# Optimising Vaccine Dose in Inoculation against SARS-CoV-2, a Multi-Factor Optimisation Modelling Study to Maximise Vaccine Safety and Efficacy

^{1}

^{2}

^{*}

## Abstract

**:**

^{10}, 1.0 × 10

^{11}and 1.5 × 10

^{11}viral particles. We estimated the optimal dose for three objectives, finding: (A) the minimum dose that may induce herd immunity, (B) the dose that maximises immunogenicity and safety and (C) the dose that maximises immunogenicity and safety whilst minimising cost. Results suggest optimal dose [95% confidence interval] in viral particles per person was (A) 1.3 × 10

^{11}[0.8–7.9 × 10

^{11}], (B) 1.5 × 10

^{11}[0.3–5.0 × 10

^{11}] and (C) 1.1 × 10

^{11}[0.2–1.5 × 10

^{11}]. Optimal dose exceeded 5.0 × 10

^{10}viral particles only if the cost of delivery exceeded £0.65 or cost per 10

^{11}viral particles was less than £6.23. Optimal dose may differ depending on the objectives of developers and policy-makers, but further research is required to improve the accuracy of optimal-dose estimates.

## 1. Introduction

- (1)
- Using published data, calibrate mathematical models to the relationship between dose and seroconversion, safety and cost of a single inoculation.
- (2)
- Identify the minimum dose that is predicted to theoretically induce herd immunity.
- (3)
- Identify the dose that maximises immunogenicity and safety.
- (4)
- Identify the dose that maximises immunogenicity and safety whilst minimising cost.

## 2. Materials and Methods

#### 2.1. Data

^{10}, 1 × 10

^{11}and 1.5 × 10

^{11}Viral Particles (VP)) and their responses were measured at day 28.

#### 2.2. Objective 1. Using Published Data, Calibrate Mathematical Models to the Relationship between Dose and Seroconversion, Safety and Cost of a Single Inoculation

#### 2.2.1. Dose-Seroconversion Relationship

^{15}VP, to ensure previous adenoviral dosing ranges are explored [21] and state the dose that would induce 50% and 90% seroconversion.

#### 2.2.2. Dose-Safety Relationship

^{15}VP.

#### 2.2.3. Dose-Cost Relationship

^{15}VP were calculated using this formula and parameters in Table 2.

_{Delivery}) was calculated as £5.24, and the cost per 10

^{11}VP (Cost

_{Dose-dependent}) of adenovirus was £0.76 ( Table 2).

#### 2.3. Objective 2. Identify the Minimum Dose that Is Predicted to Theoretically Induce Herd Immunity

#### 2.4. Objective 3. Identify the Dose that Maximises Immunogenicity and Safety

_{s}, and the probability of grade 3+ adverse events, P

_{t}, were mutually independent, the probability of a safe seroconversion was equal to

_{Costless}, to be maximised was

#### 2.5. Objective 4. Identify the Dose that Maximises Immunogenicity and Safety Whilst Minimising Cost

_{Costless}(Dose) (Equation (10)) is precisely the numerator of the U

_{Costed}(Dose) (Equation (11)). A 95% confidence interval for optimal dose was again determined using a parametric bootstrapping approach (Supplementary S2.3.2).

#### Threshold Analysis

^{11}, 1 × 10

^{11}and 5 × 10

^{10}VP as the thresholds of interest.

_{Delivery}, we fixed all other parameters at the calibrated/literature derived value and allowed Cost

_{Delivery}to vary. The region over which we varied Cost

_{Delivery}was +/− 3 orders of magnitudes of the value (£5.24) we used in the main model. In other words, we considered the effect of Cost

_{Delivery}being 1000 times larger or smaller (from £0.0052 per vaccination to £5240 per vaccination) on the prediction of optimal dose. This range was considered certainly to almost contain a reasonable estimate of the dose-independent costs of a single vaccination. This procedure was then repeated for Cost per 10

^{11}viral particles, ranging from £0.00076 to £760 per 10

^{11}VP.

_{Costed}(Dose) were above and below the stated thresholds (5 × 10

^{11}, 1 × 10

^{11}, 5 × 10

^{10}VP).

