Smooth structures on definite four-manifolds with infinite fundamental group

For each odd integer $p>1$, we construct infinitely many pairwise non-diffeomorphic irreducible smooth structures on a definite 4-manifold with infinite fundamental group whose abelianization is $\mathbb{Z}\mathrm{/}2p\mathbb{Z}\times \mathbb{Z}\mathrm{/}2\mathbb{Z}$.