# Competition, Collaboration, and Optimization in Multiple Interacting Spreading Processes

## TL;DR

This paper introduces a novel dynamic message-passing framework for modeling and controlling two interacting spreading processes on networks, enabling optimal resource allocation for either promoting or limiting spread.

## Contribution

It derives exact equations for two interacting processes on trees, extends them to general graphs, and develops an optimization framework for controlling spread under constraints.

## Key findings

- Accurate modeling of interacting processes on networks.
- Effective algorithms for maximizing or limiting spread.
- Validated on synthetic and real-world networks.

## Abstract

Competition and collaboration are at the heart of multi-agent probabilistic spreading processes. The battle on 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 importantly, 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 spreading processes on tree graphs, and develop systematic low-complexity models that predict the spread on general graphs. We also develop a theoretical framework for an optimal control of interacting spreading processes through an 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.