Figure 4: Mechanics of disease spread in theoretical networks.

(a) Star graphs, or networks of interconnected stars, are an example of networks with large variance in degree distribution. Hubs facilitate the spread of the first disease in a susceptible population. (b) New disease strains are likely to appear in the leaves. Hubs are likely to be already infected, hindering invasion. (c) Susceptible hubs are likely to be quickly reinfected by leaves infected with the resident strain. Therefore, the fixation probability of new strains on star-like graphs is low. (d) Small-world networks are made up of mainly local connections with variable rewiring to create shortcuts. (e) The initially infected individual can potentially infect all its neighbours, while those subsequently infected have more limited options. (f) Shortcuts allow the disease to jump to fully susceptible areas of the network, facilitating spread. They are less important for the second disease, as all parts of the network are already infected. Therefore, fixation probability of new strains on uniform, locally connected networks does not depend on the rewiring probability. (g,h) The degree distribution of the full network (green; left) is compared with the residual network (red; right) of susceptible individuals remaining at a particular time point during endemic equilibrium. (g) Uniform network (equivalent to gamma-distributed network with σ=0). (h) Gamma network with σ=3. Dotted lines represent the mean of the distributions.