The effect of role-based resource allocation on epidemic dynamics

We propose a coupled dynamical model of resource allocation and epidemic spread, inspired by the hierarchical structure of real-world therapeutic resource allocation. In this framework, network nodes are assigned distinct roles as either resource allocators or resource recipients. As the average number of links per recipient from allocators increases, the prevalence exhibits one of four distinct response patterns across conditions: monotonically increasing, monotonically decreasing, U-shaped trend, or a sudden decrease with large fluctuations. A mechanistic analysis uncovers three central insights: (i) a trade-off between efficient resource allocation and infection risk faced by allocators, (ii) the critical need to avoid resource redundancy when therapeutic efficiency is high, and (iii) the emergence of cascade-induced bistability in the coupled system.

💡 Research Summary

The paper introduces a novel “role‑based resource allocation” framework to study how therapeutic resource distribution influences epidemic dynamics. Unlike previous works that treat resources as a fixed budget or assume neighbor‑based sharing, the authors explicitly separate network nodes into two functional classes: resource allocators (designated as 𝘋, e.g., doctors, pharmacists) and resource recipients (𝘎, e.g., patients). The system is built on a two‑layer multiplex network: a physical‑contact layer that carries the SIS disease transmission and a social‑behavior layer that carries the flow of therapeutic resources from allocators to recipients. Key modeling assumptions are: (i) there are no 𝘋‑𝘋 links, reflecting the sparsity of direct connections among medical institutions; (ii) resources are transferred only along 𝘋S‑𝘎I links, preventing cross‑infection from infected allocators; (iii) each allocator generates a total amount of resource equal to the fraction r of allocators in the population per time step, which is then evenly divided among its infected recipient neighbors.

Recovery probability depends on the amount of resource received, modeled by a sigmoid function μ(R)=μ₀/(1+α·e^{−ωR}). The three parameters capture (a) baseline recovery probability μ₀ (when R=0), (b) saturated recovery probability μ₀·α/(1+α) (when resources are abundant), and (c) treatment efficiency ω (how quickly the saturation is approached). This functional form reflects realistic features: even without treatment some recovery occurs, and additional resources yield diminishing returns.

The authors employ microscopic Markov chain theory and mean‑field approximations to derive dynamical equations for the four possible node states (𝘎S, 𝘎I, 𝘋S, 𝘋I). They analytically compute the distribution of total resources a recipient receives from its neighboring allocators, ensuring that the expected total allocated resources equals the expected total received resources—a balance missing in earlier models. By linearizing near the disease‑free equilibrium, they obtain epidemic thresholds for two limiting cases of the average number of allocator‑recipient links (k₂): when k₂ is large, resources are plentiful and the threshold reduces to β_c = μ₀·Λ(G), where Λ(G) is the largest eigenvalue of the recipient‑recipient adjacency matrix; when k₂≈0, resources are scarce and the threshold becomes β_c = (α/(1+α))·μ₀·Λ(G). These limits recover the classic SIS threshold, confirming the model’s consistency.

Extensive Monte‑Carlo simulations (N=10⁵, average recipient degree k₁=4, μ₀=0.5, β=0.12) explore three allocator fractions (r=0.01, 0.05, 0.1) and a wide range of k₂∈