Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumor growth. Understanding how variability in cell-cycle progression and local spatial constraints interact to impact population-level behavior requires modeling frameworks that explicitly represent individual-cell behavior and elucidate how these affect emergent tissue-level behavior. We develop stochastic, on-lattice agent-based models (ABMs) which incorporate volume exclusion, random movement, and multistage representations of the cell cycle. The multistage framework enables a more realistic representation of true cell-cycle time distributions. We also introduce a form of myopic behavior, in which cells sense their local environment when attempting to proliferate. For each ABM, we derive a corresponding continuum partial differential equation (PDE) description under the mean-field approximation. Using numerical simulations, we investigate how different proliferation mechanisms influence population-level dynamics in both the discrete and continuum models. In particular, we consider biologically relevant contexts of growth-to-confluence assays (using uniform initial conditions) and traveling wave behavior associated with cell invasion. We examine how the PDE solutions compare with the behavior of the corresponding ABMs averaged over many realizations.

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• Cell division
• Population dynamics
• Front propagation
• Reaction diffusion systems
• Stochastic dynamical systems
• Traveling waves