SARS-CoV-2 antibody dynamics and transmission from community-wide serological testing in the Italian municipality of Vo’

In February and March 2020, two mass swab testing campaigns were conducted in Vo’, Italy. In May 2020, we tested 86% of the Vo’ population with three immuno-assays detecting antibodies against the spike and nucleocapsid antigens, a neutralisation assay and Polymerase Chain Reaction (PCR). Subjects testing positive to PCR in February/March or a serological assay in May were tested again in November. Here we report on the results of the analysis of the May and November surveys. We estimate a seroprevalence of 3.5% (95% Credible Interval (CrI): 2.8–4.3%) in May. In November, 98.8% (95% Confidence Interval (CI): 93.7–100.0%) of sera which tested positive in May still reacted against at least one antigen; 18.6% (95% CI: 11.0–28.5%) showed an increase of antibody or neutralisation reactivity from May. Analysis of the serostatus of the members of 1,118 households indicates a 26.0% (95% CrI: 17.2–36.9%) Susceptible-Infectious Transmission Probability. Contact tracing had limited impact on epidemic suppression.


Contents Supplementary Methods
Section 1 Serological test details 3 Section 2 Contact and ground truth definitions 4 Section 3 Seroprevalence estimates details 4 Section 4 Within-household transmission model 5 Section 5 SARS-CoV-2 transmission model with contact tracing 6 Supplementary Note 1 8  Tables   Table 1 SARS-CoV-2 exposure authentication criteria 12 Table 2 Observed test results combinations in the May and November 2020 serosurveys 12 Table 3 Assay-specific performance against the different ground truth definitions 13 Table 4 Positive (+) Serological results on the subjects tested with all three assays in May and November 2020.

Supplementary Figures
13 Table 5 Association analysis on antibody titres 14 Table 6 Association analysis on antibody decay rates 14 Table 7 Frequency of comorbidities in symptomatic and asymptomatic SARS-CoV-2 infected individuals 14 Table 8 Frequency of medication type in symptomatic and asymptomatic SARS-CoV-2 infected individuals 15 Table 9 Observed within-household final size distribution in Vo' 15 Table 10 Parameter estimates from the within-household transmission model 16 Table 11 Parameter estimates from the transmission model fitted to the prevalence data among traced contacts and in the study population 17 Table 12 Real-time RT-PCR primers and probes 17

Section 1. Serological test details
Abbott ARCHITECT SARS-CoV-2 IgG assay is a chemiluminescent microparticle immunoassay (CMIA) proposed for the qualitative detection of IgG class antibodies against N recombinant SARS-CoV-2 antigen. The test was performed on ARCHITECT i2000SR platform as indicated by the manufacturer.
The serum (150 μL), the SARS-CoV-2 antigen coated paramagnetic microparticles and the assay diluent were mixed and underwent a first incubation. If IgG antibodies against N SARS-CoV-2 antigen were present in the sample, they bound to the SARS-CoV-2 antigen coated microparticles. Following a washing cycle, anti-human IgG acridinium-labelled conjugate was added and the reaction mixture was incubated again. After a second washing, the reagent solutions were added and the resulting chemiluminescent reaction was measured as a relative light unit (RLU) and then expressed in the calculated Index (S/C). The cut off is 1.4 Index (S/C), every result <1.4 was considered negative and any result >=1.4 positive.

