# Could a New COVID-19 Mutant Strain Undermine Vaccination Efforts? A Mathematical Modelling Approach for Estimating the Spread of B.1.1.7 Using Ontario, Canada, as a Case Study

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

- Reporting is relatively consistent.
- The total population in a region is constant.
- All severe cases are reported.

## 3. Results

#### 3.1. Scenario-Based Extrapolation from First Known Cases of B.1.1.7 Variant in Ontario

#### No Vaccination, No Relaxation

#### 3.2. Extension to Vaccination and Relaxation

#### 3.2.1. Vaccination without Relaxation

#### 3.2.2. Vaccination and Relaxation

#### 3.2.3. Fitting an Unknown Mutant

#### 3.2.4. Christmas as an Anomaly

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Figure validating model fitting and scenario building. The model is fit to data from 12 December 2020 to 11 January 2021. We augment the data with data from 12 January 2021 until 7 May 2021. We see that the hybrid data and scenario approach properly detected peaks out to four months in advance. Between January and April 2021, Ontario went through multiple phases of lockdown and relaxation of non-pharmaceutical interventions, which the model does not capture (as they were unknowable at the time). The peak detection makes the model a valuable tool for long-term planning. Thee pink line is the continuation of the fit, the blue line is the new wildtype trajectory when the mutant scenario is introduced, and the dashed line is the mutant strain. The black line is the combination of wildtype and mutant. The black line is the total new cases per day, and this is what should be compared to the data as the new cases per day is reported as a total. The shaded region is the $95\%$ confidence interval from the fit.

**Figure A2.**Figure 6a augmented with data up to 7 May 2021. The model is still only fit to data up to 11 January 2021. We see that the line fit (cumulative known wildtype cases) is still relatively close 4 months out. As before, green represents the cumulative known cases, purple is the total incidence, red is active mild cases, and blue is active severe cases. Dark lines are mutant compartments, and light colours are wildtype. Dashed lines are the extended scenario, and solid lines the original fit without a separation of wildtype and mutant. The light green line is what is being fit by the model. We see some anomalous behaviours in the extension due to the period of lockdown–relaxation cycles in Ontario. While the log scale obfuscates some detail, the consequence of these lockdown–relaxation cycles not being present in thee model causes an over-estimation on the order of ${10}^{4}$ cases.

**Figure A3.**The model projections from the first wave of COVID-19 in Ontario. The red dots are data not used in the model fitting. The green line is the cumulative known cases, purple is the total incidence, red is active mild cases, and blue is active severe cases. In the right panel (

**b**), we see the new cases per day. We see that the model performs well for at least two weeks when non-pharmaceutical interventions remain relatively constant. The shaded region is the $95\%$ confidence interval from the fit. The $95\%$ confidence interval was able to detect the presence of a second wave in the fall.

