Table 2 Relative sizes of the parameters used to create Figs. 3 and 4. Since the sex ratio is approximately 1:1 (\({\upgamma }_{\mathrm{m}}\cong {\upgamma }_{\mathrm{w}}\)) and the life history parameters are almost equal in the four sex categories, the magnitude relations are roughly established. In addition, the relative magnitude of \({R}_{i\to j}^{\mathrm{h}}\) is obtained from \({R}_{i\to j}^{\mathrm{h}}={C}_{i}{R}_{i\to j}^{\mathrm{v}}\). Since \({\upgamma }_{\overset{\sim }{\mathrm{m}}},{\upgamma }_{\overline{\mathrm{m}} }<{\upgamma }_{w},{\upgamma }_{\mathrm{m}}\), the route (\({R}_{\mathrm{w}\to \overset{\sim }{\mathrm{m}}}^{\mathrm{v}}\)) of sexual transmission from women to MSM can be said to be “narrower” than the opposite route (\({R}_{\overset{\sim }{\mathrm{m}}\to w}^{\mathrm{v}}\)). The effect (\({A}_{\overset{\sim }{\mathrm{m}}},{A}_{\overline{\mathrm{m}} }\)) of the vertical route from mother to MSM is also weaker than other mother-to-child transmissions (\({A}_{\mathrm{w}},{A}_{\mathrm{m}}\))
From: The effect of men who have sex with men (MSM) on the spread of sexually transmitted infections
\({R}_{\mathrm{w}\to \mathrm{m}}^{\mathrm{v}}\) | \({R}_{\mathrm{m}\to \mathrm{w}}^{\mathrm{v}}\) | \({R}_{\mathrm{w}\to \overset{\sim }{\mathrm{m}}}^{\mathrm{v}}\) | \({R}_{\overset{\sim }{\mathrm{m}}\to w}^{\mathrm{v}}\) | |
Relative size | \({\beta }_{\mathrm{w}\to \mathrm{m}}{k}_{\mathrm{hetero}}\) | \({\beta }_{\mathrm{m}\to \mathrm{w}}{k}_{\mathrm{hetero}}\) | \({\beta }_{\mathrm{w}\to \mathrm{m}}{k}_{\mathrm{hetero}}\frac{{\upgamma }_{\overset{\sim }{\mathrm{m}}}}{{\upgamma }_{\mathrm{m}}}\) | \({\beta }_{\mathrm{m}\to \mathrm{w}}{k}_{\mathrm{hetero}}\) |
\({R}_{\overset{\sim }{\mathrm{m}}\to \overline{\mathrm{m}} }^{\mathrm{v}}\) | \({R}_{\overline{\mathrm{m}}\to \overset{\sim }{\mathrm{m}} }^{\mathrm{v}}\) | \({R}_{\overset{\sim }{\mathrm{m}}\to \overset{\sim }{\mathrm{m}}}^{\mathrm{v}}\) | \({R}_{\overline{\mathrm{m} }\to \overline{\mathrm{m}} }^{\mathrm{v}}\) | |
Relative size | \({\beta }_{\overset{\sim }{\mathrm{m}}\overset{\sim }{\mathrm{m}}}{k}_{\mathrm{homo}}\frac{{\upgamma }_{\overline{\mathrm{m}}}}{{\upgamma }_{\overset{\sim }{\mathrm{m}}}+{\upgamma }_{\overline{\mathrm{m}}} }\) | \({\beta }_{\overset{\sim }{\mathrm{m}}\overset{\sim }{\mathrm{m}}}{k}_{\mathrm{homo}}\frac{{\upgamma }_{\overset{\sim }{\mathrm{m}}}}{{\upgamma }_{\overset{\sim }{\mathrm{m}}}+{\upgamma }_{\overline{\mathrm{m}}} }\) | \({\beta }_{\overset{\sim }{\mathrm{m}}\overset{\sim }{\mathrm{m}}}{k}_{\mathrm{homo}}\frac{{\upgamma }_{\overset{\sim }{\mathrm{m}}}}{{\upgamma }_{\overset{\sim }{\mathrm{m}}}+{\upgamma }_{\overline{\mathrm{m}}} }\) | \({\beta }_{\overset{\sim }{\mathrm{m}}\overset{\sim }{\mathrm{m}}}{k}_{\mathrm{homo}}\frac{{\upgamma }_{\overline{\mathrm{m}}}}{{\upgamma }_{\overset{\sim }{\mathrm{m}}}+{\upgamma }_{\overline{\mathrm{m}}} }\) |
\({A}_{\mathrm{w}}=\frac{{b}_{\mathrm{w}}}{1-{b}_{\mathrm{w}}}\) | \({A}_{\mathrm{m}}=\frac{{b}_{\mathrm{m}}}{1-{b}_{\mathrm{w}}}\) | \({A}_{\overset{\sim }{\mathrm{m}}}=\frac{{b}_{\overset{\sim }{\mathrm{m}}}}{1-{b}_{\mathrm{w}}}\) | \({A}_{\overline{\mathrm{m}} }=\frac{{b}_{\overline{\mathrm{m}}} }{1-{b}_{\mathrm{w}}}\) | |
Relative size | \(\alpha\) | \(\alpha\) | \(\frac{{\gamma }_{\overset{\sim }{\mathrm{m}}}}{{\gamma }_{\mathrm{m}}} \alpha\) | \(\frac{{\gamma }_{\overline{\mathrm{m}}}}{{\gamma }_{\mathrm{m}}} \alpha\) |