Multilevel Digital Contact Tracing

TL;DR

This work tackles scalable multilevel digital contact tracing by encoding temporal proximity data into edge labels called binary circular contact queues (CCQ) and maintaining a dynamic contact graph that stores the last $D$ incubation days. A multilevel tracing algorithm builds direct and indirect infection lists and infection pathways up to depth $L$, using a two-queue processing scheme and CCQ-based temporal reasoning, with complexity $T = \mathcal{O}(\langle q\rangle^{L} |\mathcal{I}'|)$ and space $\mathcal{O}(N \log N)$. The framework is validated with synthetic data and real COVID-19 datasets, demonstrating practical memory (e.g., ~5 GB for $N=10^6$, $D=14$, $\tau=15$ min$) and scalable tracing performance while preserving privacy through pseudonymous IDs and edge-encoded history. Overall, the approach offers a tunable, path-aware, and privacy-conscious platform capable of rapid infection-pathway reconstruction for outbreak containment across pathogens.

Abstract

Digital contact tracing plays a crucial role in alleviating an outbreak, and designing multilevel digital contact tracing for a country is an open problem due to the analysis of large volumes of temporal contact data. We develop a multilevel digital contact tracing framework that constructs dynamic contact graphs from the proximity contact data. Prominently, we introduce the edge label of the contact graph as a binary circular contact queue, which holds the temporal social interactions during the incubation period. After that, our algorithm prepares the direct and indirect (multilevel) contact list for a given set of infected persons from the contact graph. Finally, the algorithm constructs the infection pathways for the trace list. We implement the framework and validate the contact tracing process with synthetic and real-world data sets. In addition, analysis reveals that for COVID-19 close contact parameters, the framework takes reasonable space and time to create the infection pathways. Our framework can apply to any epidemic spreading by changing the algorithm's parameters.

Figures (14)

• Figure 1: Illustration of direct and Indirect contact tracing. The dotted circle represents the infected person.
• Figure 2: (a) A close contact graph ($\mathcal{G}$) with $N=6$ nodes where circular contact queues (CCQ) are on the edges and $P_2$ is marked as infected (Fig. \ref{['ExampleContactGraph']}(Day 6)). (b) Contact graph representation using the array ($\mathcal{G}.\Psi$) with two fields (Node label $2$ or UserID and Address to store CCQ). Further, $\mathcal{G}.\Theta$ stores all CCQs. Here, we consider $q=2$; thus, for $P_2$ and $P_3$, adjacent information will also be stored in the link list. (c) From $\mathcal{G}$, during the contact tracing process, we find multilevel trace list $\Gamma_{P_2} = \{P_{0}^{1}, P_{1}^{1}, P_{4}^{1}, P_{5}^{2}, P_{3}^{3}\}$. Also, one can very easily construct the infection transmission pathways by storing the directed edges, $\chi_{P_2} = \{(P_2, P_0),(P_2, P_1),(P_2, P_4),(P_0, P_5),(P_5, P_3) \}$ where $(P_i, P_j)$ represents $P_i$ transmits infection to $P_j$.
• Figure 3: Dynamic evolution of close contact graph ($\mathcal{G}$) for six days annotated with the circular contact queues ($\bm{c}$). We consider $V = \{P_0,P_1,\dots,P_9\}$, $D=5$ days, $\tau=1$ day and thus $N=|V|=10$ and size of $\bm{c}$ as $n=5$. Here, $c_0$ points to the latest, and $c_4$ points to the oldest day close contact information. Let's say initially, on the day $1$, there is a close contact between $P_4$ and $P_6$; thus, there will be an edge and left most bit position in $\bm{c}_{(P_4, P_6)}$ set to one and pointed by $c_0$. In the next day there is another five contacts ($\{(P_0,P_2),(P_3,P_4),(P_3,P_5),(P_6,P_7), (P_7,P_8)\}$) but no contact between $P_4$ and $P_6$. Thus, for day $2$, $c_0$ position is zero in $\bm{c}_{(P_4, P_6)}$ and one for the rest of the contact queues where $c_1$ points to day $1$ data. In the same way, the contact graph dynamically updates as contacts are received from individual users. After the incubation period ($5$ days) is over, on the $6$th day, we are not required to keep the day $1$ contact data. One can notice that there is an edge between $P_4$ and $P_6$ during the $5$ days; however, at $6th$ day, they have no close contact; thus, the algorithm removes the edge $(P_4, P_6)$, updates $\mathcal{G}$ and $c_0$ start pointing to the left side cell and the process repeats. On the other hand, one can also observe that during the $5$ days, there is no close contact between $P_7$ and $P_9$. However, on $6^{th}$ day, there is a close contact between $P_7$ and $P_9$; thus, the algorithm sets one bit in $\bm{c}_{(P_7, P_9)}$ pointed by $c_0$. Further, we assume on Day 6, two persons are detected as infected ($P_2$ and $P_6$).
• Figure 4: Indirect contact tracing. We unfold the indirect contact paths where $P_2$ is the infected node in Fig. \ref{['ExampleContactGraph']}(Day 6). (a) $P_3$ is in the indirect contact list of $P_2$. We can observe from the circular contact queues (CCQs) and timeline that on day $3$, there is a contact between $P_1$ and $P_3$. After that, on day $4$, there is a contact between $P_2$ and $P_1$, and no further contacts exist. Hence, infection can not spread from $P_2$ to $P_3$ via $P_1$. We can detect it by the alignment of the CCQ where $c_0$ is the least significant bit and $c_{n-1}$ is the most significant bit. We can observe that $v_1<v_2$ and $i<j$ ensure no indirect transmission. (b-d) Similarly, we can explore and detect the other paths.
• Figure 5: Depicting the counts of the traced persons for three levels for infected persons. Here, $N = 10^{5}$, $\langle q \rangle =10$, $D=10$, $L=3$ and $|\mathcal{I}^{'}|=1$ over two years. The algorithm counts the three-level traced persons for the randomly selected days and randomly selected infected persons. We mark first-level counts (red), second-level (green), and third-level (violet). For a random day, let's say on $114th$ day, a person is detected as infected by lab testing. Then, the contact trace algorithm finds the first-level contacts ($7$ persons), second-level contacts ($37$ persons), and third-level contacts ($177$ persons). The algorithm can identify the persons traced from the contact graph and create the infection pathways trees.