Survival analysis for tumor growth model with stochastic perturbation

Figure 1.  The potential $ U(x) $ as a function of $ x $ for different value $ \beta $ with $ \theta = 0.25 $

Figure 2.  The steady probability distribution function of tumor cells population $ x(t) $ for model (4) with $ \theta = 0.25 $

Figure 3.  The valid regions as a function of $ \theta(t) $ and $ \beta(t) $

Figure 4.  Solutions of extinction of tumor cells for $ (a):\sigma^2(t) = 0.02+0.004\sin t $, $ \beta(t) = 3+\sin t $; $ (b):\sigma^2(t) = 1+0.8\sin t $, $ \beta(t) = 3+\sin t $; $ (c):\sigma^2(t) = 1+0.8\sin t $, $ \beta(t) = 6+\sin t $, with the initial value $ x_0 = 0.5 $

Figure 5.  Solutions of strong persistence in the mean of tumor cells for $ (d):\sigma^2(t) = 0.002+0.001\sin t $, $ \beta(t) = 0.97+0.009\sin t $, with the initial value $ x_0 = 0.5 $

Figure 6.  Solutions of strong persistence in the mean of tumor for $ (e):\sigma^2(t) = 0.02+0.002\sin t $, $ \beta(t) = 0.8+0.008\sin t $, with the initial value $ x_0 = 0.5 $

Figure 7.  Mean time to extinction (MET) as a function of the noise intensity for different values of $ \beta $ at $ \theta = 0.25 $