Analysis of the risk and pre-emptive control of viral outbreaks accounting for within-host dynamics: SARS-CoV-2 as a case study

Significance Estimates of the risk of viral disease outbreaks occurring in different populations are important for effective allocation of limited surveillance and control resources. Here, we show how changes in viral load during infection can be included in outbreak risk calculations and demonstrate how intervention effectiveness can be assessed in greater detail by considering within-host viral dynamics. We focus on the risk of localised SARS-CoV-2 outbreaks due to the omicron variant. We find that regular population-wide antigen testing is likely to reduce the outbreak risk, but not prevent outbreaks entirely, depending on characteristics of the local population. Our results highlight the importance of considering factors such as heterogeneity in within-host viral dynamics for outbreak risk estimation and analysis of interventions.


Text S1: Derivation of within-host model from target cell-limited model
The within-host model used in our analyses (Eqs. 1 and 2 in the main text) can be derived (1,2)  where (), () and () are the number of uninfected target cells, the number of infected target cells, and the amount of free virus at time since infection , respectively.
The parameters ,  and  and  are the rate constant for virus infection, the death rate of infected cells, the viral production rate per infected cell, and the viral clearance rate, respectively.Under a quasi-steady state assumption (which can be shown to be valid provided  is much larger than , as is typically the case for a range of viruses (1)), Eq.S1.3 can be replaced by 0 =  − .This gives () = ()/, which can be substituted into Eq.S1.2 in order to obtain an equation in terms of the viral load (on which data were available), Finally, letting () = (0)() , where () gives the fraction of target cells that remain uninfected at time since infection , in Eqs.S1.1 and S1.4,we recover Eqs. 1 and 2 in the main text, where  = (0)/.

Text S2: Within-host model parameter estimation
Here, we detail how we estimated the parameters in the within-host model (Eqs. 1 and 2 in the main text) by using nonlinear mixed effects modelling to fit the model to individual viral load data (4).Estimated parameters include the within-host model parameters ,  and , in addition to the incubation period,  !"# (estimation of the incubation period amounted to estimating the time of infection of individuals in the study data, relative to recorded symptom onset times).We assumed an initial viral load value of 0.01 copies/ml (5).
In the nonlinear mixed effects model, the value of the individual parameter vector,  $ = ; $ ,  $ ,  $ ,  !"#,$ <, for a given host, , is assumed to be of the form  $ =  &'& ×  ( ! (where the operations are applied element-wise).Here,  &'& is a fixed effect (also referred to as the population value), and  $ is a random effect, assumed to be normally distributed with mean zero and covariance matrix  .For simplicity, we assumed the random effects for different parameters to be independent, with standard deviations  ) ,  * ,  + and  , "#$ (i.e.,  = diag( ) -,  * -,  + -,  , "#$ -)).We estimated both the fixed effects (Table S1 -note that the subscript pop is suppressed) and the standard deviations of the random effects (Table S2).Additionally, we estimated the standard deviation, , of the measurement error in recorded values of the log viral load (which was assumed to be normally distributed with mean zero).
The Stochastic Approximation of the Expectation-Maximization (SAEM) algorithm (6,7) was used to obtain the parameter values that maximise the likelihood of the recorded viral load data.We accounted for left censoring of viral load data (i.e., a positive test result only occurring when the measured viral load exceeds the detection limit of 10 2.66 copies/ml) in the likelihood.Initial values of estimated parameters were changed multiple times to confirm the robustness of parameter estimation and ensure a global maximum of the likelihood was obtained.We also calculated best-fit estimates (Empirical Bayes Estimates ( 7)) of within-host model parameters for each individual host (Fig. S1).Fitting was implemented in MONOLIX version 2019R2 (7).

Text S3: Probability of detection under regular antigen testing
Supposing that an infected individual conducts an antigen test when their instantaneous viral load is , we assumed (5,8) that a positive test result occurs with probability  .() = Prob; K ≥  * < .Here,  K represents a measured viral load, assumed to be normally distributed on the log scale such that log 01 ( K ) ∼ (log 01 (),  -) , independently of previous viral load measurements;  * is the detection limit (the choice of  * is described in Table S1); and the measurement error level, , was assumed to be equal to the corresponding quantity that we estimated for PCR testing (Table S1).In other words, a positive test result was assumed to occur whenever the measured viral load exceeds the detection limit.
In most of our analyses including regular antigen testing, we assumed an exponentially distributed interval between successive tests with mean  (a constant interval between tests is considered in Fig. S4B).Below, we derive (under this assumption) an expression for the probability,  2 (), of an infected individual, subject to regular antigen testing, having been detected by time since infection .
First, since we assumed that symptomatic hosts are always detected, we have , where  !"# is the individual's incubation period (which can be taken to be infinite to represent an entirely asymptomatic infection).Now, for  <  for  <  !"# .

