We note that the copy numbers $Pₐ$ are highly stochastic. Meanwhile, $M$ exists in so large copy numbers that its trajectory can be considered approximately deterministic. For models like this one, jump simulations are required to capture the stochastic behaviour of the promoter. However, the large number of jumps generated by $M$ makes such simulations excessively expensive. Here, *hybrid simulations* can be used. Hybrid simulations employ different simulation strategies for their different components. In our example, the state of the promoter could be simulated using a jump simulation, while $M$ could be simulated using an ODE.
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