# Early Phase of the COVID-19 Outbreak in Hungary and Post-Lockdown Scenarios

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Epidemiological Report

#### 2.2. Statistical Analysis

`R`statistical environment version 4.0.0 [11] using packages

`ggplot2`version 3.3.0 [12] for visualization,

`data.table`version 1.12.8 [13] for data manipulation and

`shiny`version 1.4.0.2 [14] for creating an interactive dashboard to carry out epidemiological analyses online (available in Hungarian [15]).

#### 2.2.1. Temporal Variation of the Effective Reproduction Number

#### 2.2.2. Adjusted Case Fatality Ratio

`R`package

`rstan`version 2.19.3 [35]. A Markov chain Monte Carlo approach was used to carry out the estimation with No-U-Turn sampler, using 4 chains, 1000 warmup iterations and 2000 iterations for each chain.

#### 2.2.3. Estimation of the Ascertainment Rate

#### 2.3. Transmission Model

#### 2.3.1. The Governing Equations of the Transmission Model

#### 2.3.2. Model Parameters

#### 2.3.3. Contact Matrix

#### 2.3.4. Transmission Rates and the Next Generation Matrix

#### 2.3.5. Scenarios

#### 2.3.6. Parameter Uncertainty and Other Limitations

## 3. Results

#### 3.1. Epidemiological Report

#### 3.2. Statistical Analysis

#### 3.3. Post-Lockdown Scenarios

#### 3.4. Age-Dependent Intervention Measures

#### 3.4.1. School Closures

#### 3.4.2. Protection of the Elderly

#### 3.5. Role of Seasonality

#### 3.6. Spatial Heterogeneity

#### 3.7. Sensitivity of the Peak ICU Demand to Key Parameters

#### 3.8. The Impact of Implemented Measures Since Mid-March

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Transmission diagram. Different shades of red denote infected compartments. A darker shade corresponds to a more severe state of the disease: those in compartments with the lightest shade do not transmit the disease, those in compartments with the darkest shade are in critical status. Black solid arrows denote the possible ways of transition from one compartment to another. Gray dashed arrows show possible ways of infection. Compartments being grouped together in ellipses stand for different stages of the same status.

**Figure 2.**Heatmap of the contact matrix ${M}_{\mathrm{cont}}$. The image is rotated w.r.t. how ${M}_{cont}$ is indexed: the $(1,1)$ element is in the bottom-left corner.

**Figure 3.**Epidemic curve of confirmed COVID-19 cases in Hungary by date of confirmation (reported until May 10, 2020. Data source: NPHC).

**Figure 4.**Crude case fatality rate of confirmed COVID-19 cases in Hungary by age groups (reported until May 10, 2020. Data source: NPHC).

**Figure 5.**Fourteen-day cumulative incidence of confirmed COVID-19 cases in Budapest and in other regions of Hungary (reported until 10 May 2020. Data source: NPHC).

**Figure 6.**Real-time estimation of the reproduction number during the early phase of the COVID-19 outbreak in Hungary using two different methods (shaded area depicts 95% confidence interval).

**Figure 7.**Real-time estimation of case fatality rate during the early phase of the COVID-19 outbreak in Hungary (shaded area depicts 95% confidence interval).

**Figure 8.**Hospitalization, ICU demand, and incidence curves. The figures show the required number of hospital beds (classes ${I}_{h}+{I}_{cr}$, yellow) and ICU beds (class ${I}_{c}$, red) need in the first row for $\mathcal{R}\in \{1.65,1.32,1.1\}$, respectively. The second row illustrates the daily incidence (transition from compartment S to ${L}_{1}$ in our model, orange) combining all age groups. Note that the incidence curves peak earlier than the hospitalization curves. The legend at the bottom applies for all figures. Note that the scalings of the figures are different.

**Figure 9.**Age-specific mortality and recovery. The figure shows the effect of the weak, moderate, and strong control (25%, 40% and 50% general contact reduction, respectively). Every age group covers at most one decade except the group of “middle aged” that represents three decades. According to our model, elderly people (60+) are predicted to produce most of the fatality cases in each scenario. The legend on the bottom applies for all figures.

