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In this paper we put forward a viral propagation model with nonlinearinfection rate and free boundaries and investigate the dynamical properties.This model is composed of two ordinary differential equations and one partialdifferential equation, in which the spatial range of the first equation is thewhole space $\mathbb{R}$, and the last two equations have free boundaries. As anew mathematical model, we prove the existence, uniqueness and uniformestimates of global solution, and provide the criteria for spreading andvanishing, and long time behavior of the solution components $u,v,w$. Comparingwith the corresponding ordinary differential systems, the {\it BasicReproduction 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 varyingparameters.

A viral propagation model with nonlinear infection rate and free boundaries