Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model

Figure 1.  Profile of $f$ defined in (2) (left) and of its anti-derivative $F$ (right) with parameters given by (5).

Figure 2.  Time dynamics with three different initial releases belonging to the set $RP_{50}^2(N)$ of (10), with $N/(N+N_0) = 0.75$. Integration is performed on the domain $[-L, L]$ with $L = 50 \textrm{km}$. The release box is plotted in dashed red on the first picture of each configuration. Left: Release box $[-2 L/3, 2 L/3]^2$. Center: Release box $[-L/2, L/2]^2$. Right: Release box $[-L/12.5, L/12.5]^2$. From top to bottom: increasing time $t \in \{0, 1, 25, 50, 75\}$, in days. The color indicates the value of $p$ (with the scale on the right).

Figure 3.  Comparison of minimal invasion radii $R_{\alpha}$ (obtained by energy) in dashed line and $L_{\alpha}$ (obtained by critical bubbles) in solid line, varying with the maximal infection frequency level $\alpha$. The scale is such that $\sigma=1$.

Figure 4.  Two $G_{\sigma}$ profiles and their sum (in thick line). The level $G_{\sigma} (0)$ is the dashed line. On the left, $h=\sqrt{2\log(2)\sigma}$. On the right, $h>\sqrt{2\log(2)\sigma}$.

Figure 5.  Under-estimation $\beta^{\lambda, R^*} (-L, L)$ of introduction success probability for $L$ ranging from $R^*/2 = 5.49$ to $3 R^*/2 = 16.47$. The seven curves correspond to increasing number of release points. (From bottom to top: $20$ to $80$ release points).

Figure 6.  Effect of losing the constant $2 \sqrt{2 \log(2)}$ in Proposition 6: under-estimation $\beta^{\lambda, R^*} (-L, L)$ of introduction success probability for $L$ ranging from $R^*/2 = 5.49$ to $3 R^*/2 = 16.47$, with $80$ release points.