## References

- Heesterbeek, H.; Anderson, R.M.; Andreasen, V.; Bansal, S.; De Angelis, D.; Dye, C.; Eames, K.T.; Edmunds, W.J.; Frost, S.D.; Funk, S.; et al. Modeling infectious disease dynamics in the complex landscape of global health. Science
**2015**, 347, aaa4339. [Google Scholar] [CrossRef] [PubMed][Green Version] - Stern, A.; Andino, R. Viral evolution: It is all about mutations. In Viral Pathogenesis; Elsevier: Amsterdam, The Netherlands, 2016; pp. 233–240. [Google Scholar]
- Bonhoeffer, S.; Nowak, M.A. Intra-host versus inter-host selection: Viral strategies of immune function impairment. Proc. Natl. Acad. Sci. USA
**1994**, 91, 8062–8066. [Google Scholar] [CrossRef][Green Version] - Martins, N.E.; Faria, V.G.; Teixeira, L.; Magalhães, S.; Sucena, É. Host adaptation is contingent upon the infection route taken by pathogens. PLoS Pathog.
**2013**, 9, e1003601. [Google Scholar] [CrossRef] [PubMed][Green Version] - Duffy, S. Why are rna virus mutation rates so damn high? PLoS Biol.
**2018**, 16, e3000003. [Google Scholar] [CrossRef] [PubMed][Green Version] - Binder, S.; Levitt, A.M.; Sacks, J.J.; Hughes, J.M. Emerging infectious diseases: Public health issues for the 21st century. Science
**1999**, 284, 1311–1313. [Google Scholar] [CrossRef] - Burch, C.L.; Chao, L. Evolvability of an rna virus is determined by its mutational neighbourhood. Nature
**2000**, 406, 625–628. [Google Scholar] [CrossRef] - Arenas, M.; Araujo, N.M.; Branco, C.; Castelhano, N.; Castro-Nallar, E.; Pérez-Losada, M. Mutation and recombination in pathogen evolution: Relevance, methods and controversies. Infect. Genet. Evol.
**2018**, 63, 295–306. [Google Scholar] [CrossRef] [PubMed] - Cobey, S. Pathogen evolution and the immunological niche. Ann. N. Y. Acad. Sci.
**2014**, 1320, 1. [Google Scholar] [CrossRef] [PubMed][Green Version] - MacLean, R.C.; Hall, A.R.; Perron, G.G.; Buckling, A. The evolution of antibiotic resistance: Insight into the roles of molecular mechanisms of resistance and treatment context. Discov. Med.
**2010**, 10, 112–118. [Google Scholar] - Hu, B.; Guo, H.; Zhou, P.; Shi, Z.-L. Characteristics of sars-cov-2 and covid-19. Nat. Rev. Microbiol.
**2020**, 19, 141–154. [Google Scholar] [CrossRef] - Duhon, J.; Bragazzi, N.; Kong, J.D. The impact of non-pharmaceutical interventions, demographic, social, and climatic factors on the initial growth rate of covid-19: A cross-country study. Sci. Total Environ.
**2021**, 760, 144325. [Google Scholar] [CrossRef] [PubMed] - Alam, I.; Radovanovic, A.; Incitti, R.; Kamau, A.A.; Alarawi, M.; Azhar, E.O.; Gojobori, T. Covmt: An interactive sars-cov-2 mutation tracker, with a focus on critical variants. Lancet Infect. Dis.
**2021**, 21, 602. [Google Scholar] [CrossRef] - Phan, T. Genetic diversity and evolution of sars-cov-2. Infect. Genet. Evol.
**2020**, 81, 104260. [Google Scholar] [CrossRef] - Pachetti, M.; Marini, B.; Giudici, F.; Benedetti, F.; Angeletti, S.; Ciccozzi, M.; Masciovecchio, C.; Ippodrino, R.; Zella, D. Impact of lockdown on covid-19 case fatality rate and viral mutations spread in 7 countries in europe and north america. J. Transl. Med.
**2020**, 18, 1–7. [Google Scholar] [CrossRef] [PubMed] - Epidemiological Update: Occurrence of Variants of Sars-Cov-2 in the Americas. 20 January 2021. Available online: https:www.tinyurl.com/mlqzzc6k (accessed on 2 February 2021).
- Betti, M.I.; Heffernan, J.M. A simple model for fitting mild, severe, and known cases during an epidemic with an application to the current sars-cov-2 pandemic. Infect. Dis. Model.
