Table 1.

List of symbols

Symbol	Definition	Sample value used	Parameter range
CU	Unvaccinated female children	(state variable)
AU	Unvaccinated adult women	(state variable)
CV	Vaccinated female children	(state variable)
AV	Vaccinated adult women	(state variable)
IU	Uninfected adult women	(state variable)
IV	Infected adult women	(state variable)
M	Uninfected men	(state variable)
N	Infected men	(state variable)
πW	Rate of appearance of new females	50 per year	0–100
πM	Rate of appearance of new males	50 per year	0–100
ε	Vaccine immunogenicity in female children	98%	75–98%
$\overline{\epsilon }$	Vaccine immunogenicity in adult women	98%	75–98%
p	Proportion of female children vaccinated	77%	0–100%
$\overline{p}$	Proportion of adult women vaccinated	40%	0–100%
μC	Mortality rate of children	1/70 years -1	1/140–1/13
μ	Leaving rate of adults	1/10 years-1	1/12–1
α	Rate of progression of female children to sexually activity	$\frac{1}{13-1/\mu }{\text{years}}^{-1}$	1/12–1
c	Attentuation constant	0.15 years-1	0–0.3
γ	Maximal possible rate of adult vaccination	0.1	0–0.2
$f(\overline{\epsilon }\overline{p})$	Rate at which unvaccinated adult women are vaccinated	$\frac{c\overline{\epsilon }\overline{p}}{1-\overline{\epsilon }\overline{p}+\gamma }$
βN	Probability of infection of a woman by an infected man	0.00056	0–0.00112
βM	Probability of infection of a man by an infected woman	0.0003	0–0.0006
ψ	Vaccine efficacy	95%	85–95%

Sample parameters were chosen so that $\frac{1}{\mu }+\frac{1}{\alpha }=13$ (ie the total time between vaccination and leaving was always 13 years), γc^-1 = 16.67 (ie the optimum age of vaccination for a perfect vaccine with 100% coverage was 16 years 9 months), β_N > β_M (ie the transmission probability from men to women was higher than from women to men), the total prevalence without vaccination was 24% and so that the proportion of adult-only vaccination was equal to the proportion of childhood-only vaccination required to eradicate targeted types.