# Targeted Vaccine Allocation Could Increase the COVID-19 Vaccine Benefits Amidst Its Lack of Availability: A Mathematical Modeling Study in Indonesia

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Context

#### 2.2. Model of Disease Transmission

#### 2.3. Time-Period Scenarios

#### 2.4. Targeted Allocation Scenarios

## 3. Results

#### 3.1. Time-Period Scenarios

#### 3.2. Targeted Allocation Scenarios

_{E}) values for 27 districts in West Java was 1.38, assuming no vaccination program with the current mobility restriction estimate. The mean R

_{E}values for five districts and eight districts with the highest COVID-19 cases were 1.26 and 1.25, respectively. With this R

_{E}, the model simulations showed that the number of infections would increase until September 2021, followed by a decreasing infection rate.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Symbols | Description | Unit | Values |
---|---|---|---|

$S\left(t\right)$ | # of the susceptible population at time-$t$ | person | Estimated |

$I\left(t\right)$ | # of the infected population at time-$t$ | person | Estimated |

$Q\left(t\right)$ | # of the quarantined population at time-$t$ | person | Estimated |

$R\left(t\right)$ | # of the immune population at time-$t$ | person | Estimated |

$D\left(t\right)$ | # of deaths at time-$t$ | person | Estimated |

$\beta $ | Transmission rate | 1/day | Estimated |

$\gamma $ | The recovery rate of COVID-19 | 1/day | Estimated |

$\delta $ | The death rate of COVID-19 | 1/day | Estimated |

$q$ | Quarantine rate ^{a} | 1/day | 0.4 |

$v\left(t\right)$ | Vaccination rate | 1/day | Estimated |

$\eta $ | Vaccine efficacy ^{b} | - | 0.8 |

$\zeta $ | Reinfection rate ^{c} | 1/day | 0.00035 |

$\mu $ | Natural birth rate ^{d} | 1/day | 0.00004 |

$\pi $ | Natural death rate | 1/day | 0.00004 |

^{a}The quarantine rate is a complicated parameter and challenging to be estimated. Thus, the quarantine rate value was assumed to follow the Nurani et al. (2020) study, $q=0.4$. This assumption roughly represents that only 40% of the infected people would be quarantined.

^{b}The vaccine was assumed to be 80% effective, leading to the assumption of $\eta =0.8$.

^{c}The reinfection rate was assumed as $\zeta =\frac{1}{8\cdot 12\cdot 30}=0.00035$ as the immune people can be reinfected after eight months (Reynold, S. 2021).

^{d}The natural recruitment/birth and death rates were assumed as $\pi =\mu =\frac{1}{365\cdot 70}=0.00004$1/day, based on the life expectancy in Indonesia, which is 70 years (Worldometer, 2020).

No. | City/District | # of Population | # of Total Infections | ${\mathit{R}}_{\mathit{E}}$ |
---|---|---|---|---|

1 | Bekasi City | 26,729 | 2,932,000 | 1.24 |

2 | Depok City | 25,430 | 1,869,998 | 0.72 |

3 | Bekasi District | 14,798 | 2,829,000 | 1.69 |

4 | Bandung City | 10,219 | 2,395,000 | 1.37 |

5 | Karawang District | 9192 | 2,288,000 | 1.17 |

6 | Bogor City | 8621 | 950,334 | 3.27 |

7 | Bandung District | 7671 | 3,418,000 | 0.96 |

8 | Bogor District | 6835 | 5,715,009 | 0.74 |

9 | Garut District | 6588 | 2,547,000 | 0.77 |

10 | Cirebon District | 4973 | 2,126,000 | 0.71 |

11 | Sukabumi District | 3838 | 2,434,000 | 1.06 |

12 | Cimahi City | 3652 | 561,386 | 0.95 |

13 | Kuningan District | 3231 | 1,055,000 | 0.19 |

14 | West Bandung District | 3138 | 1,624,000 | 0.46 |

15 | Tasikmalaya City | 3083 | 808,506 | 0.8 |

16 | Indramayu District | 2971 | 1,789,000 | 7.06 |

17 | Purwakarta District | 2854 | 916,912 | 1.83 |

18 | Sukabumi City | 2640 | 326,282 | 0.37 |

19 | Cirebon City | 2438 | 296,389 | 1.33 |

20 | Subang District | 1925 | 1,529,000 | 0.7 |

21 | Ciamis District | 1760 | 1,389,000 | 1.14 |

22 | Majalengka District | 1719 | 182,000 | 0.32 |

23 | Tasikmalaya District | 1649 | 1,736,000 | 4.94 |

24 | Cianjur District | 1631 | 2,829,000 | 0.76 |

25 | Sumedang District | 1535 | 1,176,000 | 1.29 |

26 | Banjar City | 530 | 182,819 | 0.91 |

27 | Pangandaran District | 510 | 422,586 | 1.34 |

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**Figure 1.**The SIQRD model applied in this study. S, susceptible; I, infected; Q, quarantined; R, recovery; D, death. Black arrows represent the logic flow of infection using SQRD model. Blue arrows represent natural recruitment ($\pi $). Red arrows represent the death rate ($\mu $). The detailed description of variables is shown in Appendix A.

**Figure 3.**The number of active cases with several scenarios of vaccine distribution given (

**a**) the severely lacking vaccines—97,080 dosages in the first four months, (

**b**) 300,000 dosages in one year, and (

**c**) the optimum available vaccines—33,000,000 dosages in one year.

**Table 1.**Estimation of required numbers of healthcare staff, vaccinators, and vaccine dosages per day for 6- and 12-month periods.

Variables | Availability | Targeted Time-Period | |||
---|---|---|---|---|---|

6 Months | 12 Months | ||||

# of targeted inoculation | 33,500,000 | ||||

# of vaccine dosage ^{a} | 67,000,000 | ||||

# of healthcare staff | 1094 | 29,000 | 14,500 | 14,500 | 7250 |

# of vaccinator | 365 | 9667 | 4833 | 4833 | 2417 |

Duration (minute/person) | 10 | 10 | 5 | 10 | 5 |

Inoculation per day ^{b} | 48 | 48 | 96 | 48 | 96 |

# of vaccine per day | 17,504 | 464,000 | 464,000 | 232,000 | 232,000 |

^{a}two-dosage per person;

^{b}estimated by 8-working hour per day.

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**MDPI and ACS Style**

Fuady, A.; Nuraini, N.; Sukandar, K.K.; Lestari, B.W.
Targeted Vaccine Allocation Could Increase the COVID-19 Vaccine Benefits Amidst Its Lack of Availability: A Mathematical Modeling Study in Indonesia. *Vaccines* **2021**, *9*, 462.
https://doi.org/10.3390/vaccines9050462

**AMA Style**

Fuady A, Nuraini N, Sukandar KK, Lestari BW.
Targeted Vaccine Allocation Could Increase the COVID-19 Vaccine Benefits Amidst Its Lack of Availability: A Mathematical Modeling Study in Indonesia. *Vaccines*. 2021; 9(5):462.
https://doi.org/10.3390/vaccines9050462

**Chicago/Turabian Style**

Fuady, Ahmad, Nuning Nuraini, Kamal K. Sukandar, and Bony W. Lestari.
2021. "Targeted Vaccine Allocation Could Increase the COVID-19 Vaccine Benefits Amidst Its Lack of Availability: A Mathematical Modeling Study in Indonesia" *Vaccines* 9, no. 5: 462.
https://doi.org/10.3390/vaccines9050462