**2021**, 6, 313–323. [Google Scholar] [PubMed] - Public Health Ontario. Covid-19 uk Variant voc-202012/01—What We Know So Far; Technical Report; Public Health Ontario: Toronto, ON, Canada, 2020. [Google Scholar]
- Korber, B.; Fischer, W.M.; Gnanakaran, S.; Yoon, H.; Theiler, J.; Abfalterer, W.; Hengartner, N.; Giorgi, E.E.; Bhattacharya, T.; Foley, B.; et al. Tracking changes in sars-cov-2 spike: Evidence that d614g increases infectivity of the covid-19 virus. Cell
**2020**, 182, 812–827. [Google Scholar] [CrossRef] [PubMed] - Office of the Premier. Ontario Delivers First Covid-19 Vaccine in the Country. 2020. Available online: https://tinyurl.com/1suzwju8 (accessed on 2 February 2021).
- Betti, M.; Bragazzi, N.L.; Heffernan, J.; Kong, J.; Raad, A. Integrated vaccination and non-pharmaceutical interventions based strategies in ontario, canada, as a case study: A mathematical modeling study. medRxiv
**2021**. [Google Scholar] [CrossRef] - Canada’s Covid-19 Immunization Plan. Available online: https://www.canada.ca/en/public-health/services/diseases/2019-novel-coronavirus-infection/canadas-reponse/canadas-covid-19-immunization-plan.html#a8 (accessed on 2 February 2021).
- Duong, D. What’s Important to Know about the New Covid-19 Variants? CMAJ
**2021**, 193, E141–E142. [Google Scholar] [CrossRef] - Koyama, T.; Weeraratne, D.; Snowdon, J.L.; Parida, L. Emergence of drift variants that may affect covid-19 vaccine development and antibody treatment. Pathogens
**2020**, 9, 324. [Google Scholar] [CrossRef] [PubMed] - Mahase, E. Covid-19: What New Variants Are Emerging and How Are They Being Investigated? BMJ
**2021**, 372. [Google Scholar] [CrossRef] - CDC. New Variants of the Virus that Causes Covid-19. 2021. Available online: https://www.cdc.gov/coronavirus/2019-ncov/transmission/variant.html (accessed on 2 February 2021).
- Van Oosterhout, C.; Hall, N.; Ly, H.; Tyler, K.M. Covid-19 Evolution during the Pandemic–Implications of New Sars-Cov-2 Variants on Disease Control and Public Health Policies. Virulence
**2021**, 12, 507–508. [Google Scholar] [CrossRef] [PubMed] - Emergencies Preparedness, Response: Sars-Cov-2 Variants. Available online: https://www.who.int/csr/don/31-december-2020-sars-cov2-variants/en/. (accessed on 2 February 2021).
- Rambaut, A.; Holmes, E.C.; O’Toole, Á.; Hill, V.; McCrone, J.T.; Ruis, C.; du Plessis, L.; Pybus, O.G. A dynamic nomenclature proposal for sars-cov-2 lineages to assist genomic epidemiology. Nat. Microbiol.
**2020**, 5, 1403–1407. [Google Scholar] [CrossRef] [PubMed] - Government of Canada. Travel Restrictions in Canada. 2021. Available online: https://travel.gc.ca/travel-covid/travel-restrictions (accessed on 2 February 2021).

