# Modelling plausible scenarios for the Omicron SARS-CoV-2 variant from early-
stage surveillance

Christopher J. Banks  Roslin Institute, University of Edinburgh Ewan Colman
Roslin Institute, University of Edinburgh Anthony Wood  Roslin Institute,
University of Edinburgh Thomas Doherty  Department of Mathematics and
Statistics, University of Strathclyde  Rowland R. Kao  Roslin Institute,
University of Edinburgh Royal (Dick) School of Veterinary Studies, University
of Edinburgh  Correspondence<EMAIL_ADDRESS>
###### Abstract

In this paper we used an adapted version of an existing simulation model of
SARS-CoV-2 transmission in Scotland to investigate the rise of the Omicron
variant of concern, in order to evaluate plausible scenarios for transmission
advantage and vaccine immune escape relative to the Delta variant. We also
explored possible outcomes of different levels of imposed non-pharmaceutical
intervention. The initial results of these scenarios were used to inform the
Scottish Government in the early outbreak stages of the Omicron variant.

We use an explicitly spatial agent-based simulation model combined with
spatially fine-grained COVID-19 observation data from Public Health Scotland.
Using the model with parameters fit over the Delta variant epidemic, some
initial assumptions about Omicron transmission advantage and vaccine escape,
and a simple growth rate fitting procedure, we were able to capture the
initial outbreak dynamics for Omicron. We also find the modelled dynamics hold
up to retrospective scrutiny.

We found that the modelled imposition of extra non-pharmaceutical
interventions planned by the Scottish Government at the time would likely have
little effect in light of the transmission advantage held by the Omicron
variant and the fact that the planned interventions would have occurred too
late in the outbreak’s trajectory. Finally, we found that any assumptions made
about the projected distribution of vaccines in the model population had
little bearing on the outcome, in terms of outbreak size and timing, rather
that the detailed landscape of immunity prior to the outbreak was of far
greater importance.

##  1 Introduction

The B.1.1.529 SARS-CoV-2 variant was first detected in South Africa and
reported to the World Health Organisation on 24th November 2021; it was
designated the Omicron variant of concern (VOC) two days later [1]. The first
cases of Omicron were detected in Scotland around 29th November [2]. Globally
Omicron was associated with rapid spread and increase in case numbers, most
likely due to some combination of increased transmission potential and
increased vaccine escape [3]. However greater infectiousness was somewhat
offset by a reduction in outcome severity.

Upon the introduction of the variant to Scotland there was an urgent need to
understand how the dynamics of transmission may be affected and how this in
turn would affect outcomes and local levels of pressure on the National Health
Service. It was also necessary to estimate the effect of control measures.

In this study we used an adapted version of an existing simulation model of
SARS-CoV-2 transmission in Scotland, SCoVMod [4], to investigate the rise of
the Omicron VOC, in order to evaluate plausible scenarios for transmission
advantage and vaccine immune escape realtive to the Delta VOC. We explored
possible outcomes of different levels of imposed non-pharmaceutical
interventions (NPI’s) and booster vaccination, in order to provide insight
into the possible severity of the epidemic in terms of the probable number of
infections.

Using the SCoVMod simulation model, we fit model parameters to the explicit
pattern of recorded cases across all local authorities in Scotland,
considering the period from August to December 2021. This was a period in
which the Delta VOC was dominant and over which the COVID-19 epidemic in
Scotland can be considered as a single infection process. We introduced a
variant infection (representing the Omicron VOC), and then modelled the period
from the 11th December to the end of March 2022. At time of writing there is
considerable information on the differences between Omicron and Delta. However
we assume knowledge only available up to 11th December when this analysis was
initiated, to demonstrate an analytical approach that is relevant to that
point in spread of Omicron. Because this was a period of sustained consistent
exponential growth, with no obvious change in interventions, this also allows
us to fit a single model assuming a single transmission rate. We examine a
range of scenarios with either fixed parameters or multipliers of the Delta
parameters for the variant process.

In order to fit the model to observed data our simulated epidemics are
compared to the spatio-temporal pattern of COVID-19 incidence in Scotland.
Non-observable parameters were estimated using the number of infections
estimated in the population. Incidence of SARS-CoV-2, here defined as the
number of new infections each day, is not directly obtainable from
surveillance data and therefore needs to be estimated. The number of confirmed
cases found through PCR and lateral flow device tests is a useful indicator or
incidence, however, a large proportion of infections are not ascertained
through these methods [5].

At local scales it is not appropriate to apply the same ascertainment rate to
all sub-regions. This is particularly true in a heterogeneous population like
Scotland where infection levels, access to testing, and test seeking
propensity vary greatly between local authority areas. Hence we also introduce
a novel method to estimate the incidence in each sub-region of Scotland. We
derive a formula that takes the number of positive and negative PCR tests
across the nation as input, and gives an estimate of the number of people
testing positive for SARS-CoV-2 in each sub-region on any given day. The
formula is derived from assumptions about the relationship between infection
prevalence and observed test data. We then re-scale the prevalence estimate to
form our estimate of incidence. The result of which is used as our observed
incidence in the model-fitting process.