**Figure 10.**Effect of school closure. Simulations suggest that school closures—if maintained for a long period—effectively decrease peak hospital bed and ICU needs and significantly postpone the peak of the epidemic.

**Figure 11.**Protection of the elderly. The figures show the effect of an additional contact reduction of elderly people in case of a weak control. The figures suggest that the selective protection of elderly people can successfully reduce the peak ICU need and the overall mortality, yet it has a theoretical limit.

**Figure 12.**Effect of seasonality. The top left figure depicts the relative transmissibility of the virus throughout the year. Purple denotes no seasonality ($c=0$), blue curves correspond to weak seasonality ($c=0.1$), turquoise curves stands for moderate seasonality ($c=0.2$), and green curves correspond to strong seasonality ($c=0.3$). The next three figures investigate the number of infected individuals under these seasonality scenarios with $\mathcal{R}=1.65,\mathcal{R}=1.32$, and $\mathcal{R}=1.1$, respectively.

**Figure 13.**Epidemic curves of the regions: sum of the infective compartments $({\mathbf{I}}_{\mathbf{p}},{\mathbf{I}}_{\mathbf{a},\mathbf{1}},{\mathbf{I}}_{\mathbf{a},\mathbf{2}},{\mathbf{I}}_{\mathbf{a},\mathbf{3}},{\mathbf{I}}_{\mathbf{s},\mathbf{1}},{\mathbf{I}}_{\mathbf{s},\mathbf{2}},{\mathbf{I}}_{\mathbf{s},\mathbf{3}})$. First, we consider identical reproduction numbers $\mathcal{R}=1.32$ for both patches (Budapest with Pest county and other regions). Without any travel reductions, the two-patch model gives identical results to the one-patch version, as seen in the left figure. Next, if travel reductions are put in place, the one-patch model overestimates slightly the size of the epidemic for equal $\mathcal{R}$ values. Finally, assuming different reproduction numbers and large reduction in travel, the peak occurs earlier in the patch with larger $\mathcal{R}$ (Budapest and Pest county); furthermore, the one-patch model and the aggregated two-patch model differ in both time and size of the peak.

**Figure 14.**Left: the impact of control measures on the epidemic trajectory. Yellow dots are cumulative numbers of reported cases, orange dots are corrected data by underascertainment rate, solid curve is simulated cumulative numbers with $\mathcal{R}=2.2$ and the absence of measures. Right: Sensitivity of the peak ICU demand to transmissibility and severity of COVID-19. The top right corner is similar to the worst case scenario of [41]. The white dot is our most pessimistic scenario (weak control).

**Table 1.**Age-independent epidemiological parameters of COVID-19. Assumed to be valid for all age groups. References and explanations are in Section 2.3.2.

Duration of | Value | |
---|---|---|

Incubation period | ${\left({\alpha}_{\mathbf{L},\mathbf{1}}^{i}\right)}^{-1}+{\left({\alpha}_{\mathbf{L},\mathbf{2}}^{i}\right)}^{-1}+{\left({\alpha}_{\mathbf{p}}^{i}\right)}^{-1}$ | $5.2$ days |

Latent period | ${\left({\alpha}_{\mathbf{L},\mathbf{1}}^{i}\right)}^{-1}+{\left({\alpha}_{\mathbf{L},\mathbf{2}}^{i}\right)}^{-1}$ | $3.2$ days |

Presymptomatic (infectious) period | ${\left({\alpha}_{\mathbf{p}}^{i}\right)}^{-1}$ | $2.0$ days |

Infectious period of ${I}_{\mathbf{a}}^{i}$ | ${\left({\gamma}_{\mathbf{a},\mathbf{1}}^{i}\right)}^{-1}+{\left({\gamma}_{\mathbf{a},\mathbf{2}}^{i}\right)}^{-1}+{\left({\gamma}_{\mathbf{a},\mathbf{3}}^{i}\right)}^{-1}$ | $3.0$ days |