**Figure 1.**Model fit given different initial conditions for the mutant strain. (

**Top row**, (

**a**,

**b**)) 100 cumulative cases on 26 December 2020. (

**Bottom row**, (

**c**,

**d**)) 1000 cumulative cases on 26 December 2020. (

**Left column**, (

**a**,

**c**)) The active and cumulative cases are shown given the model with (dashed lines) and without (solid lines) the mutant strain (dashed lines). Active mild and severe wildtype infected cases are shown in red and blue. Active and severe mutant infected populations are shown in dark red and dark blue. The cumulative known and total cases of the wildtype and mutant strains are shown in light and dark green, and light and dark purple, respectively. (

**Right column**, (

**b**,

**d**)) The new reported cases per day given the model with (wildtype—solid pink line, mutant—dashed blue line, and total—solid black line) and without (wildtype—solid blue line) the mutant. Ontario reported case data, from September 2020 to January 2021, are also shown (dots).

**Figure 2.**The proportion of active cases of the mutant strain. (

**Left**) 60 active cases (100 cumulative cases) on 26 December 2020. (

**Right**) 600 active cases (1000 cumulative cases) on 26 December 2020.

**Figure 3.**Model fit given vaccination and relaxation. (

**Top row**, (

**a**,

**b**)) vaccination without relaxation, (

**middle row**, (

**c**,

**d**)) vaccination with slow relaxation, and (

**bottom row**, (

**e**,

**f**)) vaccination with fast relaxation. Vaccination assumes that $10\%$ of the population is vaccinated by 31 March 2021 and that $75\%$ of the population is inoculated by the end of 2021. Relaxation allows for rules and behaviours to change in a way that allows for more contact between individuals. We assume that behaviours will eventually lead to pre-February 2020 contact rates between individuals. (Left column) The active and cumulative cases are shown given the model with (dashed lines) and without (solid lines) the mutant strain (dashed lines). Active mild and severe wildtype infected cases are shown in red and blue. Active and severe mutant infected populations are shown in dark red and dark blue. The cumulative known and total cases of the wildtype and mutant strains are shown in light and dark green, and light and dark purple, respectively. (Right column) The new reported cases per day given the model with (wildtype—solid pink line, mutant—dashed blue line, and total—solid black line) and without (wildtype—solid blue line) the mutant. Ontario reported case data, from September 2020 to January 2021, are also shown (dots).

**Figure 4.**The Federal Government vaccine roll-out plan, adapted from [22].

**Figure 5.**Figure showing the model fit with both the wildtype and mutant. Red is mild cases, blue is severe cases, green is the cumulative reported cases, and purple is the total cases. The light colours are the wildtype, and dark colours are the mutant.

**Figure 6.**Model fit assuming the period over Christmas to be anomalous, including vaccination and relaxation. Vaccination assumes that $10\%$ of the population is vaccinated by 31 March 2021 and that $75\%$ of the population is inoculated by the end of 2021. Relaxation allows for NPIs to be lifted on 1 May 2021. (

**Left column**, (

**a**)) The active and cumulative cases are shown given the model with (dashed lines) and without (solid lines) the mutant strain (dashed lines). Active mild and severe wild-type infected cases are shown in red and blue. Active and severe mutant infected populations are shown in dark red and dark blue. The cumulative known and total cases of the wild-type and mutant strains are shown in light and dark green, and light and dark purple, respectively. (

**Right column**, (

**b**)) The new reported cases per day given the model with (wild-type—solid pink line, mutant—dashed blue line, and total—solid black line) and without (wild-type—solid blue line) the mutant. Ontario reported case data, from September 2020 to December 2020, are also shown (dots).

**Table 1.**Table of the model parameters from the fit; used as a base for extensions. We extend the model with the parameters using hypothetical scenarios for vaccination, relaxation, and the emergence of a variant strain. These give the mean values of the model parameters with one standard deviation.

Parameter | Fitted Value |
---|---|

${\mathcal{R}}_{0}$ | $2.41\pm 0.59$ |

p | $0.25\pm 0.21$ |

r | $0.006\pm 0.02$ |

k | $0.40\pm 0.22$ |

d | $0.21\pm 0.29$ |

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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Betti, M.; Bragazzi, N.; Heffernan, J.; Kong, J.; Raad, A.
Could a New COVID-19 Mutant Strain Undermine Vaccination Efforts? A Mathematical Modelling Approach for Estimating the Spread of B.1.1.7 Using Ontario, Canada, as a Case Study. *Vaccines* **2021**, *9*, 592.
https://doi.org/10.3390/vaccines9060592

**AMA Style**

Betti M, Bragazzi N, Heffernan J, Kong J, Raad A.
Could a New COVID-19 Mutant Strain Undermine Vaccination Efforts? A Mathematical Modelling Approach for Estimating the Spread of B.1.1.7 Using Ontario, Canada, as a Case Study. *Vaccines*. 2021; 9(6):592.
https://doi.org/10.3390/vaccines9060592

**Chicago/Turabian Style**

Betti, Mattew, Nicola Bragazzi, Jane Heffernan, Jude Kong, and Angie Raad.
2021. "Could a New COVID-19 Mutant Strain Undermine Vaccination Efforts? A Mathematical Modelling Approach for Estimating the Spread of B.1.1.7 Using Ontario, Canada, as a Case Study" *Vaccines* 9, no. 6: 592.
https://doi.org/10.3390/vaccines9060592