This study is similar in scope to other early-response scenario models, for
example both Barnard et al. [6] and Keeling et al. [7]. However, we focus on
Scotland and implement a more detailed individual based model, including
explicit inter-location mobility, and with finer grained data resolution. We
make similar assumptions on vaccine efficacy and escape.

The initial results of these scenarios were used to inform the Scottish
Government and intended to aid policy decision making in the early outbreak
stages of the variant [8].

##  2 Methods

###  2.1 Data

Data for fitting Delta, estimating the seeding of Omicron, and the
distribution of COVID-19 vaccines was supplied by Public Health Scotland’s
eDRIS team [9]. We differentiate between Delta and Omicron using S-Gene Target
Failure (SGTF) in PCR tests as a proxy for Omicron infections. Community tests
where SGTF is measured represent approximately 80% of all tests at the time of
running these scenarios. We also used publicly available Scottish census data
from National Records for Scotland (NRS) [10]. We used datazone (DZ) level
resolution where DZs are population census units of approximately 500 to 1,000
residents. The data for assignment of individuals to work locations is drawn
from the NRS Census Flows data [11], Table WU01UK, which provides
origin/destination workplace data for the population from the 2011 census. We
adjust these with respect to the 2018 population estimates.

Age demographics and movement to work patterns are available at the level of
Census Output Areas (OA), each of which contains approximately 20 households
or 50 people [12]. Census data on the Scottish Index of Multiple Deprivation
(SIMD) [13] considers multiple relative deprivation measures and combines them
into a single value. Deprivation data are publicly available at the DZ level.

We also used publicly available data from Google to estimate mobility levels
over time, with respect to commuting patterns [14].

###  2.2 Model

SCoVMod is an explicitly spatial agent-based simulation model that accounts
for recorded commuter patterns and additional local movements that are
intended to capture non-work interactions such as recreation, shopping, and
school. These movements are further modulated by the recorded time-varying
mobility statistics, and geographically explicit population age structures.
Whilst this does not capture all human movement, we assume that commuting
patterns capture a large proportion of the long-range mobility and that local
movements at least partially capture the non-commuting population travelling
to shops, schools, and other local community movements. This is a similar
assumption regarding mobility to the one used in other studies, including e.g.
Barnard et al. [6]. The model also uses deprivation metrics to account for
spatial heterogeneity in outcome likelihoods. The model is parameterised
against an estimation of of the number of COVID-19 infections according to the
observed number of COVID-19 reported cases in each Council Area, using a model
for the case ascertainment ratio [5]. The model parameters were inferred using
Approximate Bayesian Computation (ABC) [15].

The core of the simulation model breaks down into the following parts:

  * •

Local transmission—a homogeneous mixing compartmental model for each OA of the
country;

  * •

National transmission—a network-based simulation of the movement of
individuals between OAs;

  * •

Parameter inference—a Bayesian estimation of the parameters for local
transmission, this also involves a model of infection incidence used as the
observed value for inference;

  * •

Transmission rate over time adjustment—the modulation of both local and
national transmission to simulate non-pharmaceutical interventions and other
changes in transmission rates over time.

The compartmental model considers key aspects of COVID-19 epidemiology
including phases for latent infection, infectious and mildly infected (showing
few or no clinical signs) and severely infected (with substantial clinical
signs) individuals, hospitalised, recovered and died, similar to other
investigations [16, 17]. These epidemiological processes are captured as
individual disease states (Figure 1). Individuals are also stratified into
three age groups: young (0–15), adult (16–64) and elderly (65+). Within-OA
transmission is assumed to be homogeneously mixed while between-OA
transmission is determined by the empirical age-specific patterns of home and
work contact (creating day/night patterns of contact). We do not consider
overnight shifts in location or introductions from outside Scotland beyond the
impact on the initial seeding.

Deprivation is also known to influence COVID-19 transmission. We therefore
adjust transmission rates in the model with the average health index in the
local council area.

Population mobility patterns are determined by the patterns of movements to
work recorded in Scottish Census data. We assume that only adults contribute
to commuter movement, in the daytime; the remaining proportion of adults and
all young and elderly individuals are assumed to move primarily within their
local OAs, which also account for non-work activities. Finally, commuting in
the model is restricted to healthy and exposed or mildly symptomatic
individuals; severely infected and hospitalised individuals do not commute.
The day/night patterns also result in two transmission rates.

#### Local transmission (within-OA)

Figure 1: Schematic of infection stages in SCoVMod. Individuals pass through
stages post infection as described by arrows. Not all stages are obligatory
for all infected individuals (e.g. some individuals recover without going to
hospital).

