  In this paper we continue the study on intrinsic Harnack inequality for non-
homogeneous parabolic equations in non-divergence form initiated by the first
author in [1]. We establish a forward-in-time intrinsic Harnack inequality,
which in particular implies the H\"older continuity of the solutions. We also
provide a Harnack type estimate on global scale which quantifies the strong
minimum principle. In the time-independent setting, this together with [1]
provides an alternative proof of the generalized Harnack inequality proven by
the second author in [9].
