A Mean-Field Team Approach to Minimize the Spread of Infection in a Network

TL;DR

This paper develops a stochastic control method using mean-field team theory to minimize infection spread in networks, providing optimal strategies for finite and infinite populations with practical verification.

Contribution

It introduces a novel mean-field team approach for infection control in networks, deriving optimal strategies via dynamic programming and Bellman equations.

Findings

Optimal control strategies are derived for finite networks.

Infinite-population solutions serve as effective sub-optimal strategies for finite networks.

The approach is validated through a social network rumor control example.

Abstract

In this paper, a stochastic dynamic control strategy is presented to prevent the spread of an infection over a homogeneous network. The infectious process is persistent, i.e., it continues to contaminate the network once it is established. It is assumed that there is a finite set of network management options available such as degrees of nodes and promotional plans to minimize the number of infected nodes while taking the implementation cost into account. The network is modeled by an exchangeable controlled Markov chain, whose transition probability matrices depend on three parameters: the selected network management option, the state of the infectious process, and the empirical distribution of infected nodes (with not necessarily a linear dependence). Borrowing some techniques from mean-field team theory the optimal strategy is obtained for any finite number of nodes using dynamic programming decomposition and the convolution of some binomial probability mass functions. For infinite-population networks, the optimal solution is described by a Bellman equation. It is shown that the infinite-population strategy is a meaningful sub-optimal solution for finite-population networks if a certain condition holds. The theoretical results are verified by an example of rumor control in social networks.