Within each OA ($i$) the infection process is governed by a compartmental
model (Figure 1) for which the frequency dependent force of infection
$\Lambda_{i}(t)$ defined in Figure S1. In the compartmental model are
infection classes $S$ (susceptible), $E$ (exposed), $I^{M}$ (mildly infected),
$I^{S}$ (severely infected), $H$ (hospitalised).

The state transitions in the model are described by the following equations:

$\displaystyle\dfrac{dS_{ia}}{\mathit{dt}}$
$\displaystyle=-\Lambda_{i}(t)\beta_{CA}S_{ia}+\nu R_{ia}$
$\displaystyle\dfrac{dE_{ia}}{\mathit{dt}}$
$\displaystyle=\Lambda_{i}(t)\beta_{CA}S_{ia}-\gamma E_{ia}$
$\displaystyle\dfrac{dI_{ia}^{M}}{\mathit{dt}}$ $\displaystyle=\gamma
E_{ia}-(\gamma_{M}+\rho_{M})I_{ia}^{M}$
$\displaystyle\dfrac{dI_{ia}^{S}}{\mathit{dt}}$
$\displaystyle=\gamma_{M}I_{ia}^{M}-(\rho_{Sa}+\mu_{Sia}+\eta)I_{ia}^{S}$
$\displaystyle\dfrac{dH_{ia}}{\mathit{dt}}$ $\displaystyle=\eta
I_{ia}^{S}-(\rho_{Ha}+\mu_{Hia})I_{ia}^{S}$
$\displaystyle\dfrac{dR_{ia}}{\mathit{dt}}$
$\displaystyle=\rho_{M}I_{ia}^{M}+\rho_{Sa}I_{ia}^{S}+\rho_{Ha}H_{ia}-\nu
R_{ia}$ $\displaystyle D_{ia}$
$\displaystyle=N_{ia}-(E_{ia}+I^{M}_{ia}+I^{S}_{ia}+H_{ia}+R_{ia})$

The force of infection, $\Lambda$, is detailed in Figure S1 and other state
transition rates are given by: $\gamma$ for $E\rightarrow I^{M}$, $\gamma_{M}$
for $I^{M}\rightarrow I^{S}$, $\eta$ for $I^{S}\rightarrow H$, $\rho_{M}$ for
$I^{M}\rightarrow R$, $\rho_{Sa}$ for $I^{S}\rightarrow R$ for age class $a$,
$\rho_{Ha}$ for $H\rightarrow R$ for age class $a$, $\mu_{Sia}$ for
$I^{S}\rightarrow D$ for age class $a$ and location $i$, $\mu_{Hia}$ for
$H\rightarrow D$ for age class $a$ and location $i$, and $\nu$ for
$R\rightarrow S$.

Transmission rates are adjusted by location, according to SIMD Health Index:

$\beta_{CA}=1+\left(\beta_{mod}(k_{CA}-k_{av})\right)$

where $\beta_{CA}$ is the transmission modifier rate for a given CA, $k_{CA}$
is the CA mean health index value (from the SIMD), and $\beta_{mod}$ is a
fitted parameter for the strength of the overall effect.

For this study the model is extended with a second strain (variant) of the
virus. The compartment structure remains the same, but individuals can be
infected with one of two strains, each with a different set of rates. We
assume complete cross immunity between strains.

The values for all parameters are either established from the literature
(Table S1) or fit (see below).

#### National transmission (between-OA movements)

Between OAs individuals move daily across a network of locations defined by
Scottish Census data adjusted by Google mobility data.

From the current population estimates we draw the number of individuals whose
primary residence is mapped onto an OA, with their age group. The total
population of Scotland from this estimate is 5,438,054 (Young: 919,580; Adult:
3,492,421; Elderly: 1,026,053). Of the adults 1,960,712 commute to work,
reduced to 647,034 under lockdown (see details below).

An individual’s workplace is assigned by distributing a proportion of the
population of each location to each work location, weighted by the proportion
of individuals from each home location in the census flows data who work in
another location. For the remaining proportion we synthetically generated
daytime locations by randomly selecting OAs either from the OAs within the
same intermediate zone (a geographical area containing approximately 4200
people), with probability 0.9, or from the OAs within a neighbouring
intermediate zone, with probability 0.1.

For each origin $o$ and destination $d$ we assign a weight $w_{od}$ from the
census flow data:

$w_{od}=\frac{n_{od}}{t_{o}}$

where $n_{od}$ is the total number of people who move from $o$ to $d$ to work,
and $t_{o}$ is the total number who move from origin $o$ to any location for
work. We take the individuals of each home location if they are eligible to
work (total $n_{o}$); in this case we assume all individuals of adult age
16–64. Each destination is assigned to $n_{o}\times w_{od}$ of these
individuals. The individuals who remain have no assigned workplace—we assume
either they do not work, or they work within their home location.

