Campaigning in Heterogeneous Social Networks: Optimal Control of SI Information Epidemics

TL;DR

This paper develops an optimal control framework for maximizing information spread in social networks modeled as SI epidemics, considering network heterogeneity and resource allocation strategies.

Contribution

It introduces a novel optimal control approach accounting for degree-dependent controls and network heterogeneity, with solutions applicable to various network types and epidemic models.

Findings

More resources are allocated to high-degree nodes in scale-free networks.

Optimal strategies outperform static and bang-bang controls.

Network degree distribution significantly influences control allocation.

Abstract

We study the optimal control problem of maximizing the spread of an information epidemic on a social network. Information propagation is modeled as a Susceptible-Infected (SI) process and the campaign budget is fixed. Direct recruitment and word-of-mouth incentives are the two strategies to accelerate information spreading (controls). We allow for multiple controls depending on the degree of the nodes/individuals. The solution optimally allocates the scarce resource over the campaign duration and the degree class groups. We study the impact of the degree distribution of the network on the controls and present results for Erdos-Renyi and scale free networks. Results show that more resource is allocated to high degree nodes in the case of scale free networks but medium degree nodes in the case of Erdos-Renyi networks. We study the effects of various model parameters on the optimal strategy and quantify the improvement offered by the optimal strategy over the static and bang-bang control strategies. The effect of the time varying spreading rate on the controls is explored as the interest level of the population in the subject of the campaign may change over time. We show the existence of a solution to the formulated optimal control problem, which has non-linear isoperimetric constraints, using novel techniques that is general and can be used in other similar optimal control problems. This work may be of interest to political, social awareness, or crowdfunding campaigners and product marketing managers, and with some modifications may be used for mitigating biological epidemics.