Text S4: Details of infectiousness model
The infectiousness profile of an undetected host,  3 (), at each time since infection, , was assumed to depend on their viral load, (), according to a prescribed functional relationship.Specifically, we assumed (9,10) in most of our analyses that  3 () =  × max_log 01 ;()< − log 01 ( * ), 0`, (S4.1) where the infectiousness limit,  * , was assumed to be equal to the detection limit for antigen testing.The choice of the scaling factor, , is described below.
We assumed the effective infectiousness (accounting for behavioural factors) of a detected individual at time since infection  (where  exceeds the time of detection) to be a factor  2 times  3 () (the choice of  2 , which lies between zero and one, is described in Table S1).In the absence of regular antigen testing, the overall individual infectiousness profile is then In Fig. S3, we considered an alternative possibility (11)(12)(13) in which Eq. S4.1 is replaced by so that infectiousness saturates at high viral loads.In this case, we took ℎ = 0.51 and  8 = 8.9 × 10 9 copies/mL as estimated in (11), while the scaling factor,  h , was chosen in the same manner as  in our default infectiousness model.

Text S5: Derivation of outbreak risk
Below, we derive an analytical expression for the outbreak risk in a heterogeneous population divided into  subgroups (the special case of a homogeneous population is obtained when  = 1), between which the infectiousness profile of infected hosts (as well as other factors such as susceptibility) may vary.
Specifically, we consider a branching process model in which susceptible depletion is neglected and infection lineages are assumed to be independent, and derive the outbreak risk following the introduction of a single newly infected host into the population.

Transmission model
We suppose that each infected host in group  transmits the pathogen to individuals in group  at total rate  :,$ () at time since infection  (a specific form of  :,$ () is considered later).The expected total number of infections generated in group  by each infected host in group  (over the course of infection) is then where the basic reproduction number (accounting for regular antigen testing, if in place),  1,455 , is the largest eigenvalue of the matrix with entries  :,$ (the nextgeneration matrix) (14).
We further assume that the transmission rates can be parameterised as  :,$ () =  :  :  $ (), where  $ () is the infectiousness profile of an infected individual in group ,  : is the proportion of the population who are in group , and  : is the relative susceptibility in group  (the possibility of heterogeneous susceptibility between different population subgroups is included here for generality, but we did not consider heterogeneous susceptibility in our numerical analyses -i.e., we took  : = 1 for each ).Additionally, we define ̅ = ∑  :  : ; :<0 to be the average population susceptibility,  : =  :  : /̅ to be the proportion of new infections that are in group  (accounting for both the relative size and susceptibility of each group),  $ to be the total integral of  $ () over all times since infection, and  $ = ̅  $ to be the expected total number of transmissions generated by an infected host in group  (accounting for the susceptibility of the population; note that in all of our numerical analyses, we had ̅ = 1, so that  $ =  $ ).

Outbreak risk
Now, we suppose that a single infected individual in group  is introduced into the population at time since infection , with the remainder of the population assumed to be uninfected at the time of introduction (and assuming no further external pathogen introductions into the population).An expression for the resulting probability of extinction (i.e., the probability that a major outbreak does not occur), denoted  $ (), can be derived by conditioning on whether or not the initial infected individual transmits the pathogen (to an individual in any population group) between times since infection  and ( + d), to obtain (neglecting the possibility that multiple transmissions occur, which has probability of order d -) In particular, we have We note that this equation has previously been derived using probability generating functions, rather than using a time-since-infection model as here (15).Now, under the parameterisation  :,$ =  :  $ (as described above), we have In this case, the overall extinction probability, following the introduction of a single newly infected individual (assuming the initial infection occurs in group  with probability  $ ), is Eq. S5.7 above can then be written as and substituting Eq.S5.9 into Eq.S5.8 then gives Finally, the outbreak risk (following the introduction of a single newly infected individual into an otherwise susceptible population),  =>?@A4BC = 1 − (0) , then satisfies While this equation may have multiple solutions (in particular,  =>?@A4BC = 0 is always a solution), by standard theory of hitting probabilities on Markov chains (16), the relevant solution is the largest solution between 0 and 1 (since the relevant solution to Eq. S5.10 is the minimal non-negative one).While we focussed on the outbreak risk starting with a single, newly infected, primary case, our approach could be extended to consider an infected individual introduced into the population later in infection, and/or multiple pathogen introductions.

