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

Abstract

This is the author's version of an article that has been published in IEEE/ACM Transcactions on Networking. Changes were made to this version by the publisher prior to publication. The final version of record is available at http://dx.doi.org/10.1109/TNET. 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 Erdős-Rényi 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 Erdős-Rényi 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.

Accelerating information diffusion in social networks under the Susceptible-Infected-Susceptible epidemic model

“…The value of the deadline is fixed at = 5 (wherever required) and the weighting factor = 15 in Eqs. (9) and (10). The initial fraction of infected population (0) = 0 = 0.01.…”

“…Maximizing information spread in an SI epidemic was a subject of study in [9]. A fixed budget was assumed and effect of degree distribution of the network on the control was investigated.…”

Node-based SIRS model on heterogeneous networks: Analysis and control

“…Recently, the study of heterogeneous networks receives more attention. In [12], the SI model is applied to campaigning in which not only the different degrees of inspected nodes but also the degrees of the neighbors are considered. In our paper, another part of heterogeneity is taken into consideration.…”

Cost effective campaigning in social networks

“…This is different from our strategy which involves incentivizing individuals to spread the message. It is possible to address the problem posed here using optimal control theory, which involves computing the optimal resource allocation in real time for ensuring maximum possible outreach size by a give deadline [13][14][15][16][17]. However, the optimal control solution is not only difficult to compute, but also very hard to implement as it requires a centralized real time controller.…”

“…However, the optimal control solution is not only difficult to compute, but also very hard to implement as it requires a centralized real time controller. Furthermore, recent work, [13][14][15][16][17], on optimal campaigning in social networks does not address the problem of minimizing the cost while gurantering an outreach size. Our formulation allows us to solve both the problems.…”