Table 2.

Symbols used.

S	proportion susceptible to both strains
Ii	proportion in primary infection with strain i={1,2}
Ri	proportion immune to strain i only
Ji	proportion in secondary infection with strain i={1,2}
R	proportion immune to both strains
V	proportion vaccinated and still immune to strain 1
IV2	proportion vaccinated and infected by strain 2
β	rate of transmission
γ	rate of recovery
μ	birth and death rate
p	vaccine coverage (proportion of newborns vaccinated)
σ	rate of loss of natural immunity
σV	rate of loss of vaccine immunity
θ	cross-protection conferred by primary infection (reduction in susceptibility)
ν	cross-protection conferred by primary infection (reduction in infectious period)
τ	cross-protection conferred by vaccination (reduction in susceptibility)
η	cross-protection conferred by vaccination (reduction in infectious period)
R0	basic reproductive ratio of the pathogen: R0=β/(γ+μ)