Cost-Effective Activity Control of Asymptomatic Carriers in Layered Temporal Social Networks

TL;DR

This work analyzes epidemic propagation in a two-layer temporal network under the SCIR model, focusing on asymptomatic carriers who maintain activity similar to susceptibles. It develops a mean-field approximation to derive epidemic thresholds in both homogeneous and heterogeneous activity settings and introduces a budget-constrained, SGP-based optimization to minimize disease spread by controlling susceptible and carrier activity. The key contribution is showing that SGP-based activity-control can substantially reduce outbreak prevalence compared to degree- or closeness-based budget allocations, with demonstrated gains on synthetic networks and a real-world Ebola dataset. The results provide a scalable framework for cost-efficient intervention design in dynamic multiplex contact structures with asymptomatic transmission.

Abstract

The robustness of human social networks against epidemic propagation relies on the propensity for physical contact adaptation. During the early phase of infection, asymptomatic carriers exhibit the same activity level as susceptible individuals, which presents challenges for incorporating control measures in epidemic projection models. This paper focuses on modeling and cost-efficient activity control of susceptible and carrier individuals in the context of the susceptible-carrier-infected-removed (SCIR) epidemic model over a two-layer contact network. In this model, individuals switch from a static contact layer to create new links in a temporal layer based on state-dependent activation rates. We derive conditions for the infection to die out or persist in a homogeneous network. Considering the significant costs associated with reducing the activity of susceptible and carrier individuals, we formulate an optimization problem to minimize the disease decay rate while constrained by a limited budget. We propose the use of successive geometric programming (SGP) approximation for this optimization task. Through simulation experiments on Poisson random graphs, we assess the impact of different parameters on disease prevalence. The results demonstrate that our SGP framework achieves a cost reduction of nearly 33% compared to conventional methods based on degree and closeness centrality.

Figures (9)

• Figure 1: The state transitions for the SCIR model over a two-layer network.
• Figure 2: Epidemic models corresponding to (a) $R^{(1)}_0$ and (b) $R^{(2)}_0$ thresholds. The number of carrier and infected neighbors of node $i$ are $n^i_{\,\textrm{C}}(t)$ and $n^i_{\,\textrm{I}}(t)$, respectively.
• Figure 3: Average infection prevalence versus the activity probability of susceptible and carrier nodes ($S^2$) in steady-state for varying $\gamma^2$ values.
• Figure 4: Evolution of the average size of all epidemic compartments over time for varying rates at which carriers either get infected or recover ($\eta'$).
• Figure 5: Basic reproduction ratio ($\mathcal{R}_0$) versus $\kappa$ for varying $S^2$ and $\beta_{\textrm{C}}$ values.

Theorems & Definitions (11)

• Lemma 1
• proof
• Proposition 1
• proof
• Lemma 2
• proof
• Proposition 2
• proof
• Lemma 3
• proof