Introduction
Group testing
Mobility networks
Epidemiology at colleges
Methodology
Data
Infection model
Description | Parameter | Value | Reference |
---|---|---|---|
Secondary attack rate | \(\beta\) | 0.09 |
Jing et al. (2020) |
\(L \rightarrow P_s\) | p | 1/3 \(\hbox {day}^{-1}\) |
Backer et al. (2020) |
\(P_s \rightarrow A_y\) | \(\alpha\) | 0.7 |
Barrett et al. (2020) |
\(A_y,S_y,Q,I \rightarrow R\) | \(\gamma\) | 1/10 \(\hbox {day}^{-1}\) |
SeyedAlinaghi et al. (2021) |
\(Q \rightarrow I\) | \(\epsilon\) | 0.02 |
Bialek et al. (2020) |
\(I \rightarrow F\) | \(\mu\) | 0.02 |
Richardson et al. (2020) |
Network model
destination_cbgs
column (see “Appendix” for definition). If the destination CBG is within our defined set of college towns, these agents will interact with other nodes in the simulation. If the destination is outside the system, nodes are infected with probability \(\mu\). We set \(\mu =0.0001\) since our focus is on the dynamics within college towns. Further information can be found in the “Appendix”.Simulation
-
Individual testing at random:
Ind Testing (Random)
chooses a fraction q from the population by selecting \(q * n\) nodes uniformly at random and test each individually. If a node tests positive, the agent moves into the quarantine state. -
Individual testing with global rank:
Ind Testing (Global)
assigns every node i an importance score \(s_i\), where \(s_i = deg(i) + \lambda * \text {num\_trips}(i)\). \(\text {num\_trips(i)}\) refers to the number of trips taken by i, updated every timestep, and \(\lambda\) is a parameter that controls the relative importance of the two terms. In our experiments, \(\lambda\) is set to 0.5. All scores s are then normalized so that \(\sum _{i=0}^{n} s_i = 1\) and we select a fraction q by treating \(s_i\) as a probability. -
Group testing at random:
Group Testing (Random)
randomly selects \(q * n\) nodes and divides them into pools of 20. We then apply the two-stage group test to each pool. -
Group testing by network:
Group Testing (Graph)
randomly selects \((q * n) / 20\) nodes. For every node i in the sample, we construct a pool from neighbors with size \(\texttt {max}(deg(i), 20)\) and apply the two-stage group test. The original node i is not included in the group test.
Ind Testing (Global)
to study the usefulness of collecting information on the underlying global network.Results
Group Testing (Graph)
demonstrates a marked improvement over the other three methods particularly when \(q=0.15\) and \(q=0.2\). The marginal benefit of increased testing diminishes sharply after \(q=0.2\). At \(q=0.3\), daily cases never pass 500 for any method.Ind Testing (Global)
, attack rate differs significantly during the course of simulation. Ind Testing (Random)
and Group Testing (Random)
show nearly identical attack rates, while our method shows a mostly flat attack rate over 60 timesteps.Ind Testing (Global)
results in the highest number of cases of all four strategies. Though the global strategy has a lower R(t) as seen in Fig. 6c, we hypothesize this is due to the large number of infections in the first 10 timesteps. After local communities are saturated, infections relative to total infected decline. Nevertheless, the global testing strategy results in higher case counts and attack rates across all levels of q. This is likely due to Ind Testing (Global)
over-testing the high-degree nodes. Figure 7 shows that global testing has the lowest probability of detecting the nodes with lower degree. Calibrating the strategy to add more randomness to the selection process would likely improve results.
Group Testing (Graph)
is robust to variation in the initial prevalence.Group Testing (Graph)
and Group Testing (Random)
.Group Testing (Graph)
generally has smaller pools than the random approach because most randomly selected nodes have less than 20 contacts, it requires fewer tests to mitigate the outbreak. We hypothesize that it has two major advantages over Group Testing (Random)
. First, the agents within the pool are more likely to be correlated. If they are all connected to a common node, then they are likely mostly uninfected or infected. Second, testing by network allows us to identify the nodes with higher degree early on. Figure 7 shows the probability of detection as a function of an agent’s degree.Ind Testing (Global)
underperformed all other testing methods. This is not to say that globally ranking and testing significant nodes is ineffective. Recall how we assign scores to nodes: \(s_i = deg(i) + \lambda * \text {num\_trips}(i)\). \(\lambda\) must be tuned to properly balance between the two terms, which may be on dramatically different scales. Moreover, \(num\_trips\) may not be indicative of a node’s importance, since the agent could be traveling to CBGs with less infection than their home CBG.Conclusion
Abbreviation | Definition |
---|---|
N | Pool size for group test |
x | Number of groups per pool |
k | Number of stages per group test |
SEIR model | Susceptible-exposed-infected-recovered model |
SLIR model | Susceptible-latent-infected-recovered model |
i.i.d | independent and identically-distributed |
R0 | Base reproduction number |
CBG | Census block group |
q | Fraction of population tested at each timestep |
n | Total population |
R(t) | Effective reproduction rate at time t |
All simulation parameters | See Table 1 |