Figure 3: Dynamics of disease evolution in heterogeneous networks and small-world networks.
From: Evolution and emergence of infectious diseases in theoretical and real-world networks
(a–d) Heterogeneous networks; (e–g) small-world networks. (a) Degree distribution for upper panels is specified by a discrete gamma distribution (see Methods) with constant mean ‹k›=4 but tunable variance σ2. (b) The probability that a single disease causes an epidemic (the emergence probability), Pemerge, 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 multi-type branching process approximation (equation (9), solid lines) is in excellent agreement with the simulations (dots). (c) The probability of being infected at endemic equilibrium versus degree k. Predictions using pair-wise approximations (equation (17), lines) are in excellent agreement with simulations (bars). (d) The probability of fixation versus the selective advantage (r=β2/β1) of a new disease variant decreases for networks with larger variance in degree. Calculations from a new combined analytical technique (equation (18), solid lines) match well with simulations (dots). (e) For the lower panels, a set of small-world networks was created with constant homogeneous degree k=4 but varying clustering coefficient φ. (f) The probability of emergence for the first strain as a function of scaled transmissibility depends on clustering. (g) The fixation probability of the second strain as a function of the selective advantage, r=β2/β1, is independent of local clustering. For small-world networks, lines are simply connections between points to guide the eye.
