# Vaccination Criteria Based on Factors Influencing COVID-19 Diffusion and Mortality

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Influence of Age

^{−3}). The relative weights of the three peaks changed, in favor of the oldest ages. We also found statistically significant differences when comparing the positive patients (Figure 2b) to the dead ones (Figure 2c) (KS-test: p-value < 10

^{−3}).

#### 3.2. Influence of Gender

_{SP}. This can be very useful when adopting informative models to describe the evolution of the COVID-19 epidemic, such as the compartment ones. In fact, this kind of models contains one parameter for the transition rate between the compartment of infected patients developing symptoms, and the one of COVID-19 diagnosis. The reciprocal of the transition rate is proportional to t

_{SP}; therefore, its distribution can be used in a Bayesian framework as a prior density [13]. The influence of the gender on this distribution was investigated. Based on the empirical distribution, G-KDE was performed to fit the data. The means obtained for the females are shorter than for males. More interestingly, the shape of the two empirical distributions looks different to each other. This difference is statistically significant, in fact the KS-test resulted in a p-value < 10

^{−3}. A further investigation is needed to study the influence of social and biological factors on these results.

^{−3}). The same pattern is observed when considering the event of death of positive COVID-19 patients in Table S2 of the Supplementary Materials. In this case, the overall probability is 9.4%, increasing to 11% for males and decreasing to 7.9% for females. Additionally, here, the difference is significant (Chi-squared gives a p-value < 10

^{−3}).

#### 3.3. Influence of Patient Care Location

^{−3}).

^{−3}).

^{−3}).

^{−3}from the Chi-squared test.

#### 3.4. Influence of Comorbidities

^{−3}). The increase can be even better appreciated by looking at Figure 5a.

^{−3}).

^{−3}).

## 4. Impact of the Results on Public Health

^{2}with nearly 5 million inhabitants.

## 5. Mathematical Implementation of Vaccination

## 6. Conclusions

## Supplementary Materials

^{−3}), Table S2: 2 × 2 contingency table relative to the influence of gender on the probability of death for patients diagnosed with COVID-19 virus. The data show that the latter probability is significantly increased for male (Chi-Square test: p-value < 10

^{−3}), Table S3: 2 × 2 contingency table relative to the influence on the probability of death of environment where patients are during their disease (COVID-19 virus). The table here concerns not being admitted in ICU and of age over 60. The probability of death is significantly increased for patient being in hospital/medical structure, with respect of being in elderly house (Chi-Square test: p-value < 10

^{−3}); Table S4: 2 × 2 contingency table relative to the influence on the probability of death of environment where patients are during their disease (COVID-19 virus). The table here concerns not being admitted in ICU and of age under 60. The probability of death is significantly increased for patient being in hospital/medical structure, with respect of being at home (Chi-Square test: p-value < 10

^{−3}); Table S5: 2 × 2 contingency table relative to the influence on the probability of death of environment where patients are during their disease (COVID-19 virus). The probability of death is significantly increased by a factor 4–5 for patients being admitted in ICU (Chi-Square test: p-value < 10

^{−3}); Table S6: 2 × 2 contingency table relative to the influence on the probability of death of environment where patients are during their disease (COVID-19 virus). The table here concerns patients of age under 60. The probability of death is significantly increased by a factor ≈ 60 for patients being admitted in ICU (Chi-Square test: p-value < 10

^{−3}); Table S7: 2 × 2 contingency table relative to the influence on the probability of death of environment where patients are during their disease (COVID-19 virus). The table here concerns patients of age over 60. The probability of death is significantly increased by a factor 2–3 for patients being admitted in ICU (Chi-Square test: p-value < 10

^{−3}); Table S8: Contingency table relative to the influence of the number of comorbidities on the probability of death for all COVID-19 diagnosed patients. The increase of probability with the number of comorbidities, as seen in the last column, is statistically significant (Chi-Square test: p-value < 10

^{−3}); Table S9: Contingency table relative to the influence on the probability of death of the number of comorbidities, for COVID-19 diagnosed patients. The table here concerns being admitted in ICU. The increase of probability with the number of comorbidities, as seen in the last column, is statistically non-significant, as obtained by the Chi-Square test; Table S10: Contingency table relative to the influence on the probability of death of the number of comorbidities, for COVID-19 diagnosed patients. The table here concerns not being admitted in ICU. The increase of probability with the number of comorbidities, as seen in the last column, is statistically significant (Chi-Square test: p-value < 10

^{−3}); Table S11: 2 × 2 contingency table relative to the influence on the probability of being admitted in ICU. The table here concerns patients of age under 60, with no comorbidity. The probability of death is significantly increased for patients admitted in ICU (Chi-Square test: p-value < 10

^{−3}).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Age distributions of COVID-19 patients relative to the Veneto region health system (Italy), in the period 28 February–15 May 2020. (

**a**–

**c**) respectively refer to: whole tested patients, positive, and dead ones. The number of patients is also reported. The age range was discretized in equally spaced subintervals of 1 year. Means and standard deviations obtained are respectively: 53.4 and 20.8 for all the patients, 60.3 and 22.0 for the positive ones, and 83.6 and 10.1 for the positive, dead patients.

**Figure 3.**Distribution of dead patients conditioned to the test positivity. To obtain the figure, we took for each age the ratio between the kernel density estimation in Figure 2c by that in Figure 2b, and then we normalized it. The age range was discretized in equally spaced subintervals of 1 year.

**Figure 4.**Time between first symptoms and first positive test of COVID-19 patients in Veneto, in the time interval 24 February–15 May 2020. The temporal range was discretized in equally spaced subintervals of 1 day. (

**a**–

**c**) refers to the positive tested whole population, females and males, respectively. The number of patients is also reported. Means and standard deviations obtained are respectively: 7.89 and 7.28 for all the patients, 7.84 and 7.5 for the females, and 7.93 and 7.06 for the males.

**Figure 5.**(

**a**): Probability of death as a function of the number of comorbidities (see also Table S8 of the Supplementary Materials). The continuous line represents the best fit given by the extended logistic function. (

**b**): the same as (a) but relative to being admitted or not to ICU (see Tables S9 and S10 of the Supplementary Materials). For the patients admitted to ICU, the best fit is given by a horizontal straight line. Instead, the best fit for the death probability of patients not being admitted to ICU is obtained with an extended logistic function (continuous curve in the panel).

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**MDPI and ACS Style**

Spassiani, I.; Gubian, L.; Palù, G.; Sebastiani, G.
Vaccination Criteria Based on Factors Influencing COVID-19 Diffusion and Mortality. *Vaccines* **2020**, *8*, 766.
https://doi.org/10.3390/vaccines8040766

**AMA Style**

Spassiani I, Gubian L, Palù G, Sebastiani G.
Vaccination Criteria Based on Factors Influencing COVID-19 Diffusion and Mortality. *Vaccines*. 2020; 8(4):766.
https://doi.org/10.3390/vaccines8040766

**Chicago/Turabian Style**

Spassiani, Ilaria, Lorenzo Gubian, Giorgio Palù, and Giovanni Sebastiani.
2020. "Vaccination Criteria Based on Factors Influencing COVID-19 Diffusion and Mortality" *Vaccines* 8, no. 4: 766.
https://doi.org/10.3390/vaccines8040766