Figure 2: Network structure influences the evolution of diseases on real and theoretical contact networks.

(a,b) Graphical representation of the networks. Large red or blue circles represent nodes with a high degree, small purple or green circles represent nodes with a low degree for the empirical and theoretical networks, respectively. (c,e) The probability that a single disease causes an epidemic (the emergence probability), P_emerge, versus the scaled transmissibility τ=β(‹k›−1)/γ. β is varied and τ represents the expression for the basic reproductive ratio for the uniform network. The thick grey line indicates the emergence probability for a well-mixed network, P_emerge=1−1/R₀. The transmissibility value at which P_emerge becomes non-zero (that is, the epidemic threshold) depends on the network. (d,f) Dynamics of new disease variants. The probability of fixation, P_fix, versus the selective advantage, r=β₂/β₁, of a new disease variant is strongly influenced by the population structure, but is not predicted by P_emerge. The thick grey line indicates the fixation probability in a well-mixed network, . (g) The selection exponent, α, is calculated by fitting P_fix versus r to equation (27). Lower values mean that selection is suppressed compared to the uniform network. For a uniform or well-mixed population we expect α=1. Fits are shown by the solid lines in panels (d) and (f).