Figure 3.

Graphical analysis of the three type-reproduction numbers. (a–c) The three type-reproduction numbers (R_m, R_f, R_j) are plotted as a function of the geometric mean of the sexual transmission rates $\sqrt{{\beta }_{\mathrm{f}\to \mathrm{m}}{\beta }_{\mathrm{m}\to \mathrm{f}}}$ for constant vertical transmission rate (α = 0.5), and (d–i) they are plotted as a function of α for constant sexual transmission rates. The left panels (a,d,g) represent the same sexual transmission rate (β_f→m = β_m→f), the middle panels (b,e,h) represent the case in which the sexual transmission rate from males to females is greater than that in the opposite direction (β_m→f = 10β_f→m), and the right panels (c,f,i) represent the case in which the sexual transmission rate from females to males is greater than that in the opposite direction (β_f→m = 10β_m→f). For the case that β_f→mβ_m→f is large (d–f), R_j is not plotted because it diverges. The other parameters are set as k_f, k_m = 0.8, c_f, c_m = 20, μ_f, ${\mu }_{\mathrm{f}}^{\text{'}}$, μ_m, ${\mu }_{\mathrm{m}}^{\text{'}}$, μ_j, ${\mu }_{\mathrm{j}}^{\text{'}}$ = 1/50, η_f, η_m, η_j = 0, δ = 0, λ = λ′ = 1/15, then α_eff = α.