## 3. Results

#### 3.1. Objective 1. Using Published Data, Calibrate Mathematical Models to the Relationship between Dose and Seroconversion, Safety, and Cost of a Single Inoculation

#### 3.1.1. Does-Seroconversion Relationship

^{10}, 1.0 × 10

^{11}and 1.5 × 10

^{11}induced 50%, 50%, 75% seroconversion on day 28, respectively. The calibrated saturating dose-seroconversion curve is displayed in Figure 2a. 50% and 95% seroconversion were predicted at a dose of 5.9 × 10

^{10}and 2.4 × 10

^{12}VP, respectively. Population demographics including age, gender and pre-existing adenovirus neutralising antibody titre were described [15] (Supplementary S3).

#### 3.1.2. Dose-Safety Relationship

^{10}, 1 × 10

^{11}and 1.5 × 10

^{11}VP induced 86%, 83% and 75% any grade adverse events and 6%, 6% and 17% grade 3+ adverse events, respectively. The calibrated saturating dose-adverse event curves are displayed in Figure 2b,c. The two thresholds of safety we previously chose were 17% and 30% grade 3+ adverse reaction proportion. The calibrated dose-adverse curve predicted that a rate of adverse events greater than 17% occurs for doses in excess of 1.58 × 10

^{11}VP and exceeds 30% at 2.45 × 10

^{11}VP.

#### 3.2. Objective 2. Identify the Minimum Dose that Is Predicted to Theoretically Induce Herd Immunity

^{11}VP would be required to reach this threshold, assuming the entire UK population was vaccinated. The 95% confidence interval for optimal dose was (8.0 × 10

^{10}, 7.9 × 10

^{11}) (Supplementary S2.3.1). Using the dose-safety model, this dose was predicted to cause 13.5% of vaccinated individuals to have a grade 3+ adverse event.

#### 3.3. Objective 3. Identify the Dose that Maximises Immunogenicity and Safety

^{11}VP (Figure 3b, red diamond). It was predicted that dosing at this magnitude would lead to a seroconversion rate of 67.6%, and cause 15.8% of vaccinated individuals to have a grade 3+ adverse event (83.0% any grade adverse events).

^{10}, 5.0 × 10

^{11}) (Supplementary S2.3.2).

#### 3.4. Objective 4. Identify the Dose that Maximises Immunogenicity and Safety Whilst Minimising Cost

^{11}VP. It was predicted that dosing at this magnitude would lead to a seroconversion rate of 62.20%, cost £6.07 per dose, and cause 10.32% of vaccinated individuals to have a grade 3+ adverse event (82.2% any grade adverse events). The 1 × 10

^{11}VP dose had the highest utility of the doses tested in the study, and both of the 5 × 10

^{10}and 1.5 × 10

^{11}VP doses appeared to be near-optimal. This analysis, therefore, suggested that if the cost was included in the utility function then a marginally reduced dose was found optimal relative to the costless utility function. The predicted cost is within the expected range [$5–$37] for a single SARS-CoV-2 vaccine dose [34].

^{10}, 1.5 × 10

^{11}) (Supplementary S2.3.3).

#### Threshold Analysis

_{Delivery}, we found that the predicted optimal dose was independent of the parameter value for large values (Figure 4). We found that the optimal dose was in excess of 1 × 10

^{11}and 5 × 10

^{10}VP for Cost

_{Delivery}values in excess of £3.79 and £0.65, respectively (hence optimal dose was only less than 5 × 10

^{10}VP for Cost

_{Delivery}less than £0.65). These values were respectively 0.7 and 0.1 times the value that was used in the main analysis. We find that the optimal dose was not in excess of 5 × 10

^{11}VP for any Cost

_{Delivery}values.

^{11}viral particles

_{,}we found that the optimal dose was independent of the parameter value for large values (Figure 5). We found that the optimal dose was in excess of 1 × 10

^{11}and 5 × 10

^{10}VP for Cost per 10

^{11}viral particles values in less than £1.06 and £6.23, respectively (hence optimal dose was only less than 5 × 10

^{10}VP for Cost per 10

^{11}viral particles greater than £6.24). These values were respectively 1.3 and 8.2 times the value that was used in the main analysis. We find that the optimal dose was not in excess of 5 × 10

^{11}VP for any Cost per 10

^{11}viral particles values.

