Figure 1.

Intuitive derivation of Eqs. (15), (20–22). (a) The two figures represent the processes through which daughters and sons are vertically infected by an infected adult woman, where the average production numbers of vertically infected juveniles are given by α_eff and $\frac{\gamma }{1-\gamma }{\alpha }_{\mathrm{eff}}$, respectively. (b) The average total number of female offspring infected vertically by a horizontally infected adult woman is derived by a geometric series with initial term α_eff and geometric ratio α_eff, which gives Eq. (21). (c) The average total number of male offspring infected vertically by a horizontally infected adult woman is derived similarly, giving Eq. (22).