Integrated vaccination and non-pharmaceutical interventions based strategies in Ontario, Canada, as a case study: a mathematical modelling study

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.

Keywords: COVID-19 pandemic; Canada; Ontario; mathematical modelling; non-pharmaceutical interventions; vaccine and immunization campaign.

Figure 1.

The Federal Government vaccine roll-out plan, adapted from [5].

Figure 2.

A compartmental diagram of Model (2.1). From a population N, we assume infection presents as either mild or severe with probability p_s. Infection spreads at rate ${\mathcal{R}}_{p}M(t)$. Infection clears at rate 1. All infections are added to two compartments: C_I, the cumulative case load of the outbreak and C_K the known case load. All severe infections are assumed to be known and reported, and a fraction r of mild infections are known and reported. The compartment C_K is highlighted as it is the compartment we use to fit to data.

Figure 3.

A visualization of equation (2.8). We can see that by March 2021, $10\text{\%}$ of the population of Ontario is expected to be vaccinated. By the end of 2021, we expect to approach $75\text{\%}$ of the population to be vaccinated.

Figure 4.

A visualization of equation (2.9). By changing θ, we are able to control the speed of relaxation efforts. A lower value of θ leads to accelerated relaxation. We relax from our fitted value of ${\mathcal{R}}_p$ to the accepted value of R₀ for COVID-19 of 2.5.

Figure 5.

Light lines: no vaccine trajectories. Dark lines: with Vaccine using (2.8). Shaded areas represent the $95\text{\%}$ confidence interval obtained from the fits. The current vaccination roll-out plan will not take hold in the population until after we reach the peak of the outbreak. Known data points are given as black dots.

Figure 6.

The blue line is the current trajectory of new reported cases per day in Ontario if the current level of non-pharmaceutical interventions are maintained. The pink line shows the possible trajectory under vaccine roll-out of equation (2.8) and non-pharmaceutical interventions and maintained without relaxation. Known data points are given as black dots.

Figure 7.

Removing non-pharmaceutical interventions on 8 December 2020 with no re-implementation and without vaccination. Again, blue line is the current trajectory, shaded region is the $95\text{\%}$ confidence area and the pink line is the modified scenario. (a) Cumulative and active cases, (b) new reported cases.

Figure 8.

Removing non-pharmaceutical interventions on 31 January 2021 creates a massive increase in cases, but vaccine roll-out has a large effect on mitigating cases. (a) Cumulative and active cases, (b) new reported cases.

Figure 9.

Removing non-pharmaceutical interventions on 31 March 2021 can be controlled. (a) θ = 20, (b) θ = 10, (c) θ = 0, (d) θ = 20, (e) θ = 10, (f ) θ = 0.

Figure 10.

Removing non-pharmaceutical interventions on 1 May 2021; we need to be fairly low on the outbreak curve to remove restrictions without phasing. (a) Cumulative and active cases, (b) new reported cases.

Figure 11.

A constant vaccination rate will allow for a mitigating outbreak peak at the expense of a longer outbreak tail. (a) Cumulative and active cases, (b) new reported cases.

Figure 12.

A reduction of ${\mathcal{R}}_{\mathrm{eff}}$ with target dates for different scenarios described above. We see that opening too early will cause ${\mathcal{R}}_{\mathrm{eff}}$ to increase above 1 which will increase the risk of localized outbreaks. If relaxation is delayed until May 2021 and phased-in, reopening can occur with very little risk.