For each day of the simulation we consider two time steps: a day step where
individuals can move to their place of work, and a night step where those
individuals move back to their home location. In each day step, we take each
destination location $d$. Let $\lambda_{d}$ be the number of eligible workers
who may move to the destination location. The number of moves $s$ is then
scaled according to the per cent change in mobility $m$ (see below) for the
given day: $s_{m}=\lfloor s(1+\frac{m}{100})\rfloor$.

In order to improve the computational efficiency of the overall simulation,
movements of commuters between OAs were batched into groups of 5, with
movements between OAs of fewer than five individuals per day retained at a
proportionate rate by drawing from a binomial distribution: $s_{mt}\sim
B(s_{m},\frac{1}{5})$. If the sampled number of workers $s_{mt}$ is less than
or equal to the number of workers who may normally move to destination $d$,
then those who move are sampled randomly from those who may normally move.
However, if $s_{mt}$ is greater than the number of workers who may normally
move to $d$, then the additional workers are drawn randomly from workers who
have no assigned destination location. While this reduces the overall network
link density, the effect on transmission dynamics in this setting is
negligible. We note that this means that interpretation of the combined
$\beta_{D}$ and $\beta_{N}$ must be made with caution and not compared
directly to other models.

For each night of the simulation, the workers who moved in the day step are
moved back to their origin location.

#### Vaccination

Vaccination is represented in the model by flagging an individual with its
vaccination status. The transmission rates affecting a vaccinated individual
are adjusted accordingly—i.e. the probability that a vaccinated individual
receives an infection is reduced according to vaccine effectiveness.
Vaccination numbers per DZ in this study were initiated as recorded in eDRIS
data, and all doses and booster doses were applied to individuals in the
model, within each DZ and each age class, in the same proportions as were
administered in the real population. Vaccine effectiveness in each dose phase
is a fixed parameter per phase and per strain.

For the period after 11th Dec 2021, we assumed a modelled distribution of the
booster doses that were being delivered at that time. We distributed booster
doses to all individuals in the model, who have had their second dose, after
three months (as per the actual distribution schedule at the time). We ran one
scenario with 100% uptake w.r.t. 2nd dose, and one with 55% uptake. At a
national level 2097633 boosters had been administered by 11 Dec 2021, 3814877
second doses had been administered by 18 Sep 2021 (12 weeks prior, thus
eligible for a booster on 11 Dec 2021), thus 55% of all eligible had had their
booster by 11 Dec.

More recently we also ran a final scenario based on the recorded vaccine
distribution beyond the 11th December for comparison.

Based on the available information at the time [18] and consistent with other
approaches [6, 7], we assume no reduction in outcome severity associated with
vaccinated individuals, but rely on the transitive effect of reducing
associated transmission.

#### Modelling COVID-19 incidence

As PHS eDRIS data gives us only the reported cases of infection, we need to
determine the likely number of infected individuals with which to seed the
model and to use as the summary statistic for validation and parameter
estimation. For this we use the model described in Colman et al. [5] to
estimate the case ascertainment ratio and thus the likely number of infected
individuals over time, for the period of simulation.

#### Modelling transmission rate changes over time

To model the changes in activity over time—e.g those that are the effect of
lockdowns, but also other more voluntary changes in behaviour—we consider two
factors. First, we thin movements in the simulation (mobility reduction) in
proportion to observed changes in mobility according to Google mobility
reports [14]. This is applied as a proportional change in the number of
individuals making between-OA movements on a given day (as above).

Second, physical distancing is incorporated via a reduction in contacts
applied to both daytime and nighttime transmission rates (transmission
reduction). Beyond the initial fit period (see below), we fit a change in
transmission rate over time only, assuming that posterior distributions for
all other parameters estimated based on the initial fit remain relevant.

#### Parameter estimation

Simulated epidemics are compared to the spatio-temporal pattern of COVID-19
spread in Scotland. Non-observable parameters were estimated using the
incidence of COVID-19, according to the model described above, during the
initial Delta-dominant period.

Estimation was performed using a Sequential Monte Carlo implementation of
Approximate Bayesian Computation (ABC-SMC) [19, 15]. We calibrated the model
output to the weekly incidence (number of estimated infections per week) due
to COVID-19 aggregated at the level of CAs, using this spatial variation in
incidence across Scotland to provide the necessary signature to properly
calibrate the role of human mobility.

Simulated and observed summary statistics are compared via a score equal to a
sum of squared errors, recorded weekly:

$\mathit{score}=\sum_{week}\sum_{CA}\left(I_{sim}-I_{obs}\right)^{2}$

where $I_{sim}$ is the weekly incidence per CA simulated and $I_{obs}$ its
observed value.

