# Epidemiological Impact of SARS-CoV-2 Vaccination: Mathematical Modeling Analyses

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## Abstract

**:**

_{S}) ≥70% can eliminate the infection. A vaccine with VE

_{S}<70% may still control the infection if it reduces infectiousness or infection duration among those vaccinated who acquire the infection, if it is supplemented with <20% reduction in contact rate, or if it is complemented with herd-immunity. At VE

_{S}of 50%, the number of vaccinated persons needed to avert one infection is 2.4, and the number is 25.5 to avert one severe disease case, 33.2 to avert one critical disease case, and 65.1 to avert one death. The probability of a major outbreak is zero at VE

_{S}≥70% regardless of the number of virus introductions. However, an increase in social contact rate among those vaccinated (behavior compensation) can undermine vaccine impact. In addition to the reduction in infection acquisition, developers should assess the natural history and disease progression outcomes when evaluating vaccine impact.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Model

#### 2.2. Model Parameterization and Fitting

#### 2.3. Product Characteristics of Candidate Vaccines

#### 2.4. Measures of Vaccine Impact

#### 2.5. Vaccination Program Scenarios

#### 2.6. Additional Analyses

#### 2.7. Uncertainty Analysis

## 3. Results

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

_{0}, Text S1D: Probability of a major outbreak. Figure S1: Schematic diagram describing the basic structure of the SARS-CoV-2 vaccine model, Figure S2: Impact of SARS-CoV-2 vaccination on the cumulative number of (A) new infections, (B) new severe disease cases, (C) new critical disease cases, and (D) new deaths in the scenario assuming vaccine scale-up to 80% coverage before epidemic onset, Figure S3: Role of SARS-CoV-2 vaccination in reducing the cumulative number of (A) new infections, (B) new severe disease cases, (C) new critical disease cases, and (D) new deaths in the scenario assuming vaccine scale-up to 80% coverage before epidemic onset, Figure S4: Impact of SARS-CoV-2 vaccination on the cumulative number of (A) new infections, (B) new severe disease cases, (C) new critical disease cases, and (D) new deaths in the scenario assuming vaccine introduction during the exponential growth phase of the epidemic, with scale-up to 80% coverage within one month, Figure S5: Role of SARS-CoV-2 vaccination in reducing the cumulative number of (A) new infections, (B) new severe disease cases, (C) new critical disease cases, and (D) new deaths in the scenario assuming vaccine introduction during the exponential growth phase of the epidemic, with scale-up to 80% coverage within one month, Figure S6: Temporal evolution of SARS-CoV-2 vaccine effectiveness in the scenario assuming vaccine scale-up to 80% coverage before epidemic onset, Figure S7: Temporal evolution of SARS-CoV-2 vaccine effectiveness in the scenario assuming vaccine introduction during the exponential growth phase of the epidemic, with scale-up to 80% coverage within one month, Figure S8: Temporal evolution of effectiveness of age-group prioritization using a SARS-CoV-2 vaccine with VE

_{S}of 50%, Figure S9: Impact of a social-distancing intervention reducing the contact rate in the population on the cumulative number of new SARS-CoV-2 infections, when introduced to supplement the impact of a vaccine that has 50% efficacy in reducing susceptibility, VE

_{S}, Figure S10: Probability of occurrence of a major outbreak following vaccination, Figure S11: Sensitivity analyses assessing vaccine effectiveness (number of vaccinated persons needed to avert one infection) at (A) varying levels of vaccine coverage and (B) high levels of assortativeness in age group mixing, Figure S12: Uncertainty analysis, Figure S13: Vaccine effectiveness of age-group prioritization and the reproduction number R

_{0}, Figure S14: Impact of varying levels of vaccine efficacy in reducing susceptibility, VE

_{S}, on the cumulative number of new SARS-CoV-2 infections when the reproduction number R0 is 3, Table S1: Definitions of population variables and symbols used in the model, Table S2: Model assumptions in terms of parameter values.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Data and Materials Availability

## One Sentence Summary

_{S}) ≥70% at ≥80% coverage could be sufficient to control the pandemic with high cost-effectiveness.

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**Figure 1.**Impact of SARS-CoV-2 vaccination on the number of (

**A**) new infections, (

**B**) new severe disease cases, (

**C**) new critical disease cases, and (

**D**) new deaths in the scenario assuming vaccine scale-up to 80% coverage before epidemic onset. The duration of vaccine protection is 10 years. Impact was assessed at $V{E}_{S}=50\%$, $V{E}_{I}=50\%$, $V{E}_{{P}_{1}}=50\%$, $V{E}_{{P}_{2}}=50\%$, $V{E}_{S}=V{E}_{I}=V{E}_{{P}_{1}}=50\%$.

**Figure 2.**Impact of SARS-CoV-2 vaccination on the number of (

**A**) new infections, (

**B**) new severe disease cases, (

**C**) new critical disease cases, and (

**D**) new deaths in the scenario assuming vaccine introduction during the exponential growth phase of the epidemic, with scale-up to 80% coverage within one month. Duration of vaccine protection is 10 years. Impact was assessed at $V{E}_{S}=50\%$, $V{E}_{I}=50\%$, $V{E}_{{P}_{1}}=50\%$, $V{E}_{{P}_{2}}=50\%$, $V{E}_{S}=V{E}_{I}=V{E}_{{P}_{1}}=50\%$.

