Leírás
Abstract:
Epidemic spread on networks can be described by continuous
time Markov chains. The size of its state space blows up exponentially
as the number of vertices is increased, hence several averaging
methods leading to low-dimensional non-linear differential equations
were derived. The approximation of the system by differential
equations, containing some characteristics of the underlying graph, is
one of the most important tools of investigation. In this talk we give
an introduction to this field with emphasis on the mathematical
methods introduced so far. Besides considering spreading processes on
static networks we will deal with adaptive networks, when the epidemic
dynamics on the network is coupled with a network which evolves in
time. Moreover, we show how this approach leads to the control of the
network process, a mathematical problem attracting significant
research interest nowadays.
Reference:
Kiss., I.Z, Miller, J.C., Simon, P.L., Mathematics of Epidemics on
Networks; From Exact to Approximate Models, Springer
(2017). http://www.springer.com/gp/book/9783319508047
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