Space-charge effects, being one of the most significant collective effects, play an important role in high intensity cyclotrons. However, for cyclotrons with small turn separation, other existing effects are of equal importance. Interactions of radially neighboring bunches are also present, but their combined effects have not yet been investigated in any great detail. In this paper, a new particle in the cell-based self-consistent numerical simulation model is presented for the first time. The model covers neighboring bunch effects and is implemented in the three-dimensional object-oriented parallel code OPAL-CYCL, a flavor of the OPAL framework. We discuss this model together with its implementation and validation. Simulation results are presented from the PSI 590 MeV ring cyclotron in the context of the ongoing high intensity upgrade program, which aims to provide a beam power of 1.8 MW (CW) at the target destination. DOI: 10.1103/PhysRevSTAB.13.064201