The total number of infected individuals at the start of the simulation (the
seeds) are fitted as part of the inference. The seeds are randomly assigned a
disease state from $E$, $I^{M}$, and $I^{S}$. Seed locations are distributed
according to the proportion of infections registered per Intermediate Zone on
the date of the start of the simulation. Intermediate zones are _neighbourhood
level_ aggregates of approximately five DZs.

Uniform prior distributions constrain all parameter values to plausible ranges
based on the available literature relevant to the early, pre-lockdown period.
Infection dynamics are simulated via a $\tau$-leap algorithm using half-day
timesteps [20]. All parameters are listed in Table S1.

The inference framework is run on a distributed application framework (Akka)
[21] running on a cloud computing infrastructure (Amazon AWS2) [22]. The model
code has been written using industry grade software engineering practices
including agile development for project task planning, test driven
development, pair programming and code reviews to produce unit tested, robust,
and reusable software components. The majority of the code has been reviewed
by at least one other software developer.

#### Fitting transmission rate changes over time

After fitting the initial parameter set, a further temporal refinement is
employed to improve the fit where the model cannot account for external
factors such as changes in transmission owing to NPIs or other changes in
human behaviour not captured by the mobility data. Here we perform a piece-
wise least-squares fit over just the transmission rate $\beta$, per Council
Area. This is piece-wise in the inflection points in the case data, which
largely correspond to the times at which NPIs were enacted or relaxed.

###  2.3 Scoping scenarios

We modelled a range of scenarios, considering two variants (Delta and Omicron)
with differing transmissibility and levels of vaccine protection. At the time
of the analysis, there were limited data on the potential of the Omicron VOC
for either greater transmission than the Delta VOC, or increased ability to
escape either natural or vaccine-induced immunity. We therefore generated
simulations over possible transmission rates and vaccine escape levels for the
Omicron variant, based on this existing evidence, in order to choose
combinations that generate plausible trajectories of SGTF cases in Scotland.
We used values for transmission potential and vaccine efficacy from the UKHSA
Technical Briefing on Variants of Concern [23].

We modelled three levels of vaccine escape: a baseline with the same vaccine
efficacy as Delta (Escape Level 1), a lower vaccine escape potential (Escape
Level 2) as described by the central estimates from the UKHSA Technical
Briefing (90% after two doses, falling to 35% after 15 weeks, and 75% after
booster), and a higher vaccine escape potential (Escape Level 3) as described
by the lower efficacy bounds (65% after two doses, falling to 10% after 15
weeks, and 60% after booster).

We modelled two levels of transmissibility for Omicron: an increased level
based on the UKHSA Technical Briefing estimate of 3.2$\times$ household
transmission, under the assumption that generalised transmission advantages,
i.e. including transmission outside the household has a similar advantage, and
an intermediate level based on 80% of the higher level, giving a 2.25$\times$
transmission rate—corresponding with the lower bound of the UKHSA estimate. We
then have two sets of scenarios. The first assumes the overall transmission
rate for Delta remains at the current level. The second assumes an NPI-based
intervention, reducing transmission rates to 80% its previous value on 17th
December 2021, to reflect a combination of voluntary behavioural change in
response to new guidance, and new restrictions. The latter scenario aims to
generate a reproduction number around 0.8 for the Delta VOC, as observed
during previous similar NPI restricted periods in Scotland [8]. While it is
not expected that the impact of the NPIs during this period are likely to be
observed in the near future, the NPI scenarios were generated to explore
whether or not meaningful impacts on infection trajectories would be
predicted.

We assumed that all parameters for the Omicron VOC were the same as for Delta,
with the exception of the transmission rate, which was assumed to be a fixed
multiplier of the transmission rates for Delta. The transmission rates for
Delta are from parameters jointly drawn from the posterior parameter
distributions fitted for Delta from the earlier period (i.e. from August 2021
to November 2021). Vaccine escape levels were implemented as a multiplier on
the within-model vaccine efficacy for Delta as in Table 1. The combination of
vaccine escape and transmission parameters generates 12 scenarios (a–l),
labelled as in Table 2.

Efficacy multiplier
---
|  | 2 dose | +15 weeks | Booster
Vaccine Escape Level | 1 | 1 | 1 | 1
2 | 1 | 0.45 | 0.8
3 | 0.72 | 0.15 | 0.63
Table 1:  Levels of vaccine escape used in our scenarios, with value 1 being
complete protection.

The transmission model does not take account of vaccine protection from severe
disease, it either completely protects individuals or fails completely and so
if infected, results in an infection as likely to be severe as would be the
case for infection in a previously wholly susceptible individual.

Vaccine Escape Level
---
|  | 1 | 2 | 3
Transmission Level | 1 | a | b | c
2 | d | e | f
1+NPI | g | h | i
2+NPI | j | k | l
Table 2:  Scenario labels as used in figures in the exploration of scenario
plausibility.