^{11}viral particles was less than 0.2 times Cost

_{Delivery}, then the predicted optimal dose was between 1.0 × 10

^{11}and 1.5 × 10

^{11}VP.

## 4. Discussion

^{11}VP of this vaccine was found to be optimal with respect to seroconversion, safety and cost. However, an increased dose of 1.3 × 10

^{11}VP or 1.5 × 10

^{11}VP could be justified depending on the objectives of developers and policymakers. These methods highlight how quantitative analysis can be used to ensure that vaccines are dosed optimally, and could aid in accelerating vaccine development.

^{11}VP would likely induce grade 3+ adverse events in greater than 30% of individuals vaccinated, which is a typical threshold for safety in clinical trials. Previous work has found that human-hosted adenoviral vector vaccine trials typically do not dose in excess of 2 × 10

^{11}[21]. This suggests that adenoviral vaccine trials are being dosed at magnitudes that ensure that grade 3+ adverse reactions remain below the 30% threshold. However, for this vaccine, the available data was not sufficient to determine whether the dose-seroconversion curve shape was better described by a peaking or saturating curve shape. This implies that we cannot be confident that the percentage of individuals that seroconvert would continue to increase as dose increases beyond those empirically tested. This is likely the result of using too few doses or not dosing at a sufficiently large dose to observe peaking or saturating dose-response behaviour. We have previously shown that curve shape could not be determined for 75% of adenoviral dose-response data [8]. However, in this case, it is possible that dosing at a large enough magnitude to determine curve shape could cause an unacceptable number of grade 3+ adverse events.

^{11}VP of the vaccine would be the dose that optimises safety, cost, and protective immunity, if vial size restricts precision on which doses can be administered then, of the previously empirically tested doses, both the 1.0 × 10

^{11}and 1.5 × 10

^{11}doses could be reasonable. We also predicted that inducing complete herd immunity in an otherwise entirely susceptible population may be feasible with this vaccine given 100% uptake, but we predict that approximately 13.5% of vaccinated individuals would experience grade 3+ adverse events and that this would require a dose of at least 1.3 × 10

^{11}VP. As the dose optimising the costless utility function was in excess of this threshold, but not the dose optimising the utility function with cost, this work implies that to fully protect the UK population with this vaccine would require accepting some level of cost inefficiency.

