Transmission heterogeneities, kinetics, and controllability of SARS-CoV-2

Abstract

A long-standing question in infectious disease dynamics concerns the role of transmission heterogeneities, which are driven by demography, behavior, and interventions. On the basis of detailed patient and contact-tracing data in Hunan, China, we find that 80% of secondary infections traced back to 15% of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) primary infections, which indicates substantial transmission heterogeneities. Transmission risk scales positively with the duration of exposure and the closeness of social interactions and is modulated by demographic and clinical factors. The lockdown period increases transmission risk in the family and households, whereas isolation and quarantine reduce risks across all types of contacts. The reconstructed infectiousness profile of a typical SARS-CoV-2 patient peaks just before symptom presentation. Modeling indicates that SARS-CoV-2 control requires the synergistic efforts of case isolation, contact quarantine, and population-level interventions because of the specific transmission kinetics of this virus.

Transmission chains, contact patterns, and transmission kinetics of SARS-CoV-2 in Hunan, China, based on case and contact-tracing data from Hunan, China.

(Top left) One realization of the reconstructed transmission chains, with a histogram representing overdispersion in the distribution of secondary infections. (Top right) Contact matrices of community, social, extended family, and household contacts reveal distinct age profiles. (Bottom) Earlier isolation of primary infections shortens the generation and serial intervals while increasing the relative contribution of transmission in the presymptomatic phase.

Fig. 1. SARS-CoV-2 transmission chains.

(Top) One realization of the reconstructed transmission chains among 1178 SARS-CoV-2–infected individuals in Hunan province. Each node in the network represents a patient infected with SARS-CoV-2, and each link represents an infector-infectee relationship. The color of the node denotes the reporting prefecture of the infected individuals. (Bottom) Distribution of the number of secondary infections. Blue bars represent the ensemble averaged across 100 stochastic samples of the reconstructed transmission chains. Orange bars represent the best fit of a negative binomial distribution to the ensemble average. Vertical lines indicate 95% CIs across 100 samples (of both data and the models’ fitting results). Some confidence intervals are narrow and not visible on the plot. For sensitivity analysis, we also fit the distribution with geometric and Poisson distributions. On the basis of the Akaike information criterion (AIC), the negative binomial distribution fit the data the best (average AIC score for negative binomial distribution: 1902; for geometric distribution: 1981; and for Poisson distribution: 2259).

Fig. 2. Heterogeneity in contact rates of SARS-CoV-2 cases and impact of interventions, separated by contact type.

Columns from left to right represent community contacts (e.g., public transportation, food, and entertainment), social contacts, extended family contacts, and household contacts. (A) Violin plots representing the distribution of per-contact transmission probability by contact type, adjusted for all other covariates in fig. S3 (probability expressed in percentage; x axis). (B) Complementary cumulative distribution function (CCDF) (y axis) for duration of exposure (i.e., the probability that exposure is longer or equal to a certain value). Dashed vertical lines indicate average values. Household contacts last the longest, and as expected, contact duration decreases as social ties loosen. (C) The distribution of the number of distinct contacts (degree distribution) of the primary cases for each contact type. The y axis indicates probability mass function (PMF). The dashed vertical lines indicate average values. The dispersion parameter k is calculated on the basis of the relationship ${\sigma }^2=\frac{\mu }{1+\mu /k}$, where μ and σ² are the mean and variance of the number of distinct contacts. Values of k < 1 indicate overdispersion. (D) Age distribution of SARS-CoV-2 case–contact pairs (contact matrices). (E) Rate ratios of negative binomial regression of the CCRs against predictors including the infector’s age, sex, presence of fever or cough, Wuhan travel history, whether symptom onset occurred before social distancing was in place (before or after 25 January 2020), and time from isolation to symptom onset. CCRs represent the sum of relevant contacts over a 1-week window centered at the date of the primary case’s symptom onset. Dots and lines indicate point estimates and 95% CIs of the rate ratios, respectively, and numbers below the dots indicate the numerical value of the point estimates. Ref., reference category. *P < 0.05; **P < 0.01; ***P < 0.001.

Fig. 3. The impact of interventions on SARS-CoV-2 transmission dynamics.

(A) Violin plot of the generation interval distributions stratified by time from symptom onset to isolation or presymptomatic quarantine, based on an ensemble of 100 realizations of the sampled transmission chains. (B) Same as (A) but for the serial interval distributions. (C) Same as (A) but for the fraction of presymptomatic transmission, among all transmission events, with vertical line indicating 50% of presymptomatic transmissions. In (A) to (C), dots represent the mean, and whiskers represent minimum and maximum. (D) Estimated average (across 100 realizations of sampled transmission chains) transmission risk of a SARS-CoV-2–infected individual since time of infection under four intervention scenarios: the red solid line represents an uncontrolled epidemic scenario modeled after the early epidemic dynamics in Wuhan before lockdown, and the dashed lines represent scenarios where quarantine and case isolation are in place and mimic phases I, II, and III of epidemic control in Hunan. The shapes of these curves match those of the generation interval distributions in each scenario, and the areas under the curve are equal to the ratios of the baseline/effective basic reproduction numbers $\left(R_0/R_0^{\mathrm{E}}\right)$. (E) Same as in (D) but with time since symptom onset on the x axis [colors are the same as in (D)]. The vertical line represents symptom onset. (F) Reduction (percentage) in the basic reproduction number as a function of mean time from symptom onset (or from peak infectiousness for asymptomatic cases) to isolation τ_iso (x axis) and fraction of SARS-CoV-2 infections being isolated (y axis). The distribution of onset to isolation follows a normal distribution with mean τ_iso and standard deviation of 2 days. The dashed lines indicate 30, 40, and 50% reductions in R₀ under interventions. (G) Effective basic reproduction number as a function of population-level reduction in contact rates (i.e., through physical distancing; expressed as a percentage, x axis) and isolation rate (fraction of total infections detected and further isolated). We assume baseline basic reproduction number R₀ = 2.19 and a normal distribution for the distribution from onset to isolation with a mean of 0 days and a standard deviation of 2 days. The dashed line represents the epidemic threshold, R^E = 1. The blue area indicates the region below the epidemic threshold (namely, controlled epidemic), and the red area indicates the region above the epidemic threshold. (H) Same as in (G) but assuming R₀ = 1.57 (a more optimistic estimate of R₀ in Wuhan, adjusted for reporting changes) and a normal distribution for the distribution from onset to isolation with a mean of 2 days and a standard deviation of 2 days.