  We consider the mean-field approximation of an individual-based model
describing cell motility and proliferation, which incorporates the volume
exclusion principle, the go-or-grow hypothesis and an explicit cell cycle
delay. To utilise the framework of on-lattice agent-based models, we make the
assumption that cells enter mitosis only if they can secure an additional site
for the daughter cell, in which case they occupy two lattice sites until the
completion of mitosis. The mean-field model is expressed by a system of delay
differential equations and includes variables such as the number of motile
cells, proliferating cells, reserved sites and empty sites. We prove the
convergence of biologically feasible solutions: eventually all available space
will be filled by mobile cells, after an initial phase when the proliferating
cell population is increasing then diminishing. By comparing the behaviour of
the mean-field model for different parameter values and initial cell
distributions, we illustrate that the total cell population may follow a
logistic-type growth curve, or may grow in a step-function-like fashion.
