Multiple modes of transmission example.

<p>Disease spread in a population with three different types of partnerships, each with a different degree distribution described in 2.2.4. Simulations in a population of individuals (solid) and theory (dashed) are in good agreement. We choose to correspond to % cumulative incidence.</p

Variable-degree serosorting model.

<p>Flow diagram showing the interplay involved in serosorting. We do not consider a recovered class, which simplifies the equations significantly. The framework can be adapted to include a recovered class. The variables give the proportion of contacts that would be formed with susceptible or infected individuals assuming that their behavior is not altered by disease. The variables are the probability that a current contact of the test node is with an individual of given type, under the assumption that the test node always behaves as if susceptible, and does not transmit to its partners. We expect that the edge breaking and rejoining rates will depend on values of and . Note that need not equal .</p

Directed CM model.

<p