# Risk Interactions of Coronavirus Infection across Age Groups after the Peak of COVID-19 Epidemic

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{j,t}) followed a generalized Poisson distribution to account for over-dispersion of case counts (i.e., observed variance is larger than expected variance) [25]. The model also included case counts from previous days (lags) across age groups as predictors to form a dynamic model (see Appendix A for details). Therefore, the current risk of infection in each age group was predicted not only by previous case counts in its own group but also by previous counts from other age groups.

_{j,t}could be viewed as a random effect to account for the correlation of daily counts between age groups. The b

_{j,t}was assumed a multivariate normal distribution.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

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

COVID-19 | coronavirus infectious disease 2019 |

GAM | generalized additive model |

VAR | vector autoregressive regression |

NB | negative binomial model |

REML | restricted maximum likelihood |

PMF | probability mass function |

## Appendix A

#### Appendix A.1. Obtained Smoothed Predicted Daily Cases with Generalized Additive Model (GAM)

_{ij}represents the observed case counts of day i and group j, and E(Y

_{ij}) is the expected (predicted) value. The variable time

_{i}represents day (1,…,I), b

_{k}( ) represents a basis function for the kth term to the smooth temporal trend, and β

_{j,k}s are regression coefficients for the smooth term k and group j. The restricted maximum likelihood (REML) approach was used in the parameter estimation. The R mgcv package was used [23], and smooth terms were fitted using a thin plate regression spline with 16 knots. The number of knots is typically determined empirically, commonly with 8–20 knots. A smaller number of knots yields a smoother curve while a larger number of knows results in a rougher curve. We observed that 16 knots are reasonable to capture the nonlinearity of the epidemic curve without introducing too many spikes.

#### Appendix A.2. Model Setups and Comparisons

**ξ**[43] as quoted in Hilbe JM. 2014 [27]. The PMF is

_{j,t}that can be viewed as a random effect. The b

_{j,t}was assumed a multivariate normal distribution.

## Appendix B. Additional Table

**Table A1.**Risk interactions in coronavirus infection across age groups based on negative binomial models, COVID-19, South Korea.

Model Outcomes | Predictors | Lags of Predictors | ||||
---|---|---|---|---|---|---|

Lag 1 | Lag 2 | Lag 3 | Lag 4 | Lag 5 | ||

Aged 60 or above | ||||||

60 or above | 1.93 (1.14–3.19) * | 1.09 (0.66–1.80) | 1.02 (0.61–1.82) | 0.99 (0.57–1.67) | 1.11 (0.68–1.87) | |

40–59 | 1.03 (0.53–2.02) | 1.66 (0.83–3.01) | 0.69 (0.36–1.46) | 1.26 (0.72–2.25) | 1.00 (0.57–1.71) | |

20–39 | 0.94 (0.54–1.69) | 1.30 (0.66–2.42) | 1.42 (0.73–2.68) | 0.50 (0.25–1.01) | 1.21 (0.63–2.37) | |

0–19 | 1.10 (0.72–1.78) | 1.29 (0.79–1.98) | 0.85 (0.51–1.35) | 0.62 (0.40–0.98) # | 1.52 (0.88–2.55) | |

Aged 40–59 | ||||||

60 or above | 1.64 (1.12–2.41) * | 0.75 (0.50–1.09) | 0.97 (0.67–1.49) | 1.01 (0.69–1.53) | 1.02 (0.69–1.53) | |

40–59 | 1.15 (0.68–1.96) | 1.55 (0.92–2.46) | 1.14 (0.64–2.24) | 0.90 (0.54–1.39) | 0.95 (0.63–1.47) | |

20–39 | 1.10 (0.59–1.73) | 1.13 (0.70–1.81) | 1.54 (0.95–2.47) | 0.63 (0.37–1.27) | 0.89 (0.44–1.56) | |

0–19 | 1.09 (0.77–1.53) | 1.23 (0.87–1.78) | 1.16 (0.82–1.64) | 1.16 (0.82–1.60) | 1.15 (0.79–1.68) | |

Aged 20–39 | ||||||

60 or above | 1.00 (0.71–1.44) | 0.93 (0.65–1.39) | 1.00 (0.69–1.48) | 1.58 (1.10–2.26) * | 0.90 (0.64–1.29) | |

40–59 | 1.12 (0.69–1.86) | 1.09 (0.67–1.72) | 0.96 (0.58–1.53) | 0.97 (0.65–1.44) | 1.08 (0.72–1.61) | |

20–39 | 1.63 (1.09–2.48) * | 1.04 (0.66–1.64) | 1.35 (0.86–2.11) | 0.99 (0.58–1.56) | 0.96 (0.60–1.56) | |

0–19 | 1.04 (0.74–1.44) | 0.95 (0.69–1.29) | 0.89 (0.63–1.23) | 0.95 (0.67–1.40) | 0.73 (0.51–1.04) | |

Aged 0–19 | ||||||

60 or above | 1.77 (1.17–2.76) * | 1.35 (0.82–2.14) | 1.00 (0.62–1.61) | 0.81 (0.50–1.32) | 1.52 (0.97–2.44) | |

40–59 | 0.76 (0.39–1.42) | 0.71 (0.39–1.27) | 0.86 (0.43–1.64) | 0.94 (0.53–1.66) | 0.96 (0.58–1.60) | |

20–39 | 1.53 (0.87–2.72) | 1.46 (0.82–2.69) | 1.05 (0.57–1.92) | 0.78 (0.41–1.41) | 0.90 (0.49–1.74) | |

0–19 | 0.94 (0.63–1.44) | 0.83 (0.57–1.25) | 0.88 (0.58–1.33) | 0.92 (0.59–1.44) | 1.52 (0.95–2.42) |

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**Figure 1.**Observed daily new cases of COVID-19 and predicted epidemic curve from the generalized additive model, South Korea, from 10 March to 30 April 2020, by age groups.

