3 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
Epidemic Spreading with External Agents
We study epidemic spreading processes in large networks, when the spread is
assisted by a small number of external agents: infection sources with bounded
spreading power, but whose movement is unrestricted vis-\`a-vis the underlying
network topology. For networks which are `spatially constrained', we show that
the spread of infection can be significantly speeded up even by a few such
external agents infecting randomly. Moreover, for general networks, we derive
upper-bounds on the order of the spreading time achieved by certain simple
(random/greedy) external-spreading policies. Conversely, for certain common
classes of networks such as line graphs, grids and random geometric graphs, we
also derive lower bounds on the order of the spreading time over all
(potentially network-state aware and adversarial) external-spreading policies;
these adversarial lower bounds match (up to logarithmic factors) the spreading
time achieved by an external agent with a random spreading policy. This
demonstrates that random, state-oblivious infection-spreading by an external
agent is in fact order-wise optimal for spreading in such spatially constrained
networks
Distinguishing Infections on Different Graph Topologies
The history of infections and epidemics holds famous examples where
understanding, containing and ultimately treating an outbreak began with
understanding its mode of spread. Influenza, HIV and most computer viruses,
spread person to person, device to device, through contact networks; Cholera,
Cancer, and seasonal allergies, on the other hand, do not. In this paper we
study two fundamental questions of detection: first, given a snapshot view of a
(perhaps vanishingly small) fraction of those infected, under what conditions
is an epidemic spreading via contact (e.g., Influenza), distinguishable from a
"random illness" operating independently of any contact network (e.g., seasonal
allergies); second, if we do have an epidemic, under what conditions is it
possible to determine which network of interactions is the main cause of the
spread -- the causative network -- without any knowledge of the epidemic, other
than the identity of a minuscule subsample of infected nodes?
The core, therefore, of this paper, is to obtain an understanding of the
diagnostic power of network information. We derive sufficient conditions
networks must satisfy for these problems to be identifiable, and produce
efficient, highly scalable algorithms that solve these problems. We show that
the identifiability condition we give is fairly mild, and in particular, is
satisfied by two common graph topologies: the grid, and the Erdos-Renyi graphs