Text S6: Wider applicability of generalised outbreak risk formulation
The result in Eq.S5.11, while derived here in the context of a time-sinceinfection model in a heterogeneous population, is in fact widely applicable to a range of (branching process) models.Specifically, taking the limit of a continuous distribution of population subgroups in Eq.S5.11 gives the equation Here  ∈ Θ is a continuous variable (which may be either real-valued or higherdimensional) indexing population subgroups and/or possible "types" of infection, () is the probability density that a new infection is of type , and () gives the expected total number of transmissions generated by an infected host with infection type .We briefly note that the continuous formulation in Eq.S6.1 is applicable to the scenario of heterogeneous within-host dynamics that we considered in Fig. 4, but in practice it was easier to calculate the outbreak risk by sampling the within-host dynamics of a large number of hosts as described in Text S7.
As an example to demonstrate the applicability of Eq.S6.1, we consider a branching process approximation of the stochastic SIR compartmental epidemic model.In this case, the possible "types" of infection are indexed by the infectious period,  =  F ∈ [0, ∞) , with () =  exp(− F ) (i.e., an exponentially distributed infectious period is assumed) and () =  1  F (i.e., the expected number of transmissions by an infected host is proportional to their infectious period).Substituting into Eq.S6.1 then gives Integrating and taking the largest solution between 0 and 1 of the resulting quadratic equation then reproduces the well-known formula, Similarly, the outbreak risk under branching process approximations of a wide range of more complex compartmental models, for example models with nonexponentially distributed infectious periods and/or age structure, could also be represented using Eq.S6.1.

Text S7: SARS-CoV-2 local outbreak risk with heterogeneous within-host dynamics
To account for heterogeneous within-host dynamics, we used the estimated fixed (Table S1) and random (Table S2) effects to sample within-host model parameters and incubation periods for  = 10,000 infected individuals.The infectiousness profile,  $ (), of each individual,  = 1, … , , was obtained, where this profile was averaged over different possible detection times when analysing regular antigen testing (since this assumption was found to have a very small effect on outbreak risk estimates in Fig. S4A).These individual infectiousness profiles were assumed to represent every possible infection pathway in the framework in Text S5, each equally likely, so that the outbreak risk,  =>?@A4BC , satisfies (i.e., we took  $ = 1/ for each ), where is the individual reproduction number of individual  (accounting for regular antigen testing if carried out).

Text S8: SARS-CoV-2 local outbreak risk with asymptomatic infections
We accounted for entirely asymptomatic infections using the framework in Text S5 with  = 2, with the two population subgroups corresponding to infected individuals who develop symptoms (making up a proportion,  0 = 0.745, of all infected individuals (18)) and those who remain asymptomatic throughout infection (with  -= 0.255 ; different proportions of asymptomatic infected hosts are considered in Fig. S5).
Asymptomatic infected individuals were assumed to remain undetected throughout infection if regular antigen testing is not carried out.
We assumed no difference in within-host model parameters between entirely asymptomatic infected hosts and those who develop symptoms.However, we multiplied the infectiousness profiles of symptomatic and asymptomatic hosts by different constant factors, allowing the expected total number of transmissions generated by an infected host who develops symptoms,  0 , and the corresponding quantity for an asymptomatic infected host,  -, to be varied independently.
Specifically, we chose the  0 and  -values corresponding to specified values of both the basic reproduction number,  1 =  0  0 +  - -, and the relative overall transmissibility of asymptomatic infected hosts,  G =  -/ 0 , in the absence of regular antigen testing.
We considered  G values of 0 (so that some infected individuals are entirely asymptomatic, but these individuals generate no transmissions), 0.32 (the central estimate obtained in a meta-analysis (19) conducted using data up to July 2021, prior to the emergence of the omicron variant), 1 and 2.77 (corresponding to a scenario where all undetected individuals are equally infectious at a given time since infection, regardless of whether or not they go on to develop symptoms).
In this framework, the proportion of all transmissions arising from entirely asymptomatic infectors (in the absence of regular antigen testing) is given by The  G values of 0, 0.32, 1 and 2.77 (with  -= 0.255) give values of the percentage of total transmissions that are generated by asymptomatic hosts (without antigen testing) of 0%, 10%, 26% and 49%, respectively.

