key: cord-0279129-8zcjabo6
authors: Gozzi, N.; Chinazzi, M.; Davis, J. T.; Mu, K.; Pastore y Piontti, A.; Vespignani, A.; Perra, N.
title: Preliminary modeling estimates of the relative transmissibility and immune escape of the Omicron SARS-CoV-2 variant of concern in South Africa
date: 2022-01-05
journal: nan
DOI: 10.1101/2022.01.04.22268721
sha: a072ef4604f049d585a2a4501f98950b7f3923b2
doc_id: 279129
cord_uid: 8zcjabo6

We develop a stochastic, multi-strain, compartmental epidemic model to estimate the relative transmissibility and immune escape of the Omicron variant of concern (VOC) in South Africa. The model integrates population, non-pharmaceutical interventions, vaccines, and epidemiological data and it is calibrated in the period May 1st, 2021 - November 23rd, 2021. We explore a parameter space of relative transmissibility with respect to the Delta variant and immune escape for Omicron by assuming an initial seeding, from unknown origin, in the first week of October 2021. We identify a region of the parameter space where combinations of relative transmissibility and immune escape are compatible with the growth of the epidemic wave. We also find that changes in the generation time associated with Omicron infections strongly affect the results concerning its relative transmissibility. The presented results are informed by current knowledge of Omicron and subject to changes.

has a marked growth advantage over the Delta VOC. The rapid diffusion of Omicron, in a background of receding Delta, might be explained by increased transmissibility, immune escape, or a combination of both. Early evidence from statistical analysis of possible reinfections, suggests indeed significant capabilities of escape from naturally acquired immunity [7] .

Here, we develop a multi-strain, stochastic, compartmental epidemic model for South Africa to identify some of the features of the Omicron VOC compatible with epidemiological observations. The model takes as input data about demographics, age-stratified contact patterns, non-pharmaceutical interventions (NPIs), vaccine rollout, and confirmed COVID-19 deaths and cases (see Materials and Methods for details). We perform a multi-stage calibration applying an Approximated Bayesian Computation (ABC) method [8] . For Omicron, we explore a parameter space defined by the combination of the relative transmissibility with respect to Delta and immune escape with respect to both naturally acquired immunity and vaccines. We obtain the joint posterior distribution of these parameters compatible with the observations for the confirmed cases until December 13 th , 2021 (rescaled to account for under-reporting). The results highlight the non-identifiability of both relative transmissibility and immune escape. Rather, at this stage it is possible to define a region of credible values where an increase in relative transmissibility is compensated by a reduction of immune escape and vice-versa. It is important to notice how the joint posterior distribution is function of the seeding timing and size as well as of the generation time of Omicron infections. Short generation times (i.e., 3.5 days) with respect to the Delta VOC (i.e., 5.5 days) shift the joint posterior distribution to a region with lower values of transmissibility advantage for Omicron. The presented results are informed by current knowledge of the variant and subject to changes as new evidence and data will be available. data on confirmed deaths and cases (see more information in the Material and Methods section). In order to estimate the properties of the Omicron variant we adopt a multi-stage calibration process. Starting around May 2021, the country experienced a third pandemic wave fuelled by the Delta VOC [7] . This variant was able to replace the Beta VOC, which was responsible for the second wave. Before the appearance of Omicron, Delta was responsible for the large majority of cases. Hence, we first fit the model allowing just for one strain in the period May 1 st , 2021 -November 23 rd , 2021. To this end, we adopt the ABC method applied to the weekly confirmed deaths (see Material and Methods). In particular, we obtain the posterior distributions for transmissibility, delay between deaths and their reporting, initial conditions, seasonality, infection fatality rates multiplier respect to the estimates from Ref. [9] , and under-reporting in deaths (see Material and Methods for more details). Across the board we estimate that the surveillance system in South Africa was able to detect 1 out of 16 infections in the period from May to November , 2021. These numbers are in line with independent estimates done by Institute for Health Metrics and Evaluation (IHME) which suggests the detection of 1 out of 15 cases [10, 11] . We then study the impact of Omicron by assuming an initial seeding, from unknown origin, in the first week of October 2021. Preliminary evidences from phylogenetic analysis suggest the median date of the common ancestor, of all available Omicron samples, in early October (90% CI: [30 September -20 October]) [12] .

As we do not have information about the number of initial seeds, we sample a flat prior distribution σ = [10 − 1000] seeds. We define the Omicron transmissibility by setting η = R Omicron 0 /R Delta 0 as the ratio of the basic reproductive numbers for Omicron and Delta (see Materials and Methods for more details). The immunity evasion of Omicron is introduced with single factor α which describes the reduction of vaccine efficacy and protection from reinfection (see Material and Methods for more details). We explore the η × α × σ parameter space and apply an Approximate Bayesian Computation approach to select values compatible with the evidence for the number of confirmed cases.

