Bifurcation diagram for our model. Bifurcation diagram for malaria. The dashed line shows and the arrows show the behavior of the system: in the white area, to the left of the manifold, the disease will die out while to the right of the manifold, in the shaded area, the disease will persist. The dark-shaded region represents the area in which malaria can invade and persist and the light-shaded area in which it persists, even though it would not invade. In these figures, all parameters are held constant except τ
. (a) A forward bifurcation occurs at . ρ=0.8. (b) A backwards bifurcation occurs at . ρ=4.