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Updated: Oct 29, 2025

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Integrated vaccination and non-pharmaceutical interventions based strategies in Ontario, Canada, as a case study: a
Matthew Betti1, Nicola Luigi Bragazzi2,3, Jane M Heffernan2,4
1Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick, Canada.
Abstract:
Recently, two coronavirus disease 2019 (COVID-19) vaccine products have been authorized in Canada. It is of crucial importance to model an integrated/combined package of non-pharmaceutical (physical/social distancing) and pharmaceutical (immunization) public health control measures. A modified epidemiological, compartmental SIR model was used and fit to the cumulative COVID-19 case data for the province of Ontario, Canada, from 8 September 2020 to 8 December 2020. Different vaccine roll-out strategies were simulated until 75% of the population was vaccinated, including a no-vaccination scenario. We compete these vaccination strategies with relaxation of non-pharmaceutical interventions. Non-pharmaceutical interventions were supposed to remain enforced and began to be relaxed on 31 January, 31 March or 1 May 2021. Based on projections from the data and long-term extrapolation of scenarios, relaxing the public health measures implemented by re-opening too early would cause any benefits of vaccination to be lost by increasing case numbers, increasing the effective reproduction number above 1 and thus increasing the risk of localized outbreaks. If relaxation is, instead, delayed and 75% of the Ontarian population gets vaccinated by the end of the year, re-opening can occur with very little risk. Relaxing non-pharmaceutical interventions by re-opening and vaccine deployment is a careful balancing act. Our combination of model projections from data and simulation of different strategies and scenarios, can equip local public health decision- and policy-makers with projections concerning the COVID-19 epidemiological trend, helping them in the decision-making process.
Insights
Delaying public health measure relaxation and achieving high COVID-19 vaccination rates in Ontario can mitigate outbreak risks. Early reopening can negate vaccination benefits, increasing case numbers and transmission.
Area of Science:
- Epidemiology
- Public Health
- Mathematical Modeling
Background:
- Two COVID-19 vaccines authorized in Canada necessitate integrated control strategies.
- Modeling combined non-pharmaceutical interventions (NPIs) and vaccination is crucial for pandemic management.
Purpose of the Study:
- To model and compare various COVID-19 vaccine rollout strategies alongside NPI relaxation scenarios in Ontario.
- To project the epidemiological impact of different public health interventions on case numbers and transmission.
Main Methods:
- Utilized a modified compartmental SIR model fitted to Ontario's COVID-19 case data (Sept-Dec 2020).
- Simulated vaccination strategies targeting 75% population coverage and various NPI relaxation timelines (Jan, Mar, May 2021).
Main Results:
- Early relaxation of NPIs, irrespective of vaccination, led to increased COVID-19 cases and reproduction numbers.
- Delayed NPI relaxation combined with achieving 75% vaccination coverage by year-end minimized outbreak risks.
Conclusions:
- Coordinated vaccine deployment and delayed NPI relaxation are essential for safe reopening.
- Modeling provides valuable projections for public health decision-makers to manage COVID-19 trends.
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