###  2.4 Fitting of plausible scenarios

From the scoping scenarios, we carried forward only those that were plausible,
being closest to the observed SGTF incidence trajectory. We then adjusted the
transmission rates of each to fit the growth rate observed in incidence.

$\text{Growth rate}=\frac{\ln I(t_{f})-\ln I(t_{0})}{t}$

where $I(t)$ is the number of infected at time $t$ from an initial point
($t=t_{0}$) fitted to match the SGTF incidence trajectory. We use the time
period for which we have confirmed observed Omicron cases. We then take the
growth rates for the modelled scenario ($g_{m}$) and for the observed
incidence ($g_{o}$) and increase the scenario transmission rate by
$\frac{g_{o}}{g_{m}}$.

We then took a range of further scenarios:

| NPI Level
---|---
| 1 | 2 | 3 | 4
Lower vaccine escape | m | o | q | s
Higher vaccine escape | n | p | r | t

where NPI Level 1 is as considered previously, an initial drop to 80% of the
original transmission rate. Levels 2, 3, and 4 have a further post-Christmas
restriction applied with a further drop to 64%, 48%, and 40% of the original
transmission rates respectively, imposing these restrictions on 27th December
2021. As the mean of the fitted trajectories of the fitted Delta period were
observed to stabilize after 100 runs, further simulations were restricted to
this number.

##  3 Results

###  3.1 Model fit / parameters

The fit of the initial ABC-based parameter estimation to the observed data,
with the resultant posterior distribution of estimated parameters is shown in
Figure S2. Figure 2 shows the trajectory of incidence in the model compared to
the observed data (accounting for case ascertainment), with detail at the
Council Area level shown in Figure S3. Notably, the final inflection point in
the piece-wise temporal transmission rate fit is at the start of October 2021,
with the final inflection point in mid-November being a natural result of the
modelled dynamics.

Figure 2: Model fit to observed data (incidence) for the Delta variant, after
the inital ABC-based parameter estimation and temporal transmission rate fit,
national scale. Vertical line shows the final inflection point in the piece-
wise temporal fit.

###  3.2 Scoping scenario results

The dynamics of infection with respect to the Delta and Omicron variants are
directly compared in Figure 3 showing trajectories both with and without NPI’s
in place.

Figure 3: Comparison of scenarios with no additional NPIs (left) and
additional NPIs (right). Central estimate from 200 model runs, from the
vaccination distribution scheme with 55% uptake. With lower transmission rate:
a–c, g–i; higher transmission rate: d–f, j–l; and increasing vaccine escape
within each group. The trajectory of the Delta variant is shown as a dashed
line.

Figure S4 and Figure S5 provide additional detail, showing respectively
trajectories without and with further NPI’s in place from 17th December, and
showing the range of simulations and a comparison to the observed incidence.

###  3.3 Selection of plausible scenarios

We compared scenarios to the observed incidence of SGTF-only cases adjusted by
our modelled case to infection ratio. Only a few scenarios, all with the
higher transmission rate were close to estimating the true trajectory (growth
rate) of Omicron infections (Figures S6 and S7). Hence, we restricted further
scenario development to the most plausible of these.

We carry forward only scenarios k and l as being closest to the observed SGTF
case trajectory, also under the assumption that the measures already in place
would have had some impact. Scenario k has the lower and l the higher estimate
for vaccine escape. Both have the higher transmission rate estimate. We then
adjust the transmission rates of each to fit the growth rate observed in
cases.

###  3.4 Fit scenario results

By fitting the growth rate to that of the observed Omicron cases, we achieved
an initial modelled growth rate consistent with the limited knowledge of the
early Omicron outbreak. Figure 4 shows the fit to observed case data
(including knowledge of observed Omicron cases after 11th December that were
not known at the time of original modelling).

Figure 4: Adjusted transmission rate scenarios (log scale) for the 55% uptake
vaccine distribution scheme: lower vaccine escape (left), higher vaccine
escape (right). Dots represents bounds for 95% of 200 simulations. Observed
values prior to the vertical line (11th December) were the data available at
the time of fitting, used to fit the growth rate; observed values subsequent
to this date were added later for comparison.

We saw little significant difference between the different strategies for
forward distribution of vaccines (55% and 100% uptake of boosters with respect
to the uptake of 2nd doses). Figure S8 shows in detail the effect of the
different strategies, including a model with the actual uptake post-11th
December for comparison.

We estimated Omicron to have a transmission rate advantage over Delta of
5.3$\times$ in the lower vaccine escape scenario, and an advantage of
5.1$\times$ in the higher vaccine escape scenario.

Not even the severest restrictions (a reduction of transmission rate to 40% of
the rate in mid November) is there observed a significant reduction in cases,
implying that restrictions alone were not likely to be sufficient to reduce
the reproduction number below one. Figure 5 shows the range of post-Christmas
NPI scenarios. Figure S9 details the NPI scenarios with confidence intervals.