DiaSorin
LIAISON® SARS-CoV-2 S1/S2 IgG produced by DiaSorin, is a chemiluminescence immunoassay (CLIA) test. It is employed for the quantitative measurement of antibodies of class IgG directed against antigens S1 and S2 of SARS-CoV-2 and its results have been directly related to the titres of neutralizing antibodies against SARS-CoV-2 identified by plaque-reduction neutralization test (PRNT) [1]. The test was performed on LIAISON® XL Analyzer as indicated by the manufacturer. In brief, magnetic particles coated by recombinant S1 and S2 specific antigens were used as solid phase in presence of mouse monoclonal antibodies anti-human IgG bound to an isoluminol derivative.
During the first incubation, the anti-SARS-CoV-2 IgG antibodies sited in the calibrators, controls and possibly samples, bound to the solid phase via recombinant S1 and S2 antigens. During the second incubation, the conjugated mouse antibodies reacted with the anti-SARS-CoV-2 IgG already bound to the solid phase. After each incubation, unbound material was removed by a wash cycle. The starter reagents were then added to induce a chemiluminescence reaction. The light signal, and then the quantity of antibody-isoluminol conjugate still present as bound to the IgG, was measured by a photomultiplier, in relative light units (RLU), then expressed in arbitrary units (AU/mL). A result < 12 AU/ml has to be evaluated as negative, from 12 to 15 AU/ml equivocal and >15 AU/ml positive.

Roche
Elecsys® Anti-SARS-CoV-2 is an electro-chemiluminescence immunoassay (ECLIA) based on doubleantigen sandwich assay, intended for the qualitative detection of IgG antibodies directed against SARS-CoV-2 N antigen in human serum and plasma. The test was performed on Cobas e 601 Analyzer as indicated by the manufacturer.
In sum, 20 μL of the patient's serum were incubated in presence of biotinylated and ruthenylated N antigen. If SARS-CoV-2 antibodies were in the sample, they developed double-antigen sandwich immune complexes with the recombinant N antigen. During the second incubation, the addition of streptavidin-coated microparticles allowed the binding of the complexes to the solid phase. The particles composing the solid phase were then magnetically captured onto the surface of an electrode to which a voltage was applied, inducing an electrochemiluminescence reaction. The signal was measured with a photomultiplier and expressed as an index. Therefore, a result < 1 cut-off index (COI) was evaluated as negative, >=1 COI as positive.

Contact definition
'Direct contact' definition includes i) contacts as reported by the infected subjects in the contact tracing forms or in the follow up interviews (denoted with code "1" in the dataset) and ii) contacts inferred based on household composition (denoted with code "3"). The 'indirect contacts' definition includes subjects who had a direct contact with a subject having a positive Abbott, DiaSorin, Roche or PCR test (i.e., positive to either test, denoted with code "2" in the dataset). Due to the limited information on the type of contact occurring in two contact settings (variables ending in 'place' in the data), we considered all contacts reported in those settings as indirect contacts.

Ground truth definitions
In the baseline definition, we considered as SARS-CoV-2 infected all subjects who had (a) positive PCR test in February or March 2020 and/or (b) positive results to two serological tests with different target and/or (c) micro-neutralisation titres > 1:40 (1/dil). The 'direct contacts' definition defines as SARS-CoV-2 infections all subjects who met the baseline definition and also includes subjects who had a positive result to any serological assay and a history of direct contact with an infection meeting the baseline ground truth definition. The 'indirect contacts' definition defines as SARS-CoV-2 infection all subjects who met the criteria of the 'direct contact' definition plus those who had a positive result to any serological assay and a history of indirect contact with a subject meeting the baseline or direct contact ground truth definition (Table S1).

Section 3. Seroprevalence estimates details
The log-likelihood of the model is given by: where and respectively denote the number of samples tested in-house to assess the sensitivity and specificity of assay (Table 3, see footnote); and respectively denote the number of positive samples from the in-house experiments assessing the sensitivity and specificity of assay (Table 3, see footnote); and denote the sensitivity and specificity parameters of assay ; and denotes the number of samples in category for j positive (+) or negative (-) ( Table  S2, May). Let denote the probability of having been infected by SARS-CoV-2. The probability of observing is given by and 1 + ( ) = 1 if = + and 0 otherwise, while 1 − ( ) = 1 if = − and 0 otherwise. We assumed uniform prior distributions and explored the posterior distribution of the parameters using the Metropolis-Hastings algorithm using 100,000 iterations, a thinning factor of 1 every 100 and a burn-in period of 100 samples. The p-value was calculated from the goodness of fit chi-squared statistic with 6 degrees of freedom, obtained from the central posterior estimates. For each assay, we estimate the positive predictive value (PPV) and negative predictive value (NPV) from the posterior distribution of the assay-specific sensitivity, specificity and prevalence using equations (5) and (6)

