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. 2013 Jan 8;8(1):e53128. doi: 10.1371/journal.pone.0053128

Table 3. 2-host, 2-vector R 0 and possible approximations based on the 2-host, 1-vector formula.

Symbol Description † Formula in terms of R 11 and R 22 T  =  25oC T  =  15oC
a b c d
Inline graphic Inline graphic Inline graphic Inline graphic
R 0 Equation (1) 3.0736 3.4271 2.5860 3.5539
R 0,sum No cross-infection Inline graphic 4.3464 4.9829 2.8098 3.7631
R 0,minβ Total m with min β and Inline graphic Inline graphic 2.2492 2.0425 0.7776 0.7061
R 0,wtsum Weighted sum of R 0,minβ and R 0,maxβ Inline graphic 2.7086 2.7721 2.5261 3.4492
R 0,ave Total m with mean β and Inline graphic Inline graphic 5.4032 5.8104 1.9875 2.1372
R 0,maxβ Total m with max β and Inline graphic Inline graphic 7.3028 10.0674 2.7010 3.7235

Parameter values (1 = C. imicola, 2 = C. bolitinos): b 1 = 0.9, b 2 = 0.9, r C = 1/20.6, r S = 1/16.4, d C = 0, d S = 0.005, m S1 = m C1, m S2 = m C2, β 1, β 2, a 1, a 2, μ 1, μ 2, ν 1 and ν 2 are determined by temperature, (a) m C1 = 500, m C2 = 50, T = 25°C, σ 1 = 0.5 and σ 2 = 0.5, (b) m C1 = 500, m C2 = 50, T = 25°C, σ 1 = 1 and σ 2 = 0, (c) m C1 = 50, m C2 = 500, T = 15°C, σ 1 = 0.5 and σ 2 = 0.5, (d) m C1 = 50, m C2 = 500, T = 15°C, σ 1 = 1 and σ 2 = 0.

†

For the approximations R 0,minβ, R 0,wtsum, R 0,ave and R 0,maxβ, the formula given is for Inline graphic only. There is insufficient space to give the more general expressions.