Figure 5: Adjusted transmission rate scenarios, lower vaccine escape (left),
higher vaccine escape (right), with a range of post-Christmas NPI levels.

##  4 Conclusions

In this study we have adapted an existing model, that was used to provide the
Scottish government with medium term projections of cases of COVID-19 across
Scotland over much of the “emergency” period of COVID-19 restrictions. The
model was adapted to account for the transmission of two strains of SARS-CoV-2
with different levels of vaccine immune escape, in order to mimic the
properties of the emergent Omicron VOC as known at time of analysis. In these
models we showed that, under plausible scenarios of immune escape, only
transmission rate advantages of between 5.1 and 5.3 result in trajectories
consistent with the observed numbers of cases with SGTF (assumed to be the
Omicron variant). While further combinations of transmission advantage and
vaccine escape may of course be plausible, in our view the scenarios we
examined provided a suitable backdrop on which to further investigate the
impact of interventions beyond those imposed in mid-December and to provide
reasonable mid-range forward projections of case numbers.

We saw little significant difference between the different strategies for
forward distribution of vaccines in the model. This is most likely because the
landscape of immunity already present at the time of the Omicron outbreak is
much more decisive in the effect on transmission than the relatively small
number of doses administered in the short period after the outbreak. Hence we
consider a reasonable best estimate at projected distribution is sufficient
for modelling a short to medium-term projection of infections. This would most
likely not be the case for longer-term projections.

We also saw that the imposition of post-Christmas NPI restrictions that were
likely to have little effect, firstly because the transmission rate advantage
of the Omicron variant was so high, but also because post-Christmas the rapid
outbreak would likely have already peaked meaning any restrictions at that
time would likely have come too late.

One important assumption in the model was that vaccinated individuals who
become infected, were as likely to experience severe disease as others. While
it is known that vaccines do provide very good protection against severe
infection with the Delta VOC, such data were not available at the time for the
Omicron VOC. With its observed greater ability to evade vaccine induced
protection, this was chosen as the more conservative option. We also assumed
complete cross immunity between strains. It is known now that that this is not
the case, but again there was little data available at the time to make an
assessment on this.

We observe that our final adjusted scenarios remained consistent with observed
Omicron cases beyond the observations available at the time of fitting.
Despite assumptions, we have shown that it was possible, with a model that had
been developed over the course of the Delta variant period to make a rapid and
reasonable estimate of the impact of a new variant with little knowledge about
its detailed dynamics. We believe this to be largely owing to the tracking of
immunity throughout the population during the Delta period at fine
geographical scale, and thus the model’s ability to simulate the finer detail
of the spatial spread of the new variant.

Looking back in comparison with observation data known now, but not yet
observed at the time, we can see that the model allowed a reasonable estimate
of both the scale and timing of the Omicron outbreak and the likely utility,
or lack thereof, of post-Christmas NPIs. In general, we can see that the
landscape of immunity prior to a variant outbreak, if it has a significant
transmission advantage, is much more important for modelling the dynamics of
the initial outbreak than any shorter-term change in immunity or contact
patterns after the outbreak has taken hold.

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## Supplementary Figures

Within each OA $i$ the infection process is governed by the frequency
dependent force of infection at time $t$:

$\displaystyle\Lambda_{i}(t)=-\Bigg{[}\Bigg{.}$
$\displaystyle\left(\beta_{N}+\beta_{D}\right)\sum_{a{\in}Y,E}\left(yI_{ia}^{M}+I_{ia}^{S}\right)+\beta_{N}\left(yI_{ia}^{M}+I_{ia}^{S}\right)+\beta_{D}I_{ia}^{S}$
$\displaystyle+\beta_{D}\Bigg{\\{}\Bigg{.}\Big{\\{}\Big{.}\sum_{j}(1-\sum_{j}x_{\mathit{ij}})(yI_{ia}^{M})\Big{\\}}\Big{.}$
$\displaystyle\hskip
36.00006pt+\sum_{j}\Big{\\{}\Big{.}x_{\mathit{ij}}\Big{(}\Big{.}\sum_{k}(1-x_{\mathit{jk}})(yI_{ja}^{M})+I_{ja}^{S}+\sum_{a{\in}Y,E}(yI_{ja}^{M}+I_{ja}^{S})\Big{)}\Big{.}\Big{\\}}\Big{.}\Bigg{\\}}\Bigg{.}\Bigg{]}\Bigg{.}/N_{i}$

where:

  * •

$\beta_{N}$ and $\beta_{D}$ are the nighttime and daytime transmission rates,

  * •

$a\in\\{Y,A,E\\}$ is the age class (Young, Adult, Elderly),

  * •

$y$ is the transmission rate modifier for mildly infected individuals,

  * •

$I_{ia}^{M}$ is the number of mildly infected at location $i$ in age class
$a$,

  * •

$I_{ia}^{S}$ is the number of severely infected at location $i$ in age class
$a$,

  * •

$x_{ij}$ is the proportion of individuals commuting between locations $i$ and
$j$,

  * •

$N_{i}$ is the population of location $i$.