Spreading and immune escape potential. In Figure 1 we plot the joint posterior distribution of η and α values. We consider two cases: in the first one, Omicron has the same generation time of Delta (T G = 5.5 days), while in the second one we assume a shorter generation time (T G = 3.5 days) [13] .

We start with a flat three-dimensional prior (on η, α, and number of initial seeds). Note how the twodimensional plot is a projection of the posterior values of the initial seeds. While large regions of the parameter space are rejected by the ABC approach, it emerges a plausible region that corresponds to the non-identifiable nature of both parameters. Generally speaking, the higher the immune escape α, the smaller η. Intuitively, Omicron's large value of immune escape can be compensated by changes in the relative transmissibility with respect to Delta and vice versa. The number of initial seeds plays a role. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 5, 2022. Path towards dominance. In Figure 2 we plot the share of cases due to the Omicron VOC considering the joint posterior distribution for η, α and σ. The plot suggests that Omicron reached dominance (i.e., more than 50% of cases) in mid-November and replaced Delta by early December. This finding is in line with current genomics data from the sample collected in the region [14] . To put this into perspective, estimates about the time to dominance of the Alpha variant across Europe are between 3 to 4 months [15] .

Reproduction number estimates. In Figure 3 -A we plot the reproductive numbers R t (estimated via Epiestim [16] ) for the Delta and Omicron VOC assuming the same generation time T G = 5.5 days.

The first observation is that the Delta VOC is subcritical (i.e., R t ∼ 0.8). This finding is consistent with the decreasing trends before the emergence of Omicron. The values of the reproductive number of Omicron are above 1.6 until the last few data points where we see an inflection. By looking at both variants together we observe how the arrival of Omicron quickly shifted the values of R t from below one to values around 1.7 in about two months since the seeding. In Figure 3 -B, we plot the ratio between the 4 . CC-BY-ND 4.0 International license It is made available under a perpetuity.

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The copyright holder for this this version posted January 5, 2022. 

Key questions about the Omicron VOC revolve around its relative transmissibility with respect to Delta, the potential for immune escape, and its severity. Although large uncertainties are surrounding Omicron, early statistical analyses suggest the variant is indeed able to reinfect individuals at rates higher than previous VOCs [7] and vaccines might be less effective against infection [5] . Our results are in line with these findings and identify a joint posterior distribution for the relative transmissibility with respect to Delta (η), and immune escape (α) of the Omicron variant. Current data however does not allow to identify uniquely both parameters, and we find a region where a large spreading advantage might be compensated by a limited immune escape and vice versa. Interestingly, we found that the assumed is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 5, 2022. 

Demographic and epidemiological data. We use epidemiological data from the COVID-19 Data

Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University and from official sources [18, 19] . The number of individuals in different age groups is taken from the United Nation World Population Prospects [20] . is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 5, 2022. ; https://doi.org/10.1101/2022.01.04.22268721 doi: medRxiv preprint CoV-2 variant (which was prevalent in South Africa during the period considered before the arrival of Omicron), we set ϵ −1 = 3 days and µ −1 = 2.5 days [21] [22] [23] . We consider individuals divided into 10 age groups: [0 − 9, 10 − 19, 20 − 24, 25 − 29, 30 − 39, 40 − 49, 50 − 59, 60 − 69, 70 − 79, 80+], and we describe frequency of contacts between age groups with a country-specific contacts matrix from Ref. [24] . The transmission rate is β and the force of infection depends on the age-stratified contact matrix.

We compute the daily number of deaths from individuals entering the R compartment using the age-stratified Infection Fatality Rate (IFR) from Ref. [9] . To account for delays due to reporting and hospitalization we record deaths computed on the recovered in day t after ∆ days. We also introduce a seasonal term to account for changes in factors such as humidity and temperature that can influence transmissibility [25, 26] . This implies a modulation of the effective reproductive number

where i refers to the hemisphere considered, and t max,i is the day associated to the maximum of the rescaling function. For the southern hemisphere it is fixed to July 15 th . In the simulations, we set α max = 1 and consider α min as a free parameter (see more details below).

We extend this framework with specific compartments to account for vaccinations and the introduction of the Omicron VOC. First, we model vaccinations as follows. Individuals who received the 1 s t dose of vaccine transition to a new compartment V 1 . Infection probability for V 1 individuals is reduced by a factor 1−V E S1 , where V E S1 represents the effectiveness of vaccine against infection. If they get infected their IFR is also reduced by a factor 1 − V E M 1 . It follows that the overall efficacy of the 1 st dose against

. V 1 individuals then receive the second inoculation and transition to the compartment V 2 . The 2 nd dose has an efficacy V E S2 and V M 2 (overall efficacy against

). We consider all vaccinated individuals are less infectious by a factor (1 − V E I ) [27] . We assume that S, L, and R individuals can get the vaccine and since protection is not immediate, we introduce a delay of ∆ V days between administration (of both 1 st and 2 nd dose) and actual effect of the vaccine. We consider the number of 1 s t and 2 nd doses administered daily in South Africa from Ref. [28] and we assume that the vaccine rollout proceeded prioritizing the elderly.