Section 4. Within-household transmission model
We quantified the extent of within-household SARS-CoV-2 transmission implementing the methods developed by Fraser et al. 2 , which are an extension of the classic Reed-Frost chain-binomial model. Let ( , ) denote the number of households of size n with m infections. The mean attack rate by household size is the proportion of subjects infected by household size and is defined as The secondary attack rate by household size is the proportion of infected household members of an infected subject and is defined as The number of non-primary infections by household size is given by ( − 1) ( ). The household attack rate by household size is the proportion of households with at least one infected household member and is defined as The household size distribution is denoted where is the number of households sampled = ∑ ∑ ( , ) .

Let
, 0 denote the probability of observing infections in a household of size given 0 susceptible individuals, denote the escape probability from sources of infection outside the household (i.e., 1 − denotes the probability of infection from sources outside the household) and ℎ the hazard of infection for each members of a household of size . Fraser et al. 2 show that , 0 can be estimated as the solution of the system of equations where Φ ( ) = [exp (−ℎ )] is the moment generating function of the distribution of hazards in households of size . The Susceptible-Infectious Transmission Probability (SITP) is given by = 1 − Φ (1). Following Fraser et al. 2 , the baseline assumption is that Φ ( ) = = − . In model variants V we assume that ℎ has a Gamma distribution with mean and shape , i.e., Φ ( ) = /( + ) . In model variant P we assume that = / and = otherwise. In model variant X we assume that a proportion of subjects isolate and the probability of observing infections in a household of size with 0 susceptible individuals is given by In model variant A we allow for a proportion of subjects to serorevert (i.e., test seronegative despite having been infected) and in this model variant the probability of observing infections in a household of size with 0 susceptible individuals is given by All models estimate and and the basic Reed-Frost model is obtained for = 0, ⟶ +∞, = 0 and = 0 which are the default parameter values. We explore all possible 2 4 model variants (i.e., parameter combinations). For instance, model PVX estimates , , , and . We define model variant Z, an extension of model variant P, with an additional parameter that provides an alternative interpolation between frequency and density dependent transmission, = /( − ) . We also tested a two-group model, denoted by T, where the moment generating function was given by The final distribution was given by = , and parameter inference was conducted in a Bayesian framework, using the Metropolis-Hastings algorithm. We used the Deviance Information Criterion (DIC) for model selection, which is based on the deviance . We used uniform prior distributions, run the chains for 10,000 iterations, thinned them by a factor of 1/100 and used a burn-in period of 100 iterations. The overall Susceptible Infectious Transmission Probability (SITP) was estimated from 1,000 samples of the posterior distribution using formula where

