Abstract
Competition and collaboration are at the heart of multiagent probabilistic spreading processes. The battle for public opinion and competitive marketing campaigns are typical examples of the former, while the joint spread of multiple diseases such as HIV and tuberculosis demonstrates the latter. These spreads are influenced by the underlying network topology, the infection rates between network constituents, recovery rates, and, equally important, the interactions between the spreading processes themselves. Here, for the first time, we derive dynamic message-passing equations that provide an exact description of the dynamics of two, interacting, unidirectional spreading processes on tree graphs, and we develop systematic low-complexity models that predict the spread on general graphs. We also develop a theoretical framework for the optimal control of interacting spreading processes through optimized resource allocation under budget constraints and within a finite time window. Derived algorithms can be used to maximize the desired spread in the presence of a rival competitive process and to limit the spread through vaccination in the case of coupled infectious diseases. We demonstrate the efficacy of the framework and optimization method on both synthetic and real-world networks.
- Received 7 October 2020
- Revised 21 December 2020
- Accepted 7 January 2021
DOI:https://doi.org/10.1103/PhysRevX.11.011048
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Epidemics, antivaccine campaigns, and advertising are all manifestations of spreading processes. Sometimes, multiple competing or collaborating agents are involved, where exposure to one process facilitates or hinders the spread of another. For instance, people become entrenched in their political opinions (competitive spread), whereas the spread of HIV facilitates that of tuberculosis (collaborative). The analysis of interacting multiagent processes and the optimal use of limited resources to enhance or mitigate their spread is critical for developing efficient algorithms to mitigate epidemics and to disseminate important public health information in the presence of rumors. We address this challenge by analyzing competitive and collaborative scenarios and by offering computationally efficient algorithms for inference and resource deployment optimization.
Employing probabilistic tools, we study multiagent spreading processes and obtain an accurate description of the process. We optimize the use of limited resources to maximize the spread of one agent at the expense of another in a competitive scenario, maximize the spread of both through mutual facilitation, or contain their spread through immunization against one of them under a collaborative scenario. Optimization results for competitive and collaborative processes on benchmark networks show excellent performance compared to commonly used algorithms.
This work offers a ready-to-use theoretical framework for analyzing the spread of large-scale multiagent processes and an optimization algorithm for resource allocation. The framework can be extended to a large class of unidirectional processes with more states and different types of complex interactions. We envisage an impact on real-world problems in a variety of application domains.
