Cellular senescence is a vital cell surveillance mechanism that arrests the cell cycle in damaged cells. Molecules produced by senescent cells can spread the senescence phenotype through paracrine signalling, with molecules diffusing from a secreting senescent cell and binding to the surface of a non-senescent cell, leading to the induction of senescence. Although there is recent evidence that signalling between cells in direct contact also spreads senescence, the dynamics of senescence spread are not well understood. Senescent cells are important in ageing, wound healing, and cancer, yet it is unclear how the spread of senescence is contained in finite senescent lesions. In the absence of the immune system, senescence could theoretically spread infinitely from one cell to another, but this contradicts experimental evidence. To investigate this issue, we developed a minimal model and a stochastic simulation of senescence spread. Our results suggest that differences in the number of signalling molecules secreted between subtypes of senescent cells can limit the spread of senescence. We also found that dynamic, time-dependent paracrine signalling prevents the uncontrolled spread of senescent cells. Finally, we propose an experiment to determine a subset of system parameters and show that this is possible with Approximate Bayesian Computation.