  We show global existence and boundedness of classical solutions to a virus
infection model with chemotaxis in bounded smooth domains of arbitrary
dimension and for any sufficiently regular nonnegative initial data and
homogeneous Neumann boundary conditions.
  More precisely, the system considered is
  \[ \begin{cases}\begin{split}
  & u_t=\Delta u - \nabla\cdot(\frac{u}{(1+u)^{\alpha}}\nabla v) - uw + \kappa
- u, \\ & v_t=\Delta v + uw - v, \\ & w_t=\Delta w - w + v,
\end{split}\end{cases} \] with $\kappa\ge 0$, and solvability and boundedness
of the solution are shown under the condition that \[ \begin{cases} \alpha >
\frac 12 + \frac{n^2}{6n+4}, &\text{if } \quad 1 \leq n \leq 4 \\ \alpha >
\frac {n}4, &\text{if } \quad n \geq 5. \end{cases} \]
