesis.

#### 6.2. Spain Case

## 7. Discussion

_{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 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.

## 8. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**First preliminary System Dynamics SEIRD (Susceptible, Exposed, Infective, Recovered and Deceased) model.

**Figure 7.**PSusceptible PROCESS diagram. This diagram shows the initialization of the model where the first EVENT fromInfective, defines the initial number of infective individuals we have in the model. When we receive this SIGNAL, we start the dynamics of the model, which in SD is represented in the equations, but here is represented in the diagrams. We calculate with PROCEDURE numSusceptible, the number of exposed individuals that will be sent to the BExposed BLOCK, numExposed.

**Figure 8.**PSusceptible EMPTY state. No more susceptible individuals exist, hence the model finishes here.

**Figure 12.**Korea fits. For the “one change point” model, we use the data of active cases (infective in the model) and adjust the transmissivity rate (β) and the containment factor (ρ) but also the infectious period (γ

^{−1}). We find the best fits at γ

^{−1}= 5.4 days, being consistent with the values proposed by [22]. For the second set, we use γ as a fixed parameter to find again the new values of β and ρ. For each case, we use their fitted parameters to find an estimation of the infectious fatality rate considering the time series of confirmed deaths.

**Figure 13.**Unlike with Korea, the Spain curve does not fit well with a single or two change points in a SEIRD model.

**Figure 14.**SEIHRD compartment model diagram; it is a SEIRD model adding the hospitalized compartment.

**Figure 15.**Prevision and Key Performance Indicators (KPI) of the status of the pandemic situation in Catalonia until July 2, 2020.

Parameter | Value |
---|---|

beta | contactsday × infectivity |

alpha | 1/incubationPeriod |

gamma | 1/infectiousPeriod |

contactsday | 7.42 |

infectivity | 0.42 |

infectiousPeriod | 14.39 |

incubationPeriod | 6.38 |

fatalityRate | 0.85 |

**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.

Parameter | Notation | Model 1 | Model 2 | Remark |
---|---|---|---|---|

Initial susceptible population | S_{0} | 51.6 million | 51.6 million | S. Korea population |

Transmission rate | β | 0.952 | 0.957 | Fitted parameter |

Contention factor | ρ | 0.1372 | [0.1834, 0.1295] | Fitted stepwise function |

Contention start dates * | t (ρ) | 41.56 days | [40.19, 52.26] | Fitted intervals |

Mean incubation period | α^{−1} | 5 days | 5 days | (Lin et al. 2020) |

Mean infectious period | γ^{−1} | 5.4 days | 5.4 days | Fitted in model 1 |

Infectious fatality rate | µ | 0.48% | [0.40, 0.57] | Fitted stepwise function |

Basic reproduction number | R_{0} = β/γ | 5.16 | 5.19 | Calculated |

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**MDPI and ACS Style**

Fonseca i Casas, P.; García i Carrasco, V.; Garcia i Subirana, J. SEIRD COVID-19 Formal Characterization and Model Comparison Validation. *Appl. Sci.* **2020**, *10*, 5162.
https://doi.org/10.3390/app10155162

**AMA Style**

Fonseca i Casas P, García i Carrasco V, Garcia i Subirana J. SEIRD COVID-19 Formal Characterization and Model Comparison Validation. *Applied Sciences*. 2020; 10(15):5162.
https://doi.org/10.3390/app10155162

**Chicago/Turabian Style**

Fonseca i Casas, Pau, Víctor García i Carrasco, and Joan Garcia i Subirana. 2020. "SEIRD COVID-19 Formal Characterization and Model Comparison Validation" *Applied Sciences* 10, no. 15: 5162.
https://doi.org/10.3390/app10155162