Text S9: Outbreak risk under delayed and/or time-limited regular antigen testing
Here, we generalise our results to obtain an expression for the outbreak risk in scenarios where regular antigen testing is introduced reactively after an infection occurs and/or is only in place for a limited period of time.For simplicity, we consider homogeneous within-host dynamics (although the derivation presented here readily generalises to a heterogeneous population), supposing that each host infected at calendar time  transmits the pathogen at rate (, ) at time since infection  (i.e., at calendar time ( + )).Below, we first derive the outbreak risk for general (, ), before deriving a specific form of (, ) under delayed and/or time-limited regular antigen testing.
We suppose that an individual, who was infected at calendar time  , is introduced into an otherwise uninfected population at time since infection  (at calendar time ( + )).Then, conditioning on whether or not the initial infected host transmits the pathogen between times since infection  and ( + d) (and assuming no more external infections), we find that the extinction probability, (, ), satisfies (up to terms of order d -) (, ) = ( + d, )(0,  +  + d) × (, )d + ( + d, ) × (1 − (, )d).(S9.1) Rearranging and taking the limit d → 0 gives the differential equation, (where we have relabelled ̃ from the previous equation as ).The outbreak risk,  =>?@A4BC () = 1 − (0, ), following the introduction of a single newly infected host at time , is therefore the largest solution between 0 and 1 of the equation  =>?@A4BC () = 1 − exp T− Z  =>?@A4BC ( + )(, )d where  3 () is the infectiousness profile of an undetected individual at time since infection , and  2 is the relative infectiousness of a detected host.
Finally, we consider a scenario in which regular antigen testing is introduced after a delay of  I4P from the time of the first infection (where we may expect  I4P to be at least the length of the incubation period), and is carried out over a finite duration of time,  I>A .This scenario can be represented by taking  H?BA? = 0 and  4"I =  I>A in the above, and then using Eq.S9.5 to calculate  =>?@A4BC (− I4P ) numerically.In this scenario, for  ≥  4"I (i.e., after antigen testing has ended),  =>?@A4BC () is independent of  and can be calculated using Eq. 3 in the main text.Eq.S9.5 can then be solved iteratively on a grid of  ∈ [− I4P ,  4"I ] by considering successively lower  values and each time discretising the integral in Eq.S9.5 to calculate  =>?@A4BC (), since Eq.S9.5 allows  =>?@A4BC () to be calculated once  =>?@A4BC () is known for all  > .

Text S10: Details of discrete-time stochastic outbreak simulation algorithm
We verified our analytically derived estimates of the outbreak risk by comparing these values with corresponding estimates obtained through repeated simulation of a discrete-time, individual-based stochastic epidemic model (Fig. 2F and Fig. S2).In this section, we describe the simulation model and how it was used to estimate the outbreak risk.
Prior to running each outbreak simulation, we first determined and discretised the within-host dynamics that each individual, , in the population would follow if ever infected, according to the following steps: 1. Determine the individual's (continuous-time) viral load profile,  (:) (), where  is the time since infection, and their incubation period,  !"# (:) (in Fig. 2F and Fig. S2, we assumed homogeneous within-host dynamics, but in principle heterogeneity could be included).
2. Calculate the individual's undetected infectiousness profile,  3 (:) (), and probability of antigen test positivity,  . (:) (), as described in the main text (note that  . (:) is here defined as a function of time since infection, , rather than viral load).
3. Sample the (potential) time,  (:) , from the start of the day of infection to the exact (potential) infection time, uniformly between zero days and one day.= … † (:) +  !"# (:) ‡ˆ.Note that we only considered a single continuous incubation period, which exceeded 1, but if a non-trivial distribution is used, then it should be truncated to take values of at least 1 in order to avoid symptom onset occurring on the day of infection.
7. Calculate the relative infectiousness on the day of symptom onset (assuming the host is not detected before developing symptoms),  ' (:) (so that the individual's infectiousness on the day of symptom onset is  ' (:)  3,I!H#A (:) )), chosen to ensure that the continuous-and discrete-time infectiousness profiles give the same expected number of transmissions during this day (under the assumption of isolation immediately following the exact symptom onset time).

