Consider a network of constant size N with variable number of links. New links are established randomly at rate c. Existing links between individuals with health states p and q (p,q [ S,I,R f g) disappear at rate b pq . The time evolution of the number L pq of pqlinks can be written as a system of ordinary differential equations _ L L pq~c L M pq {L pq {b pq L pq [39, 40] . L M pq denotes the maximum number of pq-links, which depends on the number of individuals in states p and q (L M pp~p p{1 ð Þ=2 and L M pq~p q for p=q) and thereby couples the network dynamics to the disease dynamics. In the steady state of the linking dynamics ( _ L L pq~0 ), the number of links of links of each type is given by L Ã pq~wpq L M pq , with w pq~c czb pq À Á .