Fig 1.
Quantifying the impact of TTIQ interventions using a mathematical model.
A: Under testing & isolation, index cases are identified and isolated from the population after a delay Δ1 after they develop symptoms (at time ). This curtails their duration of infectiousness and reduces the number of secondary infections. This isolation occurs in a fraction f of symptomatic individuals. B: Under additional contact tracing & quarantine, the contacts of an index case can be identified and quarantined after an additional delay Δ2. This reduces the onward transmission from these secondary contacts. Only contacts that occur during the contact tracing window can be identified. This window extends from τ days before the index case developed symptoms (i.e.
) to the time at which the index case was isolated (i.e.
). A fraction g of the contacts who were infected within the contact tracing window are quarantined. The remaining individuals are not quarantined, but could be isolated if they are later detected as an index case. The distributions shown here are schematic representations of the infectivity profile and/or generation time interval, which are quantitatively displayed in Fig I in S1 Appendix. These distributions reflect an individual’s infectiousness as a function of time.
Table 1.
Parameter definitions for the TTIQ interventions.
Fig 2.
The reproductive number RTI under testing & isolation only.
A: The impact of testing & isolation on RTI as a function of the fraction of symptomatic individuals that are isolated (f; x-axis) and delay to isolation after symptom onset (Δ1; y-axis) for different baseline R values (columns). The black line represents the critical reproductive number RTI = 1. Above this line (orange zone) we have on average more than one secondary infection per infected and the epidemic is growing. Below this line (blue zone) we have less than one secondary infection per infected and the epidemic is suppressed. Dashed lines are the 95% confidence interval for this threshold, representing the uncertainty in the inferred generation time distribution and infectivity profile. B: Lines correspond to slices of panel A at a fixed delay to isolation Δ1 = 0, 2, or 4 days after symptom onset (colour). Shaded regions are 95% confidence intervals for the reproductive number, representing the uncertainty in the inferred generation time distribution and infectivity profile. Horizontal grey line is the threshold for epidemic control (RTI = 1). We fix the fraction of transmission that is attributed to asymptomatic infections to α = 20%, where asymptomatic individuals are not tested or isolated. Data provided in S1 Dataset.
Fig 3.
The impact of tracing & quarantine on the reproductive number.
The impact of tracing & quarantine on the reproductive number RTTIQ as a function of the fraction of symptomatic individuals that are isolated (f; x-axis) and delay to isolation after symptom onset (Δ1; y-axis), for different contact tracing & quarantine success probabilities g (colour) across different baseline R values (columns). We fix Δ2 = 2 days and τ = 2 days. The contours separate the regions where the epidemic is growing (RTTIQ > 1; top-left) and the epidemic is suppressed (RTTIQ < 1; bottom-right). The contours for g = 0 are equivalent to the contours in Fig 2. We fix the fraction of transmission that is attributed to asymptomatic infections to α = 20%. Asymptomatic individuals are not tested or isolated, but are subject to quarantine after contact tracing. We do not show confidence intervals for clarity of presentation. Data provided in S1 Dataset.
Fig 4.
The response of the reproductive number RTTIQ to single TTIQ parameter perturbations.
We set the baseline R = 1.5 throughout, which is the intensity of the epidemic in the absence of any TTIQ intervention. We consider four focal TTIQ parameter combinations, with f ∈ {30%, 70%}, Δ1 ∈ {0, 2} days, g = 50%, Δ2 = 1 day, and τ = 2 days. RTTIQ for the focal parameter sets are shown as thin black lines. With f = 0 (no TTIQ) we expect RTTIQ = R (upper grey line). We then vary each TTIQ parameter individually, keeping the remaining four parameters fixed at the focal values. The upper panel shows the probability parameters f and g, while the lower panel shows the parameters which carry units of time (days). The critical threshold for controlling an epidemic is RTTIQ = 1 (lower grey line). We fix the fraction of transmission that is attributed to asymptomatic infections to α = 20%. A sensitivity analysis to α is shown in Fig I in S2 Appendix. Asymptomatic individuals are not tested or isolated, but are subject to quarantine after contact tracing. Data provided in S1 Dataset.
Fig 5.
Linear discriminant analysis (LDA) of the impact of TTIQ strategies on the reproductive number RTTIQ.
We fix the baseline R = 1.5 and α = 20%, and then we randomly uniformly sample 10,000 parameter combinations from f ∈ [0%, 100%], g ∈ [0%, 100%], Δ1 ∈ [0, 5] days, Δ2 ∈ [0, 5] days, and τ ∈ [0, 5] days. The reproductive number is calculated for each TTIQ parameter combination, and the output (RTTIQ) is categorised into bins of width 0.1 (colour). We then use LDA to construct a linear combination (LD1) of the five (normalised) TTIQ parameters which maximally separates the output categories. We then predict the LD1 values for each parameter combination, and construct a histogram of these values for each category. The lower panel shows the components of the primary linear discriminant vector (LD1). By multiplying the (normalised) TTIQ parameters by the corresponding vector component, we arrive at the LD1 prediction which corresponds to the predicted reproductive number under that TTIQ strategy. Longer arrows (larger magnitude components) correspond to a parameter having a larger effect on the reproductive number. The distributions of parameters per categorised reproductive number is shown in S2 Fig. Data provided in S1 Dataset.