Calculate the total duration of infection (up to loss of infectiousness), 𝜏 A4#,I!H#A (:)
, as the earliest day of infection for which  3,I!H#A (:) ) .
An example discretised infectiousness profile (without regular antigen testing) is shown in Fig. S2A.
In the simulation algorithm, individuals are classified as being in one of the following states on each day: susceptible (), infected but undetected (), infected with symptom onset on the current day (and not detected prior to onset; ), infected and detected (), or recovered (specifically, no longer infectious following an infection; ).The  stage is included to allow for symptom onset (and therefore detection) occurring at any time of day, whereas for simplicity we assumed that regular antigen testing takes place only at the start of each day.The status of individual  (at a given step in the simulation) is denoted by  (:) ∈ {, , , , } .We write, for example,  V ; (:) <, to denote the indicator function that takes the value one if  (:) = , and zero otherwise.However, we emphasise that the simulation model is not a compartmental model, since different individuals in the same state are not treated identically.Now, the simulation algorithm has the following inputs: • The population size, .
• The number of antigen tests,  (:) (), conducted by individual  at the start of day  of the simulation (for each positive integer value of  ).We considered two possibilities: i.In Fig. 2F, we sampled  (:) () from a Poisson distribution with mean 1/ (independently for each individual and each day, where a range of  values were considered).This is consistent with our analytic outbreak risk derivation (since an exponentially distributed duration between tests, with mean  (measured in days), leads to a Poisson-distributed number of tests being taken each day, with mean 1/, although we note that tests may be taken at any time of day in the analytic approach), but leads to the possibility of more than one daily test.
ii.In Fig. S4B, we additionally considered a fixed (constant) gap of length  between days on which a test is taken.For each individual, we sampled the first day of the simulation on which a test is conducted uniformly between 1 and  (independently for different individuals).
The outbreak simulation algorithm consists of the following steps: 1. Initialise the time at  = 0 days and the status of each host at  (:) = .
2. Sample a single initial infected host, , according to the relative susceptibilities,  $ (i.e., host  is selected with probability  $ / ∑  W
d.For each  such that  (:) = , carry out the following steps (testing process): i. Generate a random number, , uniformly distributed between 0 and 1. ii.
f. Calculate the total infectious pressure exerted on each susceptible individual over the current simulation day, -. (S10.1) g.For each  such that  (:) =  , carry out the following steps (transmission process): i. Generate a random number, , uniformly distributed between 0 and 1.
For each testing scenario considered, we carried out 100,000 model simulations in a population of  = 1,000 individuals.The outbreak risk was estimated as the proportion of model simulations in which the total number of individuals ever infected exceeded 10% of the total population (see Fig. S2).---1.5 Assumed (other values considered in Fig. 3 and elsewhere) Mean interval between antigen tests when regular testing conducted  days 2 Assumed (Fig. 2BC only; a range of values considered elsewhere) Table S1: Default parameter values used in our analyses.The values given here for parameters in our within-host, detection and infectiousness models were used in our analyses except where explicitly stated otherwise.Note that the values of the within-host model parameters , ,  and  789 here are population median estimates (fixed effects); estimates of random effects are given in Table S2.

Fig. S4
Fig. S4: Effect of details of implementation of antigen testing in our modelling approach on the outbreak risk under regular antigen testing.A. The outbreak risk for different values of the mean interval between antigen tests, comparing our default analytic approach using an expected infectiousness profile that averages over the individual infectiousness profiles of hosts with different detection times (blue), and a more complex approach in which variations in detection times are accounted for directly (red dashed).Variable detection times were accounted for by sampling the detection times of 10,000 infected individuals and using Eq.S5.11 to calculate the outbreak risk (assuming the resulting infectiousness profiles of the 10,000 hosts correspond to equally likely possible infection pathways, similarly to how we accounted for heterogeneous within-host dynamics in Text S7).