**Table 1.**Risk ratios in the coronavirus infection across age groups during the COVID-19 pandemic, South Korea, 10 March to 30 April 2020.

Model Outcomes | Predictors | Lags of Predictors | ||||
---|---|---|---|---|---|---|

Lag 1 | Lag 2 | Lag 3 | Lag 4 | Lag 5 | ||

Aged 60 or above | ||||||

60 or above | 2.09 (1.28–3.17) * | 1.21 (0.78–1.80) | 0.90 (0.60–1.39) | 1.03 (0.60–1.67) | 0.96 (0.63–1.53) | |

40–59 | 0.95 (0.49–1.84) | 1.81 (0.98–3.29) | 0.59 (0.30–1.18) | 1.37 (0.85–2.23) | 1.03 (0.61–1.70) | |

20–39 | 0.89 (0.53–1.46) | 2.02 (1.12–3.47) * | 1.28 (0.72–2.31) | 0.41 (0.22–0.78) # | 1.11 (0.58–2.22) | |

0–19 | 0.90 (0.61–1.43) | 1.36 (0.95–1.95) | 0.82 (0.57–1.19) | 0.61 (0.44–0.85) # | 1.64 (1.03–2.58) * | |

Aged 40–59 | ||||||

60 or above | 1.66 (1.19–2.29) * | 0.79 (0.55–1.12) | 0.89 (0.64–1.23) | 0.98 (0.70–1.40) | 1.02 (0.71–1.40) | |

40–59 | 1.01 (0.62–1.63) | 1.76 (1.16–2.66) * | 1.23 (0.76–1.96) | 0.89 (0.62–1.29) | 0.88 (0.62–1.28) | |

20–39 | 1.13 (0.75–1.73) | 1.12 (0.76–1.67) | 1.59 (1.03–2.50) * | 0.60 (0.37–0.95) | 0.88 (0.53–1.48) | |

0–19 | 1.04 (0.79–1.37) | 1.28 (0.97–1.68) | 1.17 (0.88–1.57) | 1.14 (0.88–1.49) | 1.17 (0.84–1.62) | |

Aged 20–39 | ||||||

60 or above | 0.95 (0.69–1.29) | 0.89 (0.65–1.23) | 1.01 (0.72–1.39) | 1.54 (1.11–2.12) * | 0.97 (0.69–1.31) | |

40–59 | 1.17 (0.73–1.88) | 1.18 (0.78–1.78) | 0.98 (0.60–1.52) | 0.90 (0.64–1.26) | 1.04 (0.75–1.47) | |

20–39 | 1.56 (1.05–2.36) * | 1.02 (0.68–1.55) | 1.45 (0.96–2.24) | 1.06 (0.68–1.64) | 0.85 (0.55–1.32) | |

0–19 | 1.04 (0.79–1.37) | 0.96 (0.75–1.27) | 0.88 (0.66–1.20) | 0.97 (0.75–1.26) | 0.74 (0.54–1.00) | |

Aged 0–19 | ||||||

60 or above | 1.78 (1.23–2.61) * | 1.34 (0.86–2.06) | 0.99 (0.67–1.51) | 0.82 (0.52–1.25) | 1.55 (1.02–2.30) * | |

40–59 | 0.76 (0.41–1.38) | 0.71 (0.42–1.18) | 0.85 (0.47–1.56) | 0.91 (0.55–1.57) | 0.97 (0.62–1.54) | |

20–39 | 1.51 (0.92–2.55) | 1.50 (0.85–2.57) | 1.04 (0.61–1.80) | 0.78 (0.44–1.38) | 0.91 (0.51–1.62) | |

0–19 | 0.93 (0.64–1.36) | 0.85 (0.60–1.21) | 0.85 (0.60–1.27) | 0.92 (0.62–1.38) | 1.51 (0.99–2.31) |

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Yu, X. Risk Interactions of Coronavirus Infection across Age Groups after the Peak of COVID-19 Epidemic. *Int. J. Environ. Res. Public Health* **2020**, *17*, 5246.
https://doi.org/10.3390/ijerph17145246

**AMA Style**

Yu X. Risk Interactions of Coronavirus Infection across Age Groups after the Peak of COVID-19 Epidemic. *International Journal of Environmental Research and Public Health*. 2020; 17(14):5246.
https://doi.org/10.3390/ijerph17145246

**Chicago/Turabian Style**

Yu, Xinhua. 2020. "Risk Interactions of Coronavirus Infection across Age Groups after the Peak of COVID-19 Epidemic" *International Journal of Environmental Research and Public Health* 17, no. 14: 5246.
https://doi.org/10.3390/ijerph17145246