Pattern dynamics of a delayed eco-epidemiological model with disease in the predator

Figure 1.  Schematic diagrams of the cubic function $y(e)$ for $y_{1}>0$ in Theorem 3.3. (a) $y_{3}x y0$. (b) $y_{3}=0$ and $y_{2} < 0$. (c) $y_{3}>0$, $y_{2}^{2}-3y_{1}y_{3}>0$ and $y_{2} < 0$

Figure 2.  The bifurcation diagram of system (4) in parameter space $r-h$. (a) Parameters are $\beta_{1}=1.8$, $\mu=0.6$, $m=0.8$, $D_{1}=1$, $D_{2}=0.03$, $D_{3}=2$, $\tau=0.01$. (b) Parameters are $\beta_{1}=1.8$, $\mu=0.6$, $m=0.7$, $D_{1}=10$, $D_{2}=0.1$, $D_{3}=4$, $\tau=0.01$

Figure 3.  Coefficients of the dispersion relation of the characteristic equation (16) for $r=0.1$, $h=0.07$, $\beta_{1}=1.8$, $\mu=0.6$, $m=0.8$, $D_{1}=1$, $D_{2}=0.03$, $D_{3}=2$, $\tau=0.01$

Figure 4.  Coefficients of the dispersion relation of the characteristic equation (16) for $r=0.1$, $h=0.1$, $\beta_{1}=1.8$, $\mu=0.6$, $m=0.7$, $D_{1}=10$, $D_{2}=0.1$, $D_{3}=4$, $\tau=0.01$

Figure 5.  Schematic diagrams of the cubic function $y(e)$ for $y_{1}>0$ in Theorem 3.4. (a) $y_{2}^{2}-3y_{1}y_{3}\leq 0$. (b) $y_{3}>0$, $y_{2}^{2}-3y_{1}y_{3}>0$ and $y_{2}>0$. (c) $y_{3}=0$ and $y_{2}>0$. (d) $y_{3} < 0$. (e) $y_{3}=0$ and $y_{2} < 0$. (f) $y_{3}>0$, $y_{2}^{2}-3y_{1}y_{3}>0$ and $y_{2} < 0$

Figure 6.  Spatial patterns (top) and the corresponding spatially averaged population density (bottom). (a) Small "black-eye" pattern (r=0.1), (b) small "black-eye" pattern (r=0.15)

Figure 7.  Spatial patterns (top) and the corresponding spatially averaged population density (bottom). (a) Big "black-eye" pattern (h=0.1), (b) big "black-eye" pattern (h=0.14)