Fig. 3.

Numerically-obtained values using integral in Eq. (21) to compute the length of time it takes for the transmission dynamics to reach the value of $M=M_{†}(z,k)$ for two different initial values of $M=M\left(t_0\right),$ as shown in the legend. A range of worm death rates have been used of ${\mu }_1=1/2{\text{years}}^{-1},1/5{\text{years}}^{-1},1/8{\text{years}}^{-1},1/12{\text{years}}^{-1}$ in decreasing order, which corresponds to a fading colour in the plotted lines.