  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.
