Influence of mutations in phenotypically-structured populations in time periodic environment

Figure 1.  Proliferation and sensitivity functions chosen for the simulations

Figure 2.  Final mean populations $ \bar{\rho}_N $ represented as functions of the mutation rate $ D $ for various treatment schedules. The treatments are of the form $ C(t) = \mathbf{1}_{0\leq t \leq \tau}M/\tau $, with $ M = 2 $ and $ \tau $ varying between $ 1/4 $ and $ T = 2 $. Populations $ A $, $ B $ and $ C $ are detailed in figure 3

Figure 3.  Populations $ A $, $ B $ and $ C $ of figure 2 are detailed for $ \tau = 1/4 $. We represent the population repartition in phenotypes just before treatment, just after treatment and the mean population

Figure 4.  Illustration of the conjecture that $ \bar{\rho}_N $ is a decreasing function of the time of drug administration $ \tau $. These numerical simulations were performed for $ T = 2 $

Figure 5.  Illustration of Proposition 4 on the influence of $ T $ on the population size. These numerical simulations were performed for $ \tau = T/2 $ and a fixed diffusion coefficient $ D = 0.1 $

Figure 6.  Mean limit population $ \bar{\rho}_N $ as a function of both diffusion and drug dosage per period $ M $

Figure 7.  Populations for random changing of environment with same mean value