37 research outputs found
Epidemic Thresholds with External Agents
We study the effect of external infection sources on phase transitions in
epidemic processes. In particular, we consider an epidemic spreading on a
network via the SIS/SIR dynamics, which in addition is aided by external agents
- sources unconstrained by the graph, but possessing a limited infection rate
or virulence. Such a model captures many existing models of externally aided
epidemics, and finds use in many settings - epidemiology, marketing and
advertising, network robustness, etc. We provide a detailed characterization of
the impact of external agents on epidemic thresholds. In particular, for the
SIS model, we show that any external infection strategy with constant virulence
either fails to significantly affect the lifetime of an epidemic, or at best,
sustains the epidemic for a lifetime which is polynomial in the number of
nodes. On the other hand, a random external-infection strategy, with rate
increasing linearly in the number of infected nodes, succeeds under some
conditions to sustain an exponential epidemic lifetime. We obtain similar sharp
thresholds for the SIR model, and discuss the relevance of our results in a
variety of settings.Comment: 12 pages, 2 figures (to appear in INFOCOM 2014
Generalized Opinion Dynamics from Local Optimization Rules
We study generalizations of the Hegselmann-Krause (HK) model for opinion
dynamics, incorporating features and parameters that are natural components of
observed social systems. The first generalization is one where the strength of
influence depends on the distance of the agents' opinions. Under this setup, we
identify conditions under which the opinions converge in finite time, and
provide a qualitative characterization of the equilibrium. We interpret the HK
model opinion update rule as a quadratic cost-minimization rule. This enables a
second generalization: a family of update rules which possess different
equilibrium properties. Subsequently, we investigate models in which a external
force can behave strategically to modulate/influence user updates. We consider
cases where this external force can introduce additional agents and cases where
they can modify the cost structures for other agents. We describe and analyze
some strategies through which such modulation may be possible in an
order-optimal manner. Our simulations demonstrate that generalized dynamics
differ qualitatively and quantitatively from traditional HK dynamics.Comment: 20 pages, under revie
Finite Time Bounds for Stochastic Bounded Confidence Dynamics
In this era of fast and large-scale opinion formation, a mathematical
understanding of opinion evolution, a.k.a. opinion dynamics, acquires
importance. Linear graph-based dynamics and bounded confidence dynamics are the
two popular models for opinion dynamics in social networks. Stochastic bounded
confidence (SBC) opinion dynamics was proposed as a general framework that
incorporates both these dynamics as special cases and also captures the
inherent stochasticity and noise (errors) in real-life social exchanges.
Although SBC dynamics is quite general and realistic, its analysis is more
challenging. This is because SBC dynamics is nonlinear and stochastic, and
belongs to the class of Markov processes that have asymptotically zero drift
and unbounded jumps. The asymptotic behavior of SBC dynamics was characterized
in prior works. However, they do not shed light on its finite-time behavior,
which is often of interest in practice. We take a stride in this direction by
analyzing the finite-time behavior of a two-agent system and a bistar graph,
which are crucial to the understanding of general multi-agent dynamics. In
particular, we show that the opinion difference between the two agents is
well-concentrated around zero under the conditions that lead to asymptotic
stability of the SBC dynamics.Comment: A preliminary version of this paper appeared in the proceedings of
COMmunication Systems & NETworkS (COMSNETS) 2022. arXiv admin note:
substantial text overlap with arXiv:2112.0437