  In this paper we put forward a viral propagation model with nonlinear
infection rate and free boundaries and investigate the dynamical properties.
This model is composed of two ordinary differential equations and one partial
differential equation, in which the spatial range of the first equation is the
whole space $\mathbb{R}$, and the last two equations have free boundaries. As a
new mathematical model, we prove the existence, uniqueness and uniform
estimates of global solution, and provide the criteria for spreading and
vanishing, and long time behavior of the solution components $u,v,w$. Comparing
with the corresponding ordinary differential systems, the {\it Basic
Reproduction Number} ${\cal R}_0$ plays a different role. We find that when
${\cal R}_0\le 1$, the virus cannot spread successfully; when ${\cal R}_0>1$,
the successful spread of virus depends on the initial value and varying
parameters.