Infectious period of ${I}_{\mathbf{s}}^{i}$ | ${\left({\gamma}_{\mathbf{p},\mathbf{1}}^{i}\right)}^{-1}+{\left({\gamma}_{\mathbf{p},\mathbf{2}}^{i}\right)}^{-1}+{\left({\gamma}_{\mathbf{p},\mathbf{3}}^{i}\right)}^{-1}$ | $3.0$ days |

Hospitalization | ${\left({\gamma}_{\mathbf{h}}^{i}\right)}^{-1}$ | $10.0$ days |

Intensive care | ||

until transition to ${R}_{}^{}$ or ${I}_{\mathbf{cr}}^{i}$ | ${\left({\gamma}_{\mathbf{c}}^{i}\right)}^{-1}$ | $10.0$ days |

Recovery in ${I}_{\mathbf{cr}}^{i}$ | ${\left({\gamma}_{\mathbf{cr}}^{i}\right)}^{-1}$ | $14.0$ days |

Relative infectiousness | ||

Presymptomatic vs Symptomatic | ${\beta}_{\mathbf{p}}^{(k,i)}/{\beta}_{\mathbf{s},\_}^{(k,i)}$ | $1.0$ |

Asymptomatic vs Symptomatic | ${\beta}_{\mathbf{a},\_}^{(k,i)}/{\beta}_{\mathbf{s},\_}^{(k,i)}$ | $0.5$ |

Age Group | 0–4 | 5–14 | 15–29 | 30–59 | 60–69 | 70–79 | 80– |
---|---|---|---|---|---|---|---|

Population | 468,605 | 953,134 | 1,678,211 | 4,087,976 | 1,312,208 | 839,589 | 433,033 |

Probability/Age Group | 0–4 | 5–14 | 15–29 | 30–59 | 60–69 | 70–79 | 80– | |
---|---|---|---|---|---|---|---|---|

Asymptomatic course | ${p}_{}^{i}$ | $0.95$ | $0.8$ | $0.7$ | $0.5$ | $0.4$ | $0.3$ | $0.2$ |

Hospitalization or | ||||||||

intensive care (from ${I}_{\mathbf{s},\mathbf{3}}^{i}$) | ${h}_{}^{i}$ | $0.00045$ | $0.00045$ | $0.0042$ | $0.0442$ | $0.1162$ | $0.2682$ | $0.4945$ |

Intensive care | ||||||||

(given hospitalization) | ${\xi}_{}^{i}$ | $0.333$ | $0.333$ | $0.297$ | $0.294$ | $0.292$ | $0.293$ | $0.293$ |

Fatal outcome | ||||||||

(from ${I}_{\mathbf{cr}}^{i}$) | ${\mu}_{}^{i}$ | $0.2$ | $0.2$ | $0.216$ | $0.3$ | $0.582$ | $0.678$ | $0.687$ |

$\mathcal{R}$ | $1.0$ | $1.1$ | $1.32$ | $1.65$ | $2.2$ |

$\beta $ | 0.0210 | 0.0231 | 0.0277 | 0.0347 | 0.0462 |

Scenario | Description | Pointer |
---|---|---|

Weak control | general 25% reduction in transmission | Section 3.3 |

Moderate control | general 40% reduction in transmission | |

Strong control | general 50% reduction in transmission | |

School closure | two variants of changing the mixing patterns of schoolchildren | Section 3.4.1 |

Protection of elderly | 50–100% reduction of contacts outside the household for the elderly | Section 3.4.2 |

Seasonality | exploring various degrees of seasonal behavior | Section 3.5 |

Spatial heterogeneity | considering two patches, which are strongly or weakly connected | Section 3.6 |

**Table 6.**Number of confirmed COVID-19 cases and deaths, morbidity (per 100,000 population) and crude CFR of confirmed COVID-19 cases in Hungary by age groups.

