Fig 1.
A pictorial illustration of state transitions involved in the spread and evolution of COVID-19.
Table 1.
Disease parameters.
Fig 2.
(a) An example sub-graph consisting of 2-hop neighborhood of the source node i = 1 and edges between them. (b) A new acyclic graph
converted from the example sub-graph
shown in (a). Shadow nodes are colored in blue. (c) Probability of detection for each node i in University Student Network under 2-hop contact tracing: experimental probability (black dots), theoretical probability under the acyclic graph assumption (blue circles), and the difference between the probabilities. Nodes are numbered in ascending order according to their degree. The theoretical probability,
, given in Eq (4) closely approximates the experimental probability; the average of the differences is 0.00098.
Table 2.
Evaluation metrics.
Fig 3.
The total infection count I as a function of β ∈ [0.001, 1] for 1-hop contact tracing for various contact networks.
The first, second, and third rows respectively represent Data-Driven network, Erdős-Rényi Random Network, and Scale-Free Network. For each network topology, we consider various values of activation probability f = 0.3, 0.5, 0.9. The lines represent the MMCA formulation and the points represent MC simulation. The MMCA formulation closely approximates the MC simulation results under 1-hop contact tracing.
Fig 4.
The total infection count I as a function of β ∈ [0.001, 1] for 2-hop contact tracing for various contact networks.
The first, second, and third rows respectively represent Data-Driven network, Erdős-Rényi Random Network, and Scale-Free Network. For each network topology, we consider various values of activation probability f = 0.3, 0.5, 0.9. The lines represent the MMCA formulation and the points represent MC simulation. The MMCA formulation closely approximates the MC simulation results under 2-hop contact tracing.
Fig 5.
The total infection count I as a function of β under 2-hop contact tracing with f = 0.3 for various values of rewiring probability (a) r = 0.1, (b) r = 0.5, and (c) r = 1.0 for Watts-Strogatz networks.
Fig 6.
The total infection count I as a function of β under 2-hop contact tracing with f = 0.7 for various values of rewiring probability (a) r = 0.1, (b) r = 0.5, and (c) r = 1.0 for Watts-Strogatz networks.
Fig 7.
The ratios (a) RI1-hop and (b) RI2-hop are expressed in color as a function of attack rate (x-axis) and activation probability f (y-axis).
We choose different color codes to represent different ranges of values of the ratios (i.e., RI1-hop and RI2-hop) corresponding to values of f and attack rate. We use the data-driven network for this figure.
Fig 8.
The expected number of infections (I), and the number of detected infections (D) and undetected infections (U) as a function of activation probability f.
We use the data-driven network for this figure.
Fig 9.
Infections, detected infections, and undetected infections as a function of degree k for different contact tracing strategies.
This figure shows the probability that a node of degree k has been infected i(k), detected d(k), and infected but not detected u(k)≔ i(k) − d(k). We use the data-driven network for this figure.
Fig 10.
The ratios (a) RD1-hop and (b) RD2-hop are expressed in color as a function of attack rate (x-axis) and activation probability f (y-axis).
We choose different color codes to represent different ranges of values of the ratios (i.e., RD1-hop and RD2-hop) corresponding to values of f and attack rate. We have highlighted the case RDk-hop = 1 (black line) signaling that 0-hop and k-hop quarantine the same number of individuals. We use the data-driven network for this figure.
Fig 11.
RDk-hop, ,
with respect to the activation probability f.
We use the data-driven network for this figure.
Fig 12.
The ratio of total tests via 2-hop contact tracing to total tests via 1-hop (i.e., T2-hop/T1-hop) are expressed in color as a function of attack rate (x-axis) and activation probability f (y-axis).
We choose different color codes to represent different ranges of values of the ratio (i.e., T2-hop/T1-hop) corresponding to values of f and attack rate. We use the data-driven network for this figure.
Fig 13.
Computation time as a function of population size for Erdős Rényi random network.
Fig 14.
(a) The ratio of number of tests via 2-hop contact tracing to that under the combination of 1-hop contact tracing and random testing, . (b) The ratio of cases infected via 2-hop contact tracing to the cases infected via ‘1-hop + random testing’,
. We use the data-driven network for this figure.
Fig 15.
A pictorial illustration of state transitions when there is test fatigue.
Fig 16.
The average number of tests per day and fraction of the populace infected via 1-hop and 2-hop as a function of activation probability f.
Figures (a), (b), (c), and (d) show the results for ξ = 1/14, ξ = 1/60, ξ = 1/90 and ξ = 0, respectively. The horizontal dotted lines in the figures on the right represent the number of individuals infected when no contact tracing is performed. We use the data-driven network for this figure.