Stochastic optimal switching model for migrating population dynamics

Figures & data

Figure 1. Conceptual diagram of the population dynamics. The time is represented in the sense of mod $T$.

Figure 2. Computed reduced value function ${\mathrm{\Psi }}_0$. The contour lines represent 0.1, 0.2, 0.3, … 0.9 times of the maximum value of ${\mathrm{\Psi }}_0$ in the plotted area.

Figure 3. Computed reduced value function ${\mathrm{\Psi }}_1$. The contour lines represent 0.1, 0.2, 0.3, … 0.9 times of the maximum value of ${\mathrm{\Psi }}_1$ in the plotted area.

Figure 4. Computed sub-domains $D_{01}$ (Red) and $D_{10}$ (Blue).

Figure 5. Dependence of the sub-domain $D_{01}$ on $R_0$.

Figure 6. Dependence of the sub-domain $D_{01}$ on $r_0$.

Figure 7. Dependence of the sub-domain $D_{01}$ on ${\sigma }_0$.

Figure 8. The basic reproduction number $\mathcal{R}$ against different values of $r_0$ (1/day). The grey circles represent $\mathcal{R}>1$, while white circles represent $\mathcal{R}=1$.

Figure 9. The basic reproduction number $\mathcal{R}$ against different values of ${\sigma }_0$ (1/day^1/2). The grey circles represent $\mathcal{R}>1$, while white circles represent $\mathcal{R}=1$.

Figure 10. The basic reproduction number $\mathcal{R}$ against different values of ${\mathcal{R}}_0$ (1/day). The grey circles represent $\mathcal{R}>1$, while white circles represent $\mathcal{R}=1$.

Figure 11. The basic reproduction number $\mathcal{R}$ against different values of $a$. The grey circles represent $\mathcal{R}>1$, while white circles represent $\mathcal{R}=1$.