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.

中文翻译：

---

多个交互传播过程中的竞争，协作和优化

竞争与协作是多主体概率传播过程的核心。前者的典型例子是争取舆论之战和竞争性营销活动，而艾滋病毒和结核病等多种疾病的共同传播证明了后者。这些传播受到基础网络拓扑，网络组成部分之间的感染率，恢复率以及同样重要的是，传播过程本身之间的相互作用的影响。在这里，我们首次获得动态消息传递方程，该方程提供了树图上两个相互作用的单向扩展过程的动力学的精确描述，并开发了系统的低复杂度模型来预测普通图上的分布。我们还开发了一个理论框架，可通过在预算约束下和有限的时间范围内优化资源分配来优化控制相互传播的过程。在存在竞争性竞争过程的情况下，可以使用派生的算法来最大化所需的传播，在偶发性传染病的情况下，可以通过疫苗接种来限制传播。我们在综合网络和实际网络上展示了框架和优化方法的功效。