  We show results for the contact process on Barabasi networks. The contact
process is a model for an epidemic spreading without permanent immunity that
has an absorbing state. For finite lattices, the absorbing state is the true
stationary state, which leads to the need for simulation of quasi-stationary
states, which we did in two ways: reactivation by inserting spontaneous
infected individuals, or by the quasi-stationary method, where we store a list
of active states to continue the simulation when the system visits the
absorbing state. The system presents an absorbing phase transition where the
critical behavior obeys the Mean Field exponents $\beta=1$, $\gamma'=0$, and
$\nu=2$. However, the different quasi-stationary states present distinct
finite-size logarithmic corrections. We also report the critical thresholds of
the model as a linear function of the network connectivity inverse $1/z$, and
the extrapolation of the critical threshold function for $z \to \infty$ yields
the basic reproduction number $R_0=1$ of the complete graph, as expected.
Decreasing the network connectivity leads to the increase of the critical basic
reproduction number $R_0$ for this model.