Figure S1: Equation: Force of infection for location $i$ at time $t$. Parameter | Transition | Symbol | Age | Value | Prior |  References
---|---|---|---|---|---|---
Latency period | $E\rightarrow I^{M}$ | $1/\gamma$ | All | fitted | U(1.67,28) |  [16, 24, 25, 26, 27]
Days from mild infectiousness to recovery | $I^{M}\rightarrow R$ | $1/\rho_{M}$ | All | fitted | U(0.67,28) |  [17, 27]
Symptom onset time after infectiousness | $I^{M}\rightarrow I^{S}$ | $1/\gamma_{M}$ | All | fitted | U(2,28) |  [16, 24, 25, 26, 27, 28, 29, 30, 31]
Transmission rate for severe infectors (baseline, daytime) | $S\rightarrow E$ | $\beta_{d}$ | All | fitted | U(0,6) |
Transmission rate for severe infectors (baseline, nightime) | $S\rightarrow E$ | $\beta_{n}$ | All | fitted | U(0,6) |
Transmission rate multiplier for mild infectors | $S\rightarrow E$ | $y$ | All | fitted | U(0,2.6) |
Severe symptom onset to hospitalization | $I^{S}\rightarrow H$ | $1/\eta$ | All | 4 |  |  [30, 31, 32, 33, 34, 35, 36, 37]
Severe symptom onset to recovery | $I^{S}\rightarrow R$ | $1/\rho_{S}$ | Young | 19 |  |  [30]
for non-hospitalised |  |  | Adults | 20.7 |  |
|  |  | Elderly | 21.6 |  |
Days hospitalisation to death | $H\rightarrow D$ | $1/\mu_{H}$ | Young |  |  |  eDRIS data
|  |  | Adults | 6.97 |  |  eDRIS data
|  |  | Elderly | 6.62 |  |  eDRIS data
Proportion of hospitalised who | $H\rightarrow R$ | $\rho_{H}/(\rho_{H}+\mu_{H})$ | Young | 1 |  |  eDRIS data
recover |  |  | Adults | 0.96 |  |  eDRIS data
|  |  | Elderly | 0.84 |  |  eDRIS data
Symptoms onset to death | $I^{S}\rightarrow D$ | $1/\mu_{S}$ | Adults | 16 |  |  [31, 38, 33, 39, 37, 36]
Mortality rate multiplier (relative to average health index) |  | $\mu_{mod}$ | All | fitted | U(0,0.08) |
Number of seed infections (Delta variant) |  | $N_{s}$ | N/A | fitted | U(10, 20000) |
Number of seed recovered individuals (Delta variant) |  | $N_{R}$ | N/A | fitted | U(2m, 5m) |
Table S1: Epidemiological parameters in SCoVMod, with priors and fixed values
as appropriate. Where age is not indicated, parameters are assumed to be age
independent. All times are measured in days. Figure S2: Posterior distribution
of parameters, as a result of the initial ABC-based parameter estimation.
Figure S3: Council Area breakdown of the model fit to observed data, after the
inital ABC-based parameter estimation and temporal transmission rate fit.
Figure S4: Scoping scenarios with increasing vaccine escape from left to
right, increasing Omicron transmission rate from top to bottom. 55% uptake
vaccine distribution scheme. Figure S5: Scoping scenarios with additional NPI
reducing transmission rates to 80%: increasing vaccine escape from left to
right, increasing Omicron transmission rate from top to bottom. 55% uptake
vaccine distribution scheme. Figure S6: Scoping scenarios with increasing
vaccine escape from left to right, increasing Omicron transmission rate from
top to bottom. 55% uptake vaccine distribution scheme. (Log scale.) Figure S7:
Scoping scenarios with additional NPI reducing transmission rates to 80%:
increasing vaccine escape from left to right, increasing Omicron transmission
rate from top to bottom. 55% uptake vaccine distribution scheme. (Log scale.)

55% uptake distribution:

100% uptake distribution:

Explicit (knowledge post 11th Dec) distribution:

Figure S8: Adjusted transmission rate scenarios (log scale left, linear scale
right) for each vaccine distribution scheme with lower vaccine escape (left of
each pair) and higher vaccine escape (right of each pair). Dots represents
bounds for 95% of 200 simulations. Observed values prior to the vertical line
(11th December) were the data available at the time of fitting, used to fit
the growth rate; observed values subsequent to this date were added later for
comparison.

Linear scale:

Log scale:

Figure S9: NPI adjusted transmission rate scenarios with 55% uptake vaccine
distribution scheme.

For the purpose of open access, the author has applied a Creative Commons
Attribution (CC BY) licence to any Author Accepted Manuscript version arising
from this submission.