5,373 research outputs found
Spreading Processes over Socio-Technical Networks with Phase-Type Transmissions
Most theoretical tools available for the analysis of spreading processes over
networks assume exponentially distributed transmission and recovery times. In
practice, the empirical distribution of transmission times for many real
spreading processes, such as the spread of web content through the Internet,
are far from exponential. To bridge this gap between theory and practice, we
propose a methodology to model and analyze spreading processes with arbitrary
transmission times using phase-type distributions. Phase-type distributions are
a family of distributions that is dense in the set of positive-valued
distributions and can be used to approximate any given distributions. To
illustrate our methodology, we focus on a popular model of spreading over
networks: the susceptible-infected-susceptible (SIS) networked model. In the
standard version of this model, individuals informed about a piece of
information transmit this piece to its neighbors at an exponential rate. In
this paper, we extend this model to the case of transmission rates following a
phase-type distribution. Using this extended model, we analyze the dynamics of
the spread based on a vectorial representations of phase-type distributions. We
illustrate our results by analyzing spreading processes over networks with
transmission and recovery rates following a Weibull distribution
Disease spread over randomly switched large-scale networks
In this paper we study disease spread over a randomly switched network, which
is modeled by a stochastic switched differential equation based on the so
called -intertwined model for disease spread over static networks. Assuming
that all the edges of the network are independently switched, we present
sufficient conditions for the convergence of infection probability to zero.
Though the stability theory for switched linear systems can naively derive a
necessary and sufficient condition for the convergence, the condition cannot be
used for large-scale networks because, for a network with agents, it
requires computing the maximum real eigenvalue of a matrix of size exponential
in . On the other hand, our conditions that are based also on the spectral
theory of random matrices can be checked by computing the maximum real
eigenvalue of a matrix of size exactly
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