# Is COVID-19 Herd Immunity Influenced by Population Densities of Cities?

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## Abstract

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## 1. Introduction

- (1)
- Many studies stress the lack of knowledge and the limited understanding of the factors influencing herd immunity (e.g., [5,6,7,8,9,10,11]). Neagu (2020) [9], for example, states that: “information on the long-term immune response against SARS-CoV-2 is yet scarce.” (Abstract). Avoidance of further spread of the pandemic and investigation of the efficiency of COVID-19 vaccination might prove to be especially important from a public policy perspective.
- (2)
- We attempt to address an unexplored question, as to whether instead of a country level, COVID-19 herd immunity can evolve at a city level.
- (3)
- We propose and apply a new methodology to estimate herd immunity in cities, which makes use of population density. Based on the median population density in the sample, we classify cities according to sparsely vs. densely populated municipalities, and examine the impact of population density on the formation of herd immunity.

## 2. Materials and Methods

#### 2.1. Descriptive Statistics

^{2}with two degrees of freedom of 47.72, compared to the 1% critical Chi

^{2}, with two degrees of freedom of 9.21). Consequently, the right-tailed distribution is validated statistically. The standard deviation is 15.435 and the 99% confidence interval is (6.286, 14.802). Finally, the minimum number of cases per 10,000 persons is zero (no active cases) and the maximum is 85.4 active cases per 10,000 persons.

^{2}with two degrees of freedom of 55.96, compared to the 1% critical Chi

^{2}with two degrees of freedom of 9.21), this conclusion is validated statistically. The standard deviation is 15.435 and the 99% confidence interval is (2598, 4826). Finally, the minimum population density is 67 $\frac{persons}{sq.km}$ (Mizpe Ramon in the Negev desert) and the maximum is 26,512 $\frac{persons}{sq.km}$ (the ultra-Orthodox city of Bnei Berak).

^{2}with two degrees of freedom of 13.12, compared to the 1% critical Chi

^{2}with two degrees of freedom of 9.21). Consequently, the left-tailed distribution is validated statistically. The standard deviation is 15.41 and the 99% confidence interval is (53.12, 61.62). Finally, the minimum percent of vaccinated persons is 18.22 and the maximum is 80.21.

#### 2.2. Methods

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Active COVID-19 cases vs. percent of second vaccination (Cities = 91). Notes: The figure refers to 91 Israeli cities and towns (covering above 5,928,628 persons consisting of above $64.3\%=\frac{\mathrm{5,928,628}}{\mathrm{9,217,000}}$ of the entire Israeli population), where the number of active COVID-19 cases per 10,000 persons ≥0. The median density is 2388 $\frac{persons}{sq.km}$. The graph is based on the outcomes reported in column (1) of Table 2.

**Figure 2.**Stratification based on cities. Notes: The graph is based on the outcomes reported in column (1) of Table 2. The 95% confidence intervals are calculated based on the delta method. This explains the negative lower bound of the 95% confidence interval.

(a) Description of Variables | ||||||

Variable | Description | |||||

$Cases\_per\_{\mathrm{10,000}}_{t}$ | COVID-19 active cases divided by the population of the city and multiplied by 10,000. | |||||

$Population\_densit{y}_{t}$ | Population density measured as $\frac{persons}{sq.km}$. | |||||

$Median\_densit{y}_{t}$ | 1 = Above or equal to the median population density; 0 = otherwise. | |||||

$Second\_Vaccinatio{n}_{t}$ | Percent of vaccinated persons in the city multiplied by 100. | |||||

(b) Active Cases ≥ 0. | ||||||

Variable | Obs | Mean | Median | Std. Dev. | Min | Max |

$Cases\_per\_{\mathrm{10,000}}_{t}$ | 91 | 10.54396 | 5.0 | 15.43522 | 0 | 85.4 |

$Population\_densit{y}_{t}$ | 91 | 3711.9780 | 2388 | 4037.0320 | 67 | 26,512 |

$Median\_densit{y}_{t}$ | 91 | 0.4945 | 0.0000 | 0.5027 | 0 | 1 |

$Second\_Vaccinatio{n}_{t}$ | 91 | 57.3662 | 61.76 | 15.4098 | 18.22 | 80.21 |

(1) | |
---|---|

Variables | $Cases\_per\_{\mathrm{10,000}}_{t}$ |

Constant | 37.79 *** |

(8.96 × 10^{−9}) | |

$Median\_densit{y}_{t}$ | −20.17 ** |

(0.0171) | |

$Second\_Vaccinatio{n}_{t}$ | −0.444 *** |

(1.90 × 10^{−5}) | |

$Median\_densit{y}_{t}\times Second\_Vaccinatio{n}_{t}$ | 0.288 ** |

(0.0364) | |

Observations | 91 |

R-squared | 0.219 |

Disease | Transmission | HIT | Reference Number |
---|---|---|---|

Measles | Aerosol | 92–94% | [23,24] |

Chickenpox (varicella) | Aerosol | 90–92% | [25] |

Mumps | Respiratory droplets | 90–92% | [26] |

Rubella | Respiratory droplets | 83–86% | [27,28,29] |

Polio | Fecal–oral route | 80–86% | [27,28,29] |

Pertussis | Respiratory droplets | 82% | [30,31] |

COVID-19 (Delta variant) | Respiratory droplets and aerosol | 80% | [22,32,33] |

Smallpox | Respiratory droplets | 71–83% | [34,35] |

COVID-19 (Alpha variant) | Respiratory droplets and aerosol | 75–80% | [36] |

HIV/AIDS | Body fluids | 50–80% | [31] |

COVID-19 (ancestral strain) | Respiratory droplets and aerosol [37] | 65% (58–71%) | [38] |

SARS | Respiratory droplets | 50–75% | [39] |

Diphtheria | Saliva | 62% (41–77%) | [40] |

Ebola (2014 outbreak) | Body fluids | 44% (31–44%) | [41,42] |

Influenza (2009 pandemic strain) | Respiratory droplets | 37% (25–51%) | [43] |

Influenza (seasonal strains) | Respiratory droplets | 23% (17–29%) | [44] |

Andes hantavirus | Respiratory droplets and body fluids | 16% (0–36%) | [37] |

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**MDPI and ACS Style**

Arbel, Y.; Arbel, Y.; Kerner, A.; Kerner, M.
Is COVID-19 Herd Immunity Influenced by Population Densities of Cities? *Sustainability* **2022**, *14*, 10286.
https://doi.org/10.3390/su141610286

**AMA Style**

Arbel Y, Arbel Y, Kerner A, Kerner M.
Is COVID-19 Herd Immunity Influenced by Population Densities of Cities? *Sustainability*. 2022; 14(16):10286.
https://doi.org/10.3390/su141610286

**Chicago/Turabian Style**

Arbel, Yuval, Yifat Arbel, Amichai Kerner, and Miryam Kerner.
2022. "Is COVID-19 Herd Immunity Influenced by Population Densities of Cities?" *Sustainability* 14, no. 16: 10286.
https://doi.org/10.3390/su141610286