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Sharma, A.; Tiwari, S.; Deb, M.K.; Marty, J.L. Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2): A Global Pandemic and Treatment Strategies. Int. J. Antimicrob. Agents
**2020**, 56, 106054. [Google Scholar] [CrossRef] [PubMed] - Nicola, M.; Alsafi, Z.; Sohrabi, C.; Kerwan, A.; Al-Jabir, A.; Iosifidis, C.; Agha, M.; Agha, R. The Socio-Economic Implications of the Coronavirus Pandemic (COVID-19): A Review. Int. J. Surg.
**2020**, 78, 185–193. [Google Scholar] [CrossRef] [PubMed] - Greenwood, B. The Contribution of Vaccination to Global Health: Past, Present and Future. Philos. Trans. R. Soc. B Biol. Sci.
**2014**, 369, 20130433. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kaur, S.P.; Gupta, V. COVID-19 Vaccine: A Comprehensive Status Report. Virus Res.
**2020**, 288, 198114. [Google Scholar] [CrossRef] - Rhodes, S.J.; Knight, G.M.; Kirschner, D.E.; White, R.G.; Evans, T.G. Dose Finding for New Vaccines: The Role for Immunostimulation/Immunodynamic Modelling. J. Theor. Biol.
**2019**, 465, 51–55. [Google Scholar] [CrossRef] - Handel, A.; Li, Y.; McKay, B.; Pawelek, K.A.; Zarnitsyna, V.; Antia, R. Exploring the Impact of Inoculum Dose on Host Immunity and Morbidity to Inform Model-Based Vaccine Design. PLoS Comput. Biol.
**2018**, 14, e1006505. [Google Scholar] [CrossRef][Green Version] - Rhodes, S.J.; Zelmer, A.; Knight, G.M.; Prabowo, S.A.; Stockdale, L.; Evans, T.G.; Lindenstrøm, T.; White, R.G.; Fletcher, H. The TB Vaccine H56+IC31 Dose-Response Curve Is Peaked Not Saturating: Data Generation for New Mathematical Modelling Methods to Inform Vaccine Dose Decisions. Vaccine
**2016**, 34, 6285–6291. [Google Scholar] [CrossRef][Green Version] - Benest, J.; Rhodes, S.; Afrough, S.; Evans, T.; White, R. Response Type and Host Species May Be Sufficient to Predict Dose-Response Curve Shape for Adenoviral Vector Vaccines. Vaccines
**2020**, 8, 155. [Google Scholar] [CrossRef][Green Version] - Frazão, T.D.C.; Camilo, D.G.G.; Cabral, E.L.S.; Souza, R.P. Multicriteria Decision Analysis (MCDA) in Health Care: A Systematic Review of the Main Characteristics and Methodological Steps. BMC Med. Inform. Decis. Mak.
**2018**, 18, 90. [Google Scholar] [CrossRef] - World Health Organisation. DRAFT Landscape of COVID-19 Candidate Vaccines. Available online: https://www.who.int/publications/m/item/draft-landscape-of-covid-19-candidate-vaccines (accessed on 9 September 2020).
- Izda, V.; Jeffries, M.A.; Sawalha, A.H. COVID-19: A Review of Therapeutic Strategies and Vaccine Candidates. Clin. Immunol.
**2020**, 222, 108634. [Google Scholar] [CrossRef] - Oxford University Breakthrough on Global COVID-19 Vaccine | University of Oxford. Available online: https://www.ox.ac.uk/news/2020-11-23-oxford-university-breakthrough-global-covid-19-vaccine (accessed on 30 November 2020).
- Mahase, E. COVID-19: Vaccine Candidate May Be More than 90% Effective, Interim Results Indicate. BMJ
**2020**, 371, m4347. [Google Scholar] [CrossRef] [PubMed] - Mullard, A. COVID-19 Vaccine Development Pipeline Gears Up. Lancet
**2020**, 395, 1751–1752. [Google Scholar] [CrossRef] - Zhu, F.-C.; Li, Y.-H.; Guan, X.-H.; Hou, L.-H.; Wang, W.-J.; Li, J.-X.; Wu, S.-P.; Wang, B.-S.; Wang, Z.; Wang, L.; et al. Safety, Tolerability, and Immunogenicity of a Recombinant Adenovirus Type-5 Vectored COVID-19 Vaccine: A Dose-Escalation, Open-Label, Non-Randomised, First-in-Human Trial. Lancet
**2020**, 395, 1845–1854. [Google Scholar] [CrossRef] - Manners, C.; Larios Bautista, E.; Sidoti, H.; Lopez, O.J. Protective Adaptive Immunity Against Severe Acute Respiratory Syndrome Coronaviruses 2 (SARS-CoV-2) and Implications for Vaccines. Cureus
**2020**, 12, e8399. [Google Scholar] [CrossRef] - US Food and Drug Administration. Guidance for Industry: Toxicity Grading Scale for Healthy Adult and Adolescent Volunteers Enrolled in Preventive Vaccine Clinical Trials; US Department of Health and Human Services, Food and Drug Administration: Silver Spring, MD, USA, 2007.
- Sibille, M.; Patat, A.; Caplain, H.; Donazzolo, Y. A Safety Grading Scale to Support Dose Escalation and Define Stopping Rules for Healthy Subject First-Entry-into-Man Studies. Br. J. Clin. Pharmacol.
**2010**, 70, 736–748. [Google Scholar] [CrossRef][Green Version] - Grothendieck, G. Nls2: Non-Linear Regression with Brute Force, R package version 0.2; 2013. Available online: https://CRAN.R-project.org/package=nls2 (accessed on 5 January 2019).
- R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2018. [Google Scholar]