The introduction of a SARS-CoV-2 variant is modeled as follows. We add specific L and I compartments to account for individuals who are infected with Omicron. We assume that its transmission rate is ψβ. For example, ψ = 0.5 indicates that the transmission rate of Omicron is half that of Delta, ψ = 1.0 the same of Delta, and ψ = 2.0 twice that of Delta. In the results presented in Fig. 1 is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 5, 2022. ; https://doi.org/10.1101/2022.01.04.22268721 doi: medRxiv preprint in the infected compartments (half in I and half in L compartment), and we distribute them in different age groups proportionally to their size. When we introduce the first Omicron infection we also move R individuals to a new compartmentR. We use a parameter α to describe the ability of Omicron VOC to escape natural and vaccine acquired immunity. We assume that individuals in V 1 , V 2 , andR compartments see their protection provided by immunity reduced by a factor (1 − α). We assume also that initial protection ofR is equal to that of V 2 individuals.

Modeling of mitigation policies. We quantify the time varying variation in contacts due to mitigation policies by using Google mobility reports [29] . The Google mobility report provides the percentage change r l (t) on day t of total visitors to specific locations l with respect to a pre-pandemic baseline. We turn this quantity into a rescaling factor for contacts such as ω(t) = (1 + r l (t)/100) 2 , by considering that the number of potential contacts per location scales as the square of the the number of visitors.

The factor ω(t) is then multiplied to the overall contacts matrix C. As r l (t) we use the average of the fields workplaces percent change from baseline, retail and recreation percent change from baseline and transit stations percent change from baseline.

Model Calibration. We use an Approximate Bayesian Computation (ABC) approach [8, 30] . A prior distribution P (θ) is defined for the parameters θ. At each step of the calibration procedure, a set of parametersθ is sampled from P (θ) an an instance of the model is generated usingθ. Then an output quantity E ′ from the model is compared to the corresponding real quantity E using a distance metric s(E, E ′ ). If s(E, E ′ ) is smaller than a predefined tolerance δ, then the setsθ is accepted, otherwise is rejected. The procedure continues until N sets are accepted. The empirical distribution of the sampled θ is an approximation of the real posterior distribution of the parameters. Model estimates are then obtained generating an ensemble of trajectories sampled from the approximate posterior. Here we use the weighted mean absolute percentage error (wMAPE) as distance metric and weekly deaths as output quantity, and we set δ = 0.25. The parameters θ and the related prior distribution are:

• the transmissibility β; we explore uniformly values such that the reproductive number on the first day of simulation is between 1.0 and 2.5;

• the seasonality factor α min ∼ U (0.5, 1.0) (0.5 implies strong seasonality while 1.0 no seasonality);

• the delay in deaths ∆ ∼ U (10, 30) (discrete values);

• the initial number of infected individuals; we explore uniformly values between 1 and 10 times the number of reported cases in the week before the start of the simulation. We then assign these individuals to the infected compartments (L, I) proportionally to the time spent there by individuals (ϵ −1 for L and µ −1 for I);

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The copyright holder for this this version posted January 5, 2022. ; https://doi.org/10.1101/2022.01.04.22268721 doi: medRxiv preprint

• the initial number of recovered; we explore uniformly values between 2 and 20 times the total number of reported cases up to the start of the simulation;

• the percentage of deaths that are reported ∼ U (25%, 100%);

• a multiplier of the IFR ∼ U (0.5, 2.0)

The model is calibrated over the period May 1 st , 2021 -November 23 rd , 2021.

We use the ABC approach also to identify the posterior of Omicron parameters: relative transmissibility respect to Delta η = R Omicron 0 /R Delta 0 , immune escape potential α, and number of initial seeds σ.

We consider values of η between 0.25 and 3.0, values of α between 0% and 100%, and 10, 50, 100, 500, 1000 initial Omicron seeds introduced in first week of October 2021. We repeat the simulations over this grid of (η, α, σ) values during the period November 26 th , 2021 -December 13 th , 2021 and we compare the simulated incidence to the reported daily incidence in South Africa using the wMAPE. For each triplet (η, α, σ), we perform 1500 stochastic realizations and we compute the posterior distribution considering the top 5% runs.

. CC-BY-ND 4.0 International license It is made available under a perpetuity.

is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 5, 2022. ; https://doi.org/10.1101/2022.01.04.22268721 doi: medRxiv preprint . CC-BY-ND 4.0 International license It is made available under a perpetuity.

is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 5, 2022. ; https://doi.org/10.1101/2022.01.04.22268721 doi: medRxiv preprint . CC-BY-ND 4.0 International license It is made available under a perpetuity.

is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint

The copyright holder for this this version posted January 5, 2022. ; https://doi.org/10.1101/2022.01.04.22268721 doi: medRxiv preprint

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