# Effect of a Mismatched Vaccine against the Outbreak of a Novel FMD Strain in a Pig Population

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## Abstract

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## Simple Summary

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Epidemiological Context

#### 2.2. Data

#### 2.3. Modelling Approach

#### 2.3.1. Brief Model Description

#### 2.3.2. Model Selection and Parameter Estimation

#### 2.4. Validation and Sensitivity Analysis

## 3. Results

#### 3.1. Model Selection

#### 3.2. Parameter Values

#### 3.3. Validation

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

_{1}; Figure S3. Illustration of FMD compartment in $\mathcal{M}$

_{2}; Figure S4. Illustration of FMD compartment in $\mathcal{M}$

_{3}; Figure S5. Illustration of FMD compartment in $\mathcal{M}$

_{4}; Figure S6. Illustration of FMD compartment in $\mathcal{M}$

_{5}; Figure S7. The probability density of the posterior distribution (pink) of within-pen transmission rate (β). The blue area illustrates the prior distribution; Figure S8. The probability density of the posterior distribution of the relative decrease of $\beta $ for between-pen transmission ($\omega $) and relative decrease in $\beta $ for immunised pigs ($\phi $); Figure S9. The frequency of the posterior distribution (pink) of the latent period (${\gamma}_{1}$; left) and sub-clinically infectious period before developing clinical signs (${\gamma}_{2}$; right). The blue area illustrates the prior distributions; Figure S10. The probability density of the posterior distribution (pink) of the proportion of immunised pigs for each barn ($\rho $). The blue area illustrates the prior distribution; Figure S11. The frequency of the posterior distribution of the day of novel FMD virus introduction for each barn (τ); Table S1. The posterior distribution of all the estimated parameters in M_3; Table S2. Result of partial rank correlation coefficients for the summary statistics and accumulative number of pigs with clinical FMD in M_3. Please note that the presented result below was based on the analysis on barn 1, however, the result was similar across other barns; Table S3. The posterior distribution of all the estimated parameters in M_3 when informed priors (Original), and a uniform prior of β, γ_1, γ_2 were used.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A timeline of foot and mouth disease outbreak response at a pig farm in South Korea (2014).

**Figure 2.**The number of simulation models remained over 12 sequences of the approximate Bayesian computation process.

**Figure 3.**The median (black solid line) and 95% prediction interval (grey area) of the simulated number of pigs removed due to the development of clinical signs for each barn. The red dashed line indicates the observed number of removed pigs.

Incorporated Features | ${\mathcal{M}}_{1}$ | ${\mathcal{M}}_{2}$ | ${\mathcal{M}}_{3}$ | ${\mathcal{M}}_{4}$ | ${\mathcal{M}}_{5}$ |
---|---|---|---|---|---|

Transmission dynamics | |||||

Immunised pigs less likely develop clinical signs | - | Yes | - | Yes | - |

Immunised pigs less likely transmit disease | - | - | Yes | Yes | - |

Immunised pigs exempted from infection | - | - | - | - | Yes |

Parameters | |||||

Within-pen transmission rate (β) | Yes | Yes | Yes | Yes | Yes |

Relative decrease in β for between-pen transmission (ω) | Yes | Yes | Yes | Yes | Yes |

Latent period (${\gamma}_{1}$) | Yes | Yes | Yes | Yes | Yes |

Sub-clinically infectious period before developing clinical signs (${\gamma}_{2}$) | Yes | Yes | Yes | Yes | Yes |

Sub-clinically infectious period for immunised pigs before recovery (${\gamma}_{3}$) | - | Yes | - | Yes | - |

Relative decrease in $\beta $ for immunised pigs ($\phi $) | - | - | Yes | Yes | - |

Proportion of immunised but sub-clinically infectious pigs to recover (α) | - | Yes | - | Yes | - |

Proportion of immunised pigs in barn i (${\rho}_{i}$) | - | Yes | Yes | Yes | Yes |

Proportion of immunised pigs in barn i (${\rho}_{i}$) | Yes | Yes | Yes | Yes | Yes |

**Table 2.**The description and prior distribution of parameters examined for five models in this study.

Parameters | Prior | References |
---|---|---|

Within-pen transmission rate ($\beta $) | N (0.6, 0.1^{2}) per day 0 ≤ $\beta $ ≤ 1.5 | Calculated from [20,21] |

Relative decrease in $\beta $ for between-pen transmission ($\omega $) | U (0.0, 0.5) | [22] |

Latent period $({\gamma}_{1}$) * | Binomial (97, 0.02) day | [17] |

Sub-clinically infectious period before developing clinical signs $({\gamma}_{2}$) * | Binomial (66, 0.02) day | [17] |

Sub-clinically infectious period for immunised pigs before recovery $({\gamma}_{3}$) | U (3, 7) day | [10] |

Relative decrease in $\beta $ for immunised pigs ($\phi $) | U (0, 1) | No info. |

Proportion of immunised but sub-clinically infectious pigs to recover (α) | U (0, 1) | No info. |

Proportion of immunised pigs $({\rho}_{i}$) ^{†} | Beta (a, b) ^{‡} | Assumed |

Day of novel FMD virus introduction $({\tau}_{i}$) ^{†} | U (−8, 11) | Assumed |

^{†}The value varied between nursery pig barns.

^{‡}The values a and b were the number of samples positive and negative to FMD SP antibody ELISA in a barn, respectively.

Parameter | Median (95% Credible Interval) |
---|---|

Within-pen transmission rate ($\beta $) | 0.269 (0.066, 0.524) per day |

Relative decrease in $\beta $ for between-pen transmission ($\omega $) | 0.004 (0.000, 0.019) |

Latent period (${\gamma}_{1}$) | 2 (1, 2) days |

Sub-clinically infectious period before developing clinical signs (${\gamma}_{2}$) | 2 (1, 3) days |

Relative decrease in $\beta $ for immunised pigs ($\phi $) | 0.401 (0.031, 0.941) |

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**MDPI and ACS Style**

Han, J.-H.; Yoo, D.-S.; Lee, C.-M.
Effect of a Mismatched Vaccine against the Outbreak of a Novel FMD Strain in a Pig Population. *Animals* **2023**, *13*, 3082.
https://doi.org/10.3390/ani13193082

**AMA Style**

Han J-H, Yoo D-S, Lee C-M.
Effect of a Mismatched Vaccine against the Outbreak of a Novel FMD Strain in a Pig Population. *Animals*. 2023; 13(19):3082.
https://doi.org/10.3390/ani13193082

**Chicago/Turabian Style**

Han, Jun-Hee, Dae-Sung Yoo, and Chang-Min Lee.
2023. "Effect of a Mismatched Vaccine against the Outbreak of a Novel FMD Strain in a Pig Population" *Animals* 13, no. 19: 3082.
https://doi.org/10.3390/ani13193082