Dynamics of SARS-CoV-2 transmission without contact tracing
The flow diagram of the transmission model is given in Supplementary Figure S4. Following Lavezzo et al. 22 , we assumed that the population of Vo' was fully susceptible to SARS-CoV-2 (S compartment) at the start of the epidemic. Upon infection, subjects incubate the virus (E compartment) and have undetectable viraemia for an average of 1/ days before entering a stage (TP pre compartment) that lasts an average of 1/ days, in which subjects show no symptoms and have detectable viraemia. We assume that a proportion of the infected population remains asymptomatic throughout the whole course of the infection (IA compartment) and that the remaining proportion 1 − develops symptoms (IS compartment). We assume that symptomatic (IS), asymptomatic (IA+pTP pre ) and presymptomatic ((1-p)TP pre ) subjects contribute to the onward transmission of SARS-CoV-2 and that symptomatic, asymptomatic and pre-symptomatic subjects transmit the virus for an average of 1/ + 1/ days. We further assume that the virus can be detected by swab testing beyond the duration of the infectious period; this assumption is compatible with the hypothesis that transmission occurs for viral loads above a certain threshold but the diagnostic test can detect the presence of virus below the threshold for transmission. Compartments TP post S and TP post A respectively represent symptomatic and asymptomatic subjects who are no longer infectious but have a detectable viral load, and hence test positive. Eventually, the viral load of all infections decreases below detection and subjects move into a test negative (TN) compartment. We assume a step change in the reproduction number on the day that lockdown started. We assume that the reproduction number is given by 0 1 =  ( 1  + 1  ) at the start of the epidemic and that it drops to 2 = 0 1 after the start of the lockdown, where 1 − represents the percent reduction in 0 1 due to the intervention. We let denote the number of subjects swabbed on survey ( = 1,2) and let , and respectively denote the number of swabs testing positive among asymptomatic, pre-symptomatic (i.e. those showing no symptoms at the time of testing but developing symptoms afterwards) and symptomatic subjects, respectively. We assume that the number of positive swabs among symptomatic, pre-symptomatic and asymptomatic infections on survey follows a binomial distribution with parameters and  , where  represents the probability of testing positive on survey for class X (= A,S). For symptomatic subjects,  is given by  = , assuming perfect diagnostic sensitivity and specificity.

Modelling contact tracing
We modelled the effect of contact tracing by adding compartments indexed by Q into the model (green compartments in Supplementary Figure S4), representing susceptible traced subjects in quarantine (SQ) and infected traced subjects isolated (during any stage of the infection, EQ, TP pre Q, IQ, TP post Q and TNQ). We assumed that susceptible subjects were detected and quarantined at rate and that infected subjects (during any stage of the infection, EQ, TP pre Q, IQ, TP post Q and TNQ) were detected and isolated at a rate . We assumed two differential rates of detection and isolation to capture the simultaneous implementation of contact tracing with mass testing, which contributed to the detection of infected subjects by contact tracing. We assumed complete isolation of traced subjects, i.e., that isolated infected subjects did not transmit the disease onwards and, given the time scale of the epidemic in Vo', that quarantined susceptible subjects were completely protected against the infection for the whole duration of the first wave. We assumed that contact tracing started on 24 th February 2020. The probability that traced contacts ever testing positive is given by We assumed that the observed cumulative number of PCR positive traced subjects + (= 44) followed a binomial distribution with parameters (= 190) and probability of ever having tested positive + .
The probability of being traced among infected subjects is given by = − − + − . We assumed that the number of PCR positive traced subjects + (= 44) followed a binomial distribution with parameters (= 100) and probability .

Calibration and parameter inference
The likelihood of the model is given by the product of the binomial distributions for symptomatic, pre-symptomatic and asymptomatic subjects at times , = 1,2, the probability that traced contacts test PCR positive and the probability that PCR positive subjects are traced. Inference was conducted in a Bayesian framework, using the Metropolis-Hastings Markov Chain Monte Carlo (MCMC) method with uniform prior distributions. We fixed the average generation time (equal to 1/ + 1/ + 1/ ) to 7 days and let the model infer 1/ and 1/. We explored the following values of 0 1 : 2.1, 2.4, 2.7, which are compatible with a doubling time of 3-4 days, as observed in Vo' and elsewhere in the Veneto region. We assumed that seeding of the infection occurred on 4 February 2020. Following the results obtained in Lavezzo et al. 4 , we assumed a fixed average duration of viral detectability beyond the infectious period 1/ equal to 4 days. We estimate the number of infections introduced in the population from elsewhere at time 0 (4 February 2020), the proportion of asymptomatic infections , the average durations 1/ , 1/ and 1/, the percent reduction in 0 1 due to mass testing and the implementation of the lockdown (1 − )100% and the rates of isolation of susceptible traced contacts and infected traced contacts .