- Afrough, S.; Rhodes, S.; Evans, T.; White, R.; Benest, J. Immunologic Dose-Response to Adenovirus-Vectored Vaccines in Animals and Humans: A Systematic Review of Dose-Response Studies of Replication Incompetent Adenoviral Vaccine Vectors When Given via an Intramuscular or Subcutaneous Route. Vaccines
**2020**, 8, 131. [Google Scholar] [CrossRef][Green Version] - Wang, C.; Rosner, G.L.; Roden, R.B.S. A Bayesian Design for Phase I Cancer Therapeutic Vaccine Trials. Stat. Med.
**2019**, 38, 1170–1189. [Google Scholar] [CrossRef] - Wages, N.A.; Slingluff, C.L. Flexible Phase I–II Design for Partially Ordered Regimens with Application to Therapeutic Cancer Vaccines. Stat. Biosci.
**2020**, 12, 104–123. [Google Scholar] [CrossRef] - Le Tourneau, C.; Lee, J.J.; Siu, L.L. Dose Escalation Methods in Phase I Cancer Clinical Trials. JNCI J. Natl. Cancer Inst.
**2009**, 101, 708–720. [Google Scholar] [CrossRef][Green Version] - Safety Information by Vaccine | CDC. Available online: https://www.cdc.gov/vaccinesafety/vaccines/index.html (accessed on 15 October 2020).
- Average for the Year to 31 March 2020—GOV.UK. Available online: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/885947/Spot.csv/preview (accessed on 16 October 2020).
- Inflation Calculator. Available online: http://www.bankofengland.co.uk/monetary-policy/inflation/inflation-calculator (accessed on 16 October 2020).
- Agenda for Change—Pay Rates. Available online: https://www.healthcareers.nhs.uk/working-health/working-nhs/nhs-pay-and-benefits/agenda-change-pay-rates (accessed on 16 October 2020).
- Annual Leave and Holiday | Advice Guides | Royal College of Nursing. Available online: /get-help/rcn-advice/annual-leave-and-holiday-pay (accessed on 16 October 2020).
- Vaccinating Adults: A Step-by-Step Guide; Centers for Disease Control and Prevention: St. Paul, MI, USA, 2017.
- Pereira, C.C.; Bishai, D. Vaccine Presentation in the USA: Economics of Prefilled Syringes versus Multidose Vials for Influenza Vaccination. Expert Rev. Vaccines
**2010**, 9, 1343–1349. [Google Scholar] [CrossRef] - GE Healthcare. Scalable Process for Adenovirus Production 2018. Available online: https://cdn.cytivalifesciences.com/dmm3bwsv3/AssetStream.aspx?mediaformatid=10061&destinationid=10016&assetid=27018 (accessed on 15 October 2020).
- Kwok, K.O.; Lai, F.; Wei, W.I.; Wong, S.Y.S.; Tang, J.W.T. Herd Immunity—Estimating the Level Required to Halt the COVID-19 Epidemics in Affected Countries. J. Infect.
**2020**, 80, e32–e33. [Google Scholar] [CrossRef] [PubMed] - Raja, A.T.; Alshamsan, A.; Al-jedai, A. Current COVID-19 Vaccine Candidates: Implications in the Saudi Population. Saudi Pharm. J. SPJ
**2020**, 28, 1743–1748. [Google Scholar] [CrossRef] [PubMed] - Rhodes, S.J.; Guedj, J.; Fletcher, H.A.; Lindenstrøm, T.; Scriba, T.J.; Evans, T.G.; Knight, G.M.; White, R.G. Using Vaccine Immunostimulation/Immunodynamic Modelling Methods to Inform Vaccine Dose Decision-Making. NPJ Vaccines
**2018**, 3, 36. [Google Scholar] [CrossRef] [PubMed] - Newall, A.T.; Chaiyakunapruk, N.; Lambach, P.; Hutubessy, R.C.W. WHO Guide on the Economic Evaluation of Influenza Vaccination. Influenza Other Respir. Viruses
**2018**, 12, 211–219. [Google Scholar] [CrossRef][Green Version] - World Health Organistaion. Guidelines for Estimating Costs of Introducing New Vaccines into the National Immunization System; World Health Organisation: Geneva, Switzerland, 2002. [Google Scholar]
- Murray, C.J. Quantifying the Burden of Disease: The Technical Basis for Disability-Adjusted Life Years. Bull. World Health Organ.
**1994**, 72, 429–445. [Google Scholar] - Mercado, N.B.; Zahn, R.; Wegmann, F.; Loos, C.; Chandrashekar, A.; Yu, J.; Liu, J.; Peter, L.; McMahan, K.; Tostanoski, L.H.; et al. Single-Shot Ad26 Vaccine Protects against SARS-CoV-2 in Rhesus Macaques. Nature
**2020**, 586, 583–588. [Google Scholar] [CrossRef] - Oland, G.A.; Ovsyannikova, I.G.; Kennedy, R.B. SARS-CoV-2 Immunity: Review and Applications to Phase 3 Vaccine Candidates. Lancet
**2020**, 396, 1595–1606. [Google Scholar] [CrossRef] - Deng, W.; Bao, L.; Liu, J.; Xiao, C.; Liu, J.; Xue, J.; Lv, Q.; Qi, F.; Gao, H.; Yu, P.; et al. Primary Exposure to SARS-CoV-2 Protects against Reinfection in Rhesus Macaques. Science
**2020**, 369, 818–823. [Google Scholar] [CrossRef]

