Table 1

Parameters used in the models

Parameter	Definition	Default value	Range of values used in the model
n/a, not available.
μ	Entry rate. To maintain a constant population size, the entry and exit rates are assumed to be equal.	0.02 per year	n/a
β^A_k, β^B_k	Transmission rate of strain A or strain B to sex k per contact	0.5 per contact	0<β<1
σ^A_k, σ^B_k	Recovery rate from asymptomatic infection with A or B per year (recovery rate = 1/duration)	σ = 2 per year without treatment, increasing to 10 per year, with treatment	With treatment, recovery depends on efficacy of treatment and the average time taken to seek treatment
	σ = 2 per year—that is, average duration of 6 months without treatment, decreasing to 10 per year (1.2 months duration with treatment)
γ^A, γ^B	Proportion of contacts with superinfected individuals, which result in transmission of A or B only. (If γ^α + γ^β = 0, then all contacts result in transmission of superinfection, if γ^α + γ^β = 1, then all contacts with coinfected individuals result in the transmission of a single strain	γ^α = γ^β = 0.4	0 ≤ γ ≥1
		Therefore proportion of contacts which result direct transmission of coinfection is: 1−(γ^α + γ^β) = 0.2	γ^α + γ^β ≤1
ω^α, ω^β	Proportion of those recovering from superinfection who remain infected with strain A or B. The extreme cases are when either all recovery is from mixed infection to the susceptible class (ω^α = ω^β = 0); or all recovery is from single infections (ω^α + ω^β = 1)	ω^α = ω^β = 0.2	0 ≤ ω ≥0.5
			ω^α + ω^β ≤1
	In the examples given in the text, 40% of recovery from coinfection is from a single strain (equally split between the two strains), and 60% is recovery to the susceptible class directly, for example due to treatment
ϕ^A, ϕ^B	Protective effect of infection with strain A, or strain B on likelihood of transmission of different strains (total protective effect, no coinfection (ϕ^α = ϕ^β = 0) to no protective effect (ϕ^α = ϕ^β = 1)). An enhancing effect of transmission due to prior infection could also be given by ϕ^α or ϕ^β >1	ϕ^A = ϕ^B = 0.5	0 ≤ ϕ ≤1 for protective effect, or ϕ >1 for enhancing effect
ρ_klm	Mixing matrix, element klm is the probability that individual of sex k in activity class l will form a partnership with a member of activity class m of the opposite sex	See appendix	n/a
c_kl	Contact rate of individual of sex k, activity class l (see below)	See appendix	n/a
ε	Pattern of mixing (0 = fully assortative, 1 = random)	1 (random)	0 ≤ ε ≥ 1