Age Group (Years) | Number of Confirmed COVID-19 Cases | Morbidity (Per 100,000 Population) | Number of Deaths | Case Fatality Rate (Per 100 Confirmed COVID-19 Cases) |
---|---|---|---|---|

<1 | 3 | 3.3 | 0 | 0.0 |

1–4 | 10 | 2.6 | 0 | 0.0 |

5–14 | 31 | 3.2 | 0 | 0.0 |

15–29 | 254 | 15.5 | 0 | 0.0 |

30–39 | 267 | 19.9 | 3 | 1.1 |

40–49 | 459 | 27.7 | 8 | 1.7 |

50–59 | 485 | 38.3 | 15 | 3.1 |

60–64 | 233 | 35.4 | 20 | 8.6 |

65–69 | 254 | 39.4 | 44 | 17.3 |

70–79 | 595 | 69.5 | 133 | 22.4 |

≥80 | 693 | 163.3 | 198 | 28.6 |

Overall | 3284 | 33.1 | 421 | 12.8 |

**Table 7.**Underascertainment (ratio of all infections to reported cases) and corrected number of cumulative cases based on the estimated underascertainment.

IFR | 0.3% | 0.6% | 0.9% | 1.2% |
---|---|---|---|---|

Underascertainment (true/reported) | 54.0 | 27.0 | 18.0 | 13.5 |

Corrected cumulative number of infections by 10 May | 177,242 | 88,621 | 59,081 | 44,310 |

**Table 8.**Indicative values of the epidemics in case of the applied control measures. Hospital and ICU bed need at the peak, mortality and the number of recovered people with the expected time it takes to reach 1,000 ICU beds is shown in case our control scenarios. See the corresponding time series in Figure 8.

Transmission Reduction | Reproduction Number | Hospital Bed Need at Peak | ICU Need at Peak | Time to Reach 1000 ICU Beds | Mortality (Pers.) | Recovered (of Tot. Pop.) |
---|---|---|---|---|---|---|

25% | 1.65 | 20,973 | 7225 | 6 weeks | 21,624 | 58.25% |

40% | 1.32 | 7400 | 2477 | 10 weeks | 12,374 | 37.37% |

50% | 1.1 | 1069 | 350 | - | 4447 | 14.84% |

60% | 0.9 | - | - | - | - | - |

Date | Measure | Reported Number of Cases at the Time of Introduction |
---|---|---|

8 March | Banned visits to health care institutions and long-term care facilities | 9 |

9 March | Suspension of Northern Italy flights | 12 |

11 March | Emergency notification | 16 |

12 March | University closures, no entry for non-Hungarian passengers to Hungary from Italy, China, Korea and Iran | 19 |

16 March | School closures | 50 |

17 March | Shortened opening time of shops, ban on events | 58 |

28 March | Stay at home measures | 408 |

4 May | Partial lifting of stay at home measures and opening of restaurants in the countryside (except Pest county where from May 14) | 3065 |

18 May | Lifting of stay at home measures and opening of shops and outdoor areas of restaurants in Budapest | 3556 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Röst, G.; Bartha, F.A.; Bogya, N.; Boldog, P.; Dénes, A.; Ferenci, T.; Horváth, K.J.; Juhász, A.; Nagy, C.; Tekeli, T.;
et al. Early Phase of the COVID-19 Outbreak in Hungary and Post-Lockdown Scenarios. *Viruses* **2020**, *12*, 708.
https://doi.org/10.3390/v12070708

**AMA Style**

Röst G, Bartha FA, Bogya N, Boldog P, Dénes A, Ferenci T, Horváth KJ, Juhász A, Nagy C, Tekeli T,
et al. Early Phase of the COVID-19 Outbreak in Hungary and Post-Lockdown Scenarios. *Viruses*. 2020; 12(7):708.
https://doi.org/10.3390/v12070708

**Chicago/Turabian Style**

Röst, Gergely, Ferenc A. Bartha, Norbert Bogya, Péter Boldog, Attila Dénes, Tamás Ferenci, Krisztina J. Horváth, Attila Juhász, Csilla Nagy, Tamás Tekeli,
and et al. 2020. "Early Phase of the COVID-19 Outbreak in Hungary and Post-Lockdown Scenarios" *Viruses* 12, no. 7: 708.
https://doi.org/10.3390/v12070708