**Figure 1.**Venn diagram representation of possible outcomes of inoculation, where the left set includes individuals that experience grade 3+ adverse events and the right set includes individuals that experience seroconversion. We aimed to maximise the number of individuals that experience seroconversion and do not experience grade 3+ adverse events, represented in the green segment of the diagram. Black diamonds represent individuals that experience both outcomes, black pentagons represent individuals that experience grade 3+ adverse events with no seroconversion, and black triangles represent individuals that experience neither outcome.

**Figure 2.**The three curves displaying the relationship between dose and (

**a**) percentage of vaccinated individuals predicted to seroconvert, (

**b**) percentage of vaccinated individuals predicted to experience any grade adverse events and (

**c**) percentage of vaccinated individuals predicted to experience grade 3+ adverse events. The curves are sigmoid curves calibrated to data. Black dots represent the data the curves were calibrated to. In (

**a**) the solid and dashed red lines show respectively the doses for which 50% and 90% of individuals are predicted to seroconvert. In (

**c**) the solid and dashed red lines show respectively the doses for which 17% and 30% of individuals are predicted to experience grade 3+ adverse events. We note that the percentage of individuals experiencing any grade adverse events in (

**b**) qualitatively decreased with increasing dose, whereas the model curve was increasing. This decreasing trend could be explained by the expected stochasticity in the data, hence the sigmoid model did not seem unreasonable (Supplementary S4).

**Figure 3.**Displays of the predicted utility of doses between 10

^{0}and 10

^{15}VP. (

**a**) shows dose-seroconversion, with the horizontal red line indicating the 65.5% seroconversion threshold required for herd immunity. (

**b**) shows the relationship between dose and the costless utility function and (

**c**) shows the relationship between dose and the costed utility function. The black dots represent Table 1. 3 × 10

^{11}, (

**b**) 1.5 × 10

^{11}VP and (

**c**) 1.1 × 10

^{11}VP.

**Figure 4.**Optimal predicted dose for +/− 3 orders of magnitude around Cost

_{Delivery}. (

**a**) has Cost

_{Delivery}at a log10 scale and (

**b**) scaled normally. The black line represents the optimal dose, and the red lines indicate the threshold values of Cost

_{Delivery}for which optimal dose is 1 × 10

^{11}and 5 × 10

^{10}VP.

**Figure 5.**Optimal predicted dose (log10 scale) for +/− 3 orders of magnitude (log10 scale) around Cost per 10

^{11}viral particles. Table 1. viral particles at a log10 scale and the right is scaled normally. The black line represents the optimal dose, and the red lines indicate the threshold values of Cost per 10

^{11}viral particles for which the optimal dose was 1 × 10

^{11}and 5 × 10

^{10}VP.