**Figure 3.**SARS-CoV-2 vaccine effectiveness. Number of vaccinated persons needed to avert (

**A**) one infection, (

**B**) one severe disease case, (

**C**) one critical disease case, and (

**D**) one death, by the end of the epidemic cycle, that is, after the epidemic has reached its peak and declined to a negligible level. The scenario assumes vaccine scale-up to 80% coverage before epidemic onset. Duration of vaccine protection is 10 years. Impact was assessed at $V{E}_{S}=50\%$, $V{E}_{I}=50\%$, $V{E}_{{P}_{1}}=50\%$, $V{E}_{{P}_{2}}=50\%$, $V{E}_{S}=V{E}_{I}=V{E}_{{P}_{1}}=50\%$. Panel A does not include the result for $V{E}_{{P}_{2}}=50\%$, as this efficacy has no impact on the number of infections—it affects only severe and critical disease and death.

**Figure 4.**Effectiveness of age-group prioritization using a SARS-CoV-2 vaccine with VE

_{s}of 50%. Number of vaccinated persons needed to avert (

**A**) one infection, (

**B**) one severe disease case, (

**C**) one critical disease case, and (

**D**) one death by prioritizing different age groups for vaccination. Scenario assumes vaccine scale-up to 80% coverage before epidemic onset and duration of vaccine protection of 10 years. Effectiveness is assessed at the end of the epidemic cycle, that is, after the epidemic has reached its peak and declined to a negligible level.

**Figure 5.**Impact of varying levels of vaccine efficacy in reducing susceptibility (VE

_{s}) on (

**A**) cumulative number of new SARS-CoV-2 infections (final epidemic size) and (

**B**) number of vaccinated persons needed to avert one SARS-CoV-2 infection. Scenario assumes vaccine scale-up to 80% coverage before epidemic onset. Duration of vaccine protection is 10 years. Measures are assessed at the end of the epidemic cycle, that is, after the epidemic has reached its peak and declined to a negligible level.

**Figure 6.**Impact of vaccination with reduced adherence to social distancing for those vaccinated. Figure shows the impact of varying levels of behavior compensation post-vaccination on the vaccine-induced reduction in the cumulative number of new SARS-CoV-2 infections by the end of the epidemic cycle. Scenario assumes vaccine scale-up to 80% coverage before epidemic onset, VE

_{s}is 50%, and duration of vaccine protection is 10 years.

**Figure 7.**Probability of occurrence of a major outbreak following vaccination. Probability of occurrence of a major outbreak upon virus introduction at varying levels of (

**A**) $V{E}_{S}$, (

**B**) $V{E}_{I}$, (

**C**) $V{E}_{{P}_{1}}$, and (

**D**) $V{E}_{S}=V{E}_{I}=V{E}_{{P}_{1}}$. Scenario assumes vaccine scale-up to 80% coverage before epidemic onset. Duration of vaccine protection is 10 years. The figure does not include the result for $V{E}_{{P}_{2}}$, as this efficacy has no impact on the probability of occurrence of a major outbreak. The analysis and derivation for the probability of occurrence of a major outbreak can be found in Text S1D of the Supplementary Material.

Vaccine Characteristic | Definition | Description |
---|---|---|

$V{E}_{S}$ | Vaccine efficacy in reducing susceptibility | Proportional reduction in the susceptibility to infection acquisition among those vaccinated compared to those unvaccinated |

$V{E}_{I}$ | Vaccine efficacy in reducing infectiousness | Proportional reduction in infectiousness (lower viral load due to vaccine-primed immune response) among those who are vaccinated but acquire the infection compared to those unvaccinated |

$V{E}_{{P}_{1}}$ | Vaccine efficacy in reducing the duration of infection | Proportional reduction in the duration of mild infection (faster infection clearance due to vaccine-primed immune response) among those who are vaccinated but still acquire the infection compared to those unvaccinated |

$V{E}_{{P}_{2}}$ | Vaccine efficacy in reducing the fraction of individuals with severe or critical infection | Proportional reduction in the fraction of individuals with severe or critical infection (lower probability of developing severe or critical infection due to vaccine-primed immune response) among those who are vaccinated but still acquire the infection compared to those unvaccinated |

$D$ | Duration of vaccine protection | Duration of protection that the vaccine will elicit |

$r$ | Behavior compensation post-vaccination | Proportional increase in social contact rate (reduced social distancing) among those who are vaccinated compared to those unvaccinated |

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**MDPI and ACS Style**

Makhoul, M.; Ayoub, H.H.; Chemaitelly, H.; Seedat, S.; Mumtaz, G.R.; Al-Omari, S.; Abu-Raddad, L.J.
Epidemiological Impact of SARS-CoV-2 Vaccination: Mathematical Modeling Analyses. *Vaccines* **2020**, *8*, 668.
https://doi.org/10.3390/vaccines8040668

**AMA Style**

Makhoul M, Ayoub HH, Chemaitelly H, Seedat S, Mumtaz GR, Al-Omari S, Abu-Raddad LJ.
Epidemiological Impact of SARS-CoV-2 Vaccination: Mathematical Modeling Analyses. *Vaccines*. 2020; 8(4):668.
https://doi.org/10.3390/vaccines8040668

**Chicago/Turabian Style**

Makhoul, Monia, Houssein H. Ayoub, Hiam Chemaitelly, Shaheen Seedat, Ghina R. Mumtaz, Sarah Al-Omari, and Laith J. Abu-Raddad.
2020. "Epidemiological Impact of SARS-CoV-2 Vaccination: Mathematical Modeling Analyses" *Vaccines* 8, no. 4: 668.
https://doi.org/10.3390/vaccines8040668