Role division drives impact of resource allocation on epidemic spreading

TL;DR

The paper investigates how explicit role division between resource allocators and recipients shapes epidemic spread in a two-layer network. Using a coupled resource-epidemic model analyzed with a microscopic Markov chain, it uncovers four distinct prevalence patterns and cascade-induced bistability driven by allocator fraction and cross-layer connectivity. The work highlights three mechanisms—allocators’ infection risk, reduction of allocation redundancy, and cascade dynamics—that govern outcomes and shows when high treatment efficiency can suppress disease through distributed coverage. These insights offer practical guidance for organizing therapeutic resource flows during outbreaks and delineate the limits of mean-field analyses in capturing dynamic correlations.

Abstract

Based on the real-world hierarchical structure of resource allocation, this paper presents a coupled dynamic model of resource allocation and epidemic spreading that incorporates a role-based division of network nodes into resource allocators and 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. Analysis of the underlying physical mechanisms reveals three key features: (i) a trade-off between efficient resource allocation and infection risk for allocators, (ii) the critical importance of avoiding resource redundancy under high therapeutic resource efficiency, and (iii) cascade-induced bistability.

Figures (8)

• Figure 1: (a) Schematic illustration of the resource-epidemic model with role division. In the social-behavior layer, the thick solid lines are employed for resource distribution. In the physical-contact layer, the thick and thin solid lines are used for disease spread. (b) The transition probability trees are presented for the classes G̃I, G̃S, D̃I, and D̃S, respectively.
• Figure 2: The impact of the fraction of resource allocators ($r$) and the average number of connections from recipients to allocators ($\langle k_2\rangle$) on the prevalence ($\rho$) in the inevitable scenario of a disease outbreak. Parameters: $\beta=0.12$, $\mu_0=0.5$, initial fraction of infected individuals $\rho(0)=0.01$.
• Figure 3: The total resources in (a), average recovery probability in (b), and prevalence in (c) across different categories as functions of the variable $\langle k_2\rangle$. The parameters employed in square, circle, and triangle scatters correspond respectively to the monotonically increasing, initially decreasing and subsequently increasing, and monotonically decreasing trends observed in Fig. \ref{['fig2']}.
• Figure 4: The number of G̃I individuals $N^{\mathrm{\tilde{G}I}}$ as functions of $R$ and $\mu$, respectively. Data are from a single simulation at the final time step ($t=1000$). Parameters: $\alpha=1.0$, $r=0.01$, $\beta=0.12$, $\mu_0=0.5$, and $\rho(0)=0.01$.
• Figure 5: Time series for the fraction in (a) and the average recovery pribability in (b) of G̃I individuals. (c) The prevalence $\rho$ as a function of $\langle k_2\rangle$ with different initial infected individuals. Parameters: $\beta=0.12$, $\mu_0=0.5$, $\alpha=0.1$, $\omega=1.0$; (a) and (b) $r=0.1$, $\rho(0)=0.01$.