B. The outbreak risk for different values of the mean interval between tests, comparing our default
analytic approach with an exponentially distributed interval between tests (black dashed), and both the analytic (blue) and simulation-based approaches (red crosses) under the alternative assumption of a fixed (constant) interval between tests.Note that in the analytic approach with a fixed interval, we used sampled detection times since the expected infectiousness profile was not readily available in this case.antigen tests, assuming that the proportion of entirely asymptomatic infected hosts is 0% (black dashed), 17.0% (blue), 25.5% (red; as in Fig. 5) or 38.2% (orange) -the latter three values represent the lower 95% confidence interval limit, central estimate, and upper confidence limit obtained in a meta-analysis (18), respectively -and that when regular antigen testing does not take place, an
from the target cell-limited model (3),

4 . 5 . 6 .
For each day since infection,  I!H#A ≥ 1 (where  I!H#A is integer-valued and the day of infection is denoted day 0), calculate the discretised undetected infectiousness,  3,I!H#A (:) ( I!H#A ) , as the average value of  3 (:) () between times since infection ( I!H#A −  : ) and ( I!H#A −  : + 1).Note that implicit in our simulation algorithm is the assumption that hosts cannot transmit the pathogen on the day of infection (i.e., Calculate the probability,  .,I!H#A (:) ( I!H#A ) =  . (:) ( I!H#A −  : ), of a test taken at the start of day of infection  I!H#A ≥ 1 giving a positive result.Calculate the discretised incubation period,  !"#,I!H#A (:)

Fig. S1 :
Fig. S1: Reconstructed viral dynamics for individual hosts.Individual-level within-host model fits to longitudinal SARS-CoV-2 viral load data are shown (see the section "Within-host model and parameter estimation" of Materials and Methods in the main text).Overall, we used data from 521 individuals with SARS-CoV-2 omicron variant infections (4); here, individual model fits are shown for 100 randomly chosen individuals.In each panel (corresponding to a single individual), the dots indicate the measured viral load data, and the solid curves give the estimated viral load at different times relative to symptom onset.

Fig. S5 :
Fig. S5: Effect of the proportion of asymptomatic infected hosts on the outbreak risk under regular antigen testing.A. The outbreak risk for different values of the mean interval between asymptomatic infected individual generates (on average) a factor  > = 0.32 times the average number of transmissions generated by an individual who develops symptoms.B. Equivalent panel to A with  > = 1.C. Equivalent panel to A with  > = 2.77.

Fig. S6 :
Fig. S6: Effect of delayed and/or time-limited antigen testing.A. The outbreak risk for different delays from the time of the first infection to the introduction of regular antigen testing, assuming an infinite duration of testing, and either 1 (blue), 2 (red) or 3 (orange) days between tests (on average).B. The outbreak risk for different durations of antigen testing, assuming a delay of one incubation period (4.6 days) from the first infection to the start of testing (i.e., testing starts following the detection of a symptomatic case), and either 1 (blue), 2 (red) or 3 days (orange) between tests (on average).C. The outbreak risk for different values of the mean interval between tests with a total of 5 (blue), 10 (red), 20 (orange) or 40 (purple) tests available to each individual (on average), assuming a delay of one incubation period from the first infection to the start of testing.
per person 10 total tests per person 20 total tests per person 40 total tests per person C.
a specified individual) is exponentially distributed with mean .A similar argument to that in Text S3 can be used to show that the probability,  2 (, ), of an individual infected at calendar time  having been detected by time since infection  <  !"# (where  !"# is the incubation period, with  2 (, ) = 1 for  ≥  !"# ), is We now derive the form of (, ) under delayed and/or time-limited regular antigen testing.Specifically, we suppose that testing only takes place between calendar times  H?BA? and  4"I , and that within that time period, the interval between tests (for

Table S2 : Estimated random effects for within-host model parameters.
The estimated quantities correspond to the standard deviation between different infected hosts of individual values of the natural logarithm of the parameters , ,  and  789 (see the section "Within-host model and parameter estimation" of Materials and Methods in the main text for details; population parameter values (fixed effects) and units are given in TableS1).

Table S3 : Vaccination and previous infection histories of individuals in study dataset.
We used published viral load data from 521 individuals with SARS-CoV-2 omicron variant infections (4) in our analyses.Here, the COVID-19 vaccination and previous SARS-CoV-2 infection (i.e., prior to the infection that was considered in the study dataset) histories of these 521 individuals are summarised.Individuals labelled as fully vaccinated (not boosted) had received (at the time of latest PCR data collection) either two doses of an mRNA vaccine, or one dose of the Janssen (Ad.26.COV2.S) adenovirus vector-based vaccine, while individuals labelled as boosted had received an additional mRNA vaccine dose.