Counterfactual analysis
We fitted our baseline scenario including mass testing and lockdown and contact tracing (MT + CT scenario) to the data collected from Vo'. In a counterfactual analysis, we simulated the impact on the epidemic final size of each intervention implemented in isolation, i.e., (i) mass testing and the lockdown in the absence of contact tracing (MT scenario), and (ii) contact tracing in the absence mass testing and the lockdown (CT scenario). For both scenarios, we sampled 100 realisations from the posterior distribution of the parameters and in the MT scenario we simulated from the model having assumed no isolation due to contact tracing ( = 0 and = 0); in the CT scenario we simulated from the model having assumed no reduction in the reproduction number due to mass testing and lockdown ( = 0). We also simulated what impact increased or reduced contact tracing would have had on the epidemic final size. We explored the following scenarios: (iii) mass testing and lockdown in the presence of contact tracing with reduced (half) the estimated contact tracing efforts (MT + CTx0.5 scenario), (iv) mass testing and lockdown in the presence of contact tracing with enhanced (double) the estimated contact tracing efforts (MT + CTx2 scenario); (v) contact tracing implemented in the absence of mass testing and lockdown with enhanced (double) the estimated contact tracing efforts (CTx2 scenario); (vi) contact tracing implemented in the absence of mass testing and lockdown with enhanced (four times) the estimated tracing efforts (CTx4 scenario). In the scenarios with enhanced or reduced contact tracing efforts we multiplied the rates of isolation due to contact tracing by the assumed multiplier (e.g., for the CTx2 scenario and were fixed to 2 times the sampled realisations from the posterior distribution). In the CTx0.5, CTx2 and CTx4 scenarios we assumed no mass testing and lockdown effect (i.e., fixed = 0) while in the MT + CTx0.5 and MT + CTx2 scenarios we sampled for the posterior distribution and fixed and to half and twice the sampled posterior values, respectively. For each scenario, we estimated the relative reduction in the epidemic final size compared to the unmitigated scenario by dividing the estimated final size with interventions by the estimated final size without interventions. The relative reductions were estimated by simulating from the model having sampled 100 estimates from the posterior distribution of the parameters.

Supplementary Note 1
Using the baseline ground truth definition, we found no significant trend in the antibody titres with the number of days since symptom onset, and no significant differences in the mean antibody titres of symptomatic versus asymptomatic infections, of hospitalised versus non-hospitalised infections (except for the DiaSorin assay in November, p = 0.04), or by sex (Supplementary Table S5). We found no statistically significant difference in the antibody decay rates of symptomatic versus asymptomatic subjects, nor in hospitalized versus non-hospitalized infections, or by sex (except for DiaSorin, p = 0.05; Supplementary Table S6). Among asymptomatic infections, we observed no significant association between antibody decay rate and BMI (Supplementary Table S6). No significant association was found between symptom occurrence and age, nor between symptom occurrence and BMI category, whether or not age groups were included in the model. We also found no significant association between symptoms occurrence and comorbidities (Supplementary Table  S7) nor between symptoms occurrence and medical treatment (Supplementary Table S8 Quarantine and isolation are modelled by removing infections from the general community at rates and respectively, starting from 24 th February 2020 onwards. We assumed a closed population (i.e., no births and deaths) and neglected SARS-CoV-2 mortality due to the small number of COVID-19 deaths ( = 3) observed in Vo' during the study period. Supplementary table 1. SARS-CoV-2 exposure authentication criteria. Criteria of decreasing stringency for the definition of the ground truths (GTs) identifying all individuals exposed to SARS-CoV-2 from the putative start of infection (early February) to the first serosurvey (1-3/05/2020).

Supplementary table 3. Assay-specific performance against the different ground truth definitions.
Sensitivity, specificity, positive predictive value and negative predictive value (mean and 95%CI) of the different assays against the different ground truth definitions. Sens = sensitivity; spec = specificity; PPV = positive predictive value; NPV = negative predictive value. For sensitivity and specificity, the 95% CI represents the exact binomial CI; for PPV and NPV, the 95% CI has been calculated by bootstrapping.