Figure 1:

Comparison of R₀ values calculated for multivariate normally-distributed (solid line) and log-normally-distributed (dashed line) heterogeneities for differing values of the correlation coefficient, $r_{X_1,X_3}$, between the biting rate, X₁, and average duration of human infection, X₃. X₁ and X₃ are taken to have means equal to 1 and 5, respectively, and variances Var(X₁) = 0.2 and Var(X₃) = 4. The value of the susceptibility parameter was fixed at 1 for the entire population. Lines are obtained using the MVN and MVLN formulae (eqns 17 and 18, respectively). The horizontal dashed line denotes the value of R₀ if there was no heterogeneity, i.e. obtained using the average values, $R_0^{\mathrm{hom}}$. Note that the basic reproductive number is the same for both distributions when the correlation coefficient is equal to zero, and that this is greater than the value $R_0^{\mathrm{hom}}$ obtained using the average values because of heterogeneity in the biting rate.