Reducing Recurrent Competitive Epidemics via Dynamic Resource Allocation

TL;DR

This work addresses the challenge of competing diffusion processes on networks, where two conflicting states spread in a recurrent, SIS-like fashion. It introduces gLRIE, a dynamic score-based resource allocation strategy that greedily promotes the desired state while suppressing the competing one, generalizing LRIE to nonlinear, saturating dynamics and mutual exclusivity. The authors derive a node-score via a short-horizon analysis and show that the resulting greedy policy effectively minimizes infected nodes, with scalable complexity. Through extensive simulations on synthetic and real networks, including a semi-synthetic high school vaping campaign, gLRIE consistently outperforms baselines and demonstrates the value of using positive diffusion as a counter-contagion in targeted interventions.

Abstract

Motivated by scenarios of epidemic competition, as well as how social contagions spread at the level of individuals, this work considers the competition between two conflicting node states that spread over a social graph according to a generic diffusion process. For this setting, we introduce the Generalized Largest Reduction in Infectious Edges (gLRIE), which is a dynamic resource allocation strategy that favors the preferred state against the other. Our analysis assumes a generic continuous-time SIS-like (Susceptible-Infectious-Susceptible) diffusion model that allows for: arbitrary node transition rate functions for nodes to change state, and competition between the healthy (positive) and infected (negative) states, which are both diffusive at the same time, yet mutually exclusive at each node. The strategy follows a minimum-risk-maximum-gain principle, and its features are particularly relevant for social contagion phenomena. In accordance with the LRIE strategy that we generalize, we show that in this context the gLRIE strategy remains a greedy solution for the minimization of the number of infected network nodes over time. Ultimately, simulations are employed to compare the proposed strategy with other existing alternatives, demonstrating that gLRIE exhibits superior performance across a spectrum of scenarios, including a realistic counter-contagion campaign in a small well-monitored community.

Figures (9)

• Figure 1: Overview of multi-virus SIS models. Tree view of the main SIS extensions that consider multiple competing/cooperating infections spreading in a network. * indicates articles that propose epidemic control strategies.
• Figure 2: Minimal example comparing gLRIE and LRIE scores. a) A simple undirected and unweighted contact network between $4$ individuals, $3$ of which are infected. The edges between agents are shown as straight black lines, out of which those being dashed are the infectious edges that connect nodes in different states and hence can channel both positive and negative diffusion. The factors involved in gLRIE score (Eq. \ref{['eq:genericScore']}) appear as labeled arcs. Node boundaries, green for infected and red for healthy nodes, indicate the spontaneous self-healing and self-infection, respectively. b) Table with the values of the factors involved in the gLRIE and LRIE scores for an infected node $i$, in the case of linear infection. The parameters $\delta$, $\gamma$, and $\beta$ are the self-healing, social healing, and social infection rates, respectively. The gLRIE score prioritizes Alice over Bob and Claire, due to the added contribution of social healing she could bring when she would have recovered, while LRIE treats them equally. Dennis being healthy, he is not considered for receiving a treatment.
• Figure 3: Evolution of a single epidemic from linear to nonlinear spreading for different intervention strategies. The percentage of infected nodes over time in Erdös-Rényi graphs of $300$ nodes with average degree $8$, when different strategies are employed. Only the negative diffusion is considered ($\altmathcal{H}\,{=}\,0$). Each plot shows an average over $1000$ simulations of the generalized SIS Model \ref{['eq:genericSIS']} using Eq. \ref{['eq:spreading_absolute']}. From (a) to (d), the diffusion moves from being essentially linear to nonlinear. The saturation level is fixed to $s_{_\altmathcal{I}}\,{=}\,10$, and the number of resources to allocate is $b\,{=}\,10$.
• Figure 4: Evolution of nonlinear SIS processes with and without competition, under various intervention strategies. Percentage of infected nodes under the generalized SIS Model \ref{['eq:genericSIS']} using Eq. \ref{['eq:spreading_absolute']}, when different strategies are employed. Results for ER (a, b), PA (c, d), and hierER (e, f) networks, $300$ nodes in each case. In the plots on the left, healthy states do not diffuse ($\altmathcal{H}\,{=}\,0$). On the right though, there is competition between the positive and negative diffusion ($\altmathcal{H}\,{\neq}\,0$, $\altmathcal{I}\,{\neq}\,0$). The model's parameters are set to: $s_{_\altmathcal{I}}\,{=}\,10$, $\ell_{_\altmathcal{I}}\,{=}\,2$ for the negative diffusion, and $s_{_\altmathcal{H}}\,{=}\,2$, $\ell_{_\altmathcal{H}}\,{=}\,0.25$ for the positive diffusion (when present). At any moment in time, up to $b\,{=}\,10$ nodes are targeted with resource units of $\rho\,{=}\,155$ healing strength.
• Figure 5: Pairwise performance comparison between the gLRIE, LRIE, and MCM intervention strategies via simulations on real datasets. Left (resp. right) columns: heatmaps of the AUC-ratio between gLRIE and competitors, using the generalized SIS model (Eq. \ref{['eq:spreading_absolute']}) in the Polblogs (resp. health-advice) network with $b=30$ and $\rho = 130$ ($b=10$ and $\rho = 80$). The first row corresponds to the scenario with no positive diffusion, while the second row is the case where positive diffusion is present. The color map ranges from yellow (ratio = $1$), where the strategies perform the same, to blue (ratio = $0$), where only gLRIE manages to remove the infection. As expected, the positive diffusion reduces the difficulty of the control problem.

Theorems & Definitions (5)

• Definition 1
• Remark 1
• Remark 2
• Remark 3
• proof