(a) (b) r$_{13}$ = 0 r$_{13}$ = 0 0 50 100 150 200 250 300 Time (generations) 200 400 600 800 N Model A Model B 0 250 500 750 1000 Time (generations) 100 200 300 400 500 600 N Model A Model B Model A FIG. 5: Simulation results showing one realisation of the population dynamics of the reaction to the (transient) application of a therapeutic agent. We can see that in plot (a), which corresponds to a population with no quiescent state, the population upon application of the drug. On the contrary, a population with quiescence is able to survive to the period over which the drug is active, and recovering once the effect of the drug has worn off (plot (b)). Black lines correspond to the total population, red lines to individuals of type (1), green lines to individuals of type (2), and blue lines to quiescent (type (3)) individuals. Parameter values: r$_{12}$ = r$_{21}$ = 0 . 5, r$_{13}$ = r$_{31}$ = 0 for the upper pannel and r$_{13}$ = r$_{31}$ = 0 . 25 for the lower pannel, r$_{31}$ = 0 . 05, µ = 0 . 001, ϵ = 10 − $^{5}$, and α = 1. FIG. 6: Simulation results showing the survival probability, P [ N > 0], for the population dynamics of the reaction to the (transient) application of a therapeutic agent as a function of the parameter r$_{13}$ , i.e. the parameter controlling the flux of population between types 1 and 3. Parameter values: r$_{12}$ = r$_{21}$ = 0 . 5, r$_{31}$ = 0 . 05, µ = 0 . 001, ϵ = 10 − $^{5}$, and α = 1. 13 8