# Modeling Dynamic Responses to COVID-19 Epidemics: A Case Study in Thailand

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Review of COVID-19 in Thailand

#### 2.2. Data and Timeframe

#### 2.3. Mathematical Model

#### 2.4. The Reproduction Number

#### 2.5. Parameter Estimations

## 3. Results

#### 3.1. The First Wave

#### 3.2. The Second Wave

#### 3.3. Comparing Dynamics of the Scale of Quarantine between Two Waves

#### 3.4. Probably Improving the Effectiveness of Control Measures

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

SARS-CoV-2 | Severe acute respiratory syndrome coronavirus-2 |

COVID-19 | Coronavirus disease 2019 |

CCSA | Center for COVID-19 Situation Administration |

SEIR | Susceptible–Exposed–Infectious–Recover |

## Appendix A. Mathematical Model

## Appendix B. Interpretation of Components of the Reproduction Number

## Appendix C. Estimation of the Number of Primary Cases and Transmissibility in the Second Wave

**Figure A1.**Variation of the starting point for optimization algorithm on the absolute errors of predicted cumulative number of reported cases at the end of the first phase.

**Figure A2.**Errors were plotted with respect to the optimization results. The minimum point for asymptomatic case is one, whereas the minimum point for the symptomatic cases is twelve.

## References

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**Figure 2.**Fitting daily reported cases over a six-month period of the first wave. Small bars represent the data and solid lines present the models. The vertical dashed line indicates the boundary between phase I and II, while the peak indicates the beginning of phase III. Inset shows minor epidemics in phase I.

**Figure 3.**Curve fitting for daily case reports in the second wave. Small bars represent the data and solid lines present the models.

**Figure 4.**Dynamics of the quarantined people during the epidemic calculated by models.

**Left**and

**right**figures present the number of susceptible, exposed, and asymptomatic individuals that were quarantined in the first wave and in the second wave, respectively. Both figures are plotted with two different scales on the y-axis (colors), where the left (blue) represents the number of susceptible people in quarantine and the right (red) represents the number of infected people in quarantine.

Symbol | Definition | Value | References |
---|---|---|---|

${\beta}_{s}$ | symptomatic transmission rate | estimate | |

c | ratio of transmissibility between asymptomatic and symptomatic case | 0.418 | [10] |

$\sigma $ | outflow rate of exposed state | 1/5.2 day${}^{-1}$ | [7] |

$\alpha $ | asymptomatic ratio | 0.3 | [11] |

$\xi $ | effectiveness of quarantine | estimate | |

${\gamma}_{s}$ | recovery rate of symptomatic infection | 0.10526 day${}^{-1}$ | [7] |

${\gamma}_{a}$ | recovery rate of asymptomatic infection | 0.2 day${}^{-1}$ | [7] |

d | the rate at which an infection is detected during quarantine | estimate | |

q | quarantine rate | estimate | |

$\u03f5$ | outflow rate of quarantine | 1/14 day${}^{-1}$ | [7] |

**Table 2.**Estimation of parameters, the reproduction numbers, and percentage of reduction for the first wave.

Parameter | Phase I | Phase II | Phase III |
---|---|---|---|

${\beta}_{s}$ | 0.379 | 0.804 | 0.084 |

q | 0.015 | 0.001 | 0.015 |

$\xi $ | 0.011 | 0.001 | 0.514 |

d | 2.60$\times {10}^{-6}$ | 2.10 $\times {10}^{-5}$ | 7.20 $\times {10}^{-5}$ |

${R}_{a}$ | 0.7921 | 1.6804 | 0.1756 |

${R}_{s}$ | 3.6006 | 7.6382 | 0.7980 |

${R}_{c}$ | 2.7821 | 5.8553 | 0.5579 |

Percentage of reduction | |||

Susceptibility | 0.1909 | 0.0014 | 8.9207 |

Infectivity by latency | 0.0003 | 0.0002 | 0.0073 |

Infectivity by infectious | −12.3426 | −0.8937 | −2.5076 |

**Table 3.**Estimation of parameters, the reproduction numbers, and percentage of reduction for the second wave.

Parameter | Phase I | Phase II | Phase III |
---|---|---|---|

${\beta}_{s}$ | 1.25 | 0.2412 | 0.0943 |

q | 0.015 | 0.0151 | 0.0016 |

$\xi $ | 0.011 | 0.012 | 0.0122 |

d | 7.51$\times {10}^{-5}$ | 2.99$\times {10}^{-4}$ | 2.41$\times {10}^{-4}$ |

${R}_{a}$ | 2.6125 | 0.5041 | 0.1971 |

${R}_{s}$ | 11.8754 | 2.2915 | 0.8959 |

${R}_{c}$ | 9.1748 | 1.7696 | 0.6869 |

Percentage of reduction | |||

Susceptibility | 0.1909 | 0.2094 | 0.0267 |

Infectivity by latency | 0.0076 | 0.0303 | 0.0028 |

Infectivity by infectious | −12.3230 | −12.3193 | −1.3941 |

**Table 4.**Improvement of quarantine measure by increasing testing rate and the effectiveness of quarantine based on the parameters estimated in the second phase of the second wave.

Parameter | Scenario I | Scenario II | Scenario III |
---|---|---|---|

${\xi}^{*}$ | 0.6414 | 0.0120 | 0.0362 |

${d}^{*}$ | 0.0003 | 0.1262 | 0.1213 |

${R}_{c}$ | 1.5583 | 1.6702 | 1.6642 |

Reduced Susceptibility | 11.1924 | 0.2094 | 0.6318 |

Reduced Infectivity by latency (%) | 0.0303 | 4.6486 | 4.5825 |

Reduced Infectivity by infectious (%) | 0.0000 | 0.0000 | 0.0000 |

Control effort | 52.4471 | 421.6849 | 407.4834 |

Relative change in Rc | 0.1212 | 0.0582 | 0.0615 |

Efficiency index | 0.0023 | 0.0001 | 0.0002 |

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**MDPI and ACS Style**

Patanarapeelert, K.; Songprasert, W.; Patanarapeelert, N.
Modeling Dynamic Responses to COVID-19 Epidemics: A Case Study in Thailand. *Trop. Med. Infect. Dis.* **2022**, *7*, 303.
https://doi.org/10.3390/tropicalmed7100303

**AMA Style**

Patanarapeelert K, Songprasert W, Patanarapeelert N.
Modeling Dynamic Responses to COVID-19 Epidemics: A Case Study in Thailand. *Tropical Medicine and Infectious Disease*. 2022; 7(10):303.
https://doi.org/10.3390/tropicalmed7100303

**Chicago/Turabian Style**

Patanarapeelert, Klot, Wuttinant Songprasert, and Nichaphat Patanarapeelert.
2022. "Modeling Dynamic Responses to COVID-19 Epidemics: A Case Study in Thailand" *Tropical Medicine and Infectious Disease* 7, no. 10: 303.
https://doi.org/10.3390/tropicalmed7100303