Adverse Reaction Grade | General Descriptions |
---|---|

1 | Mild. Does not interfere with normal activity |

2 | Moderate. Interference with normal activity. Little or no treatment required. |

3 | Severe. Prevents normal activity. Requires treatment. |

4 | Serious or Potentially Life-Threatening. Generally requires hospitalisation and stopping of any clinical trial where this grade is observed. |

Name of Parameter | Value | Unit | Description | References |
---|---|---|---|---|

$Cos{t}_{Personnel}\left(\pounds pervaccination\right)=4.398707$ | ||||

$AnnualWage$ | 30,615 | $\pounds peryears$ | GBP per NHS Band 5 Income per annum (2020/21) | [28] |

$AnnualHours$ | 1740 | $hoursperyears$ | Work hours per year for average UK nurse | [29] |

$Timeper$ $vaccination$ | 0.25 | $hoursper$ $vaccination$ | Recommended hours per vaccination appointment | [30] |

$Cos{t}_{Storage}\left(\pounds pervaccination\right)=0.014$ | ||||

$Cos{t}_{Storagepermonth}$ | 0.014 | $\pounds permonth$ | GBP per vaccination per month’s storage. Converted and adjusted for inflation from $0.014 2010 USD. | [31] |

$Cos{t}_{materials}\left(\pounds pervaccination\right)=0.83$ | ||||

$Cos{t}_{Gloves}$ | 0.08 | $\pounds pervaccination$ | GBP of gloves for one vaccination. Converted and adjusted for inflation from $0.08 USD. | [31] |

$Cos{t}_{Alcohol}$ | 0.03 | $\pounds pervaccination$ | GBP of sterilising alcohol for one vaccination. Converted and adjusted for inflation from $0.03 2010 USD. | [31] |

$Cos{t}_{PFS}$ | 0.40 | $\pounds pervaccination$ | GBP of the pre-filled syringe for one vaccination. Converted and adjusted for inflation from $0.39 2010 USD. | [31] |

$Cos{t}_{Needles}$ | 0.32 | $\pounds pervaccination$ | GBP of needle for one vaccination. Converted and adjusted for inflation from $0.31 2010 USD. | [31] |

$Costperviralparticle\left(\pounds perVP\right)=7.6\times {10}^{-12}$ | ||||

$Cos{t}_{AdenoviralBatch}$ | 342,000 | $\pounds perBatch$ | GBP per single-use reference process batch (converted from 450,000 US Dollars) | [32] |

$Adenoviral$ $Concentration$ | 9 × 10^{13} | $VPperL$ | Viral Particles per litre in single-use reference process batch | [32] |

$Batchvolume$ | 500 | $LperBatch$ | Volume of Adenovirus produced in single-use reference process batch | [32] |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Benest, J.; Rhodes, S.; Quaife, M.; Evans, T.G.; White, R.G. Optimising Vaccine Dose in Inoculation against SARS-CoV-2, a Multi-Factor Optimisation Modelling Study to Maximise Vaccine Safety and Efficacy. *Vaccines* **2021**, *9*, 78.
https://doi.org/10.3390/vaccines9020078

**AMA Style**

Benest J, Rhodes S, Quaife M, Evans TG, White RG. Optimising Vaccine Dose in Inoculation against SARS-CoV-2, a Multi-Factor Optimisation Modelling Study to Maximise Vaccine Safety and Efficacy. *Vaccines*. 2021; 9(2):78.
https://doi.org/10.3390/vaccines9020078

**Chicago/Turabian Style**

Benest, John, Sophie Rhodes, Matthew Quaife, Thomas G. Evans, and Richard G. White. 2021. "Optimising Vaccine Dose in Inoculation against SARS-CoV-2, a Multi-Factor Optimisation Modelling Study to Maximise Vaccine Safety and Efficacy" *Vaccines* 9, no. 2: 78.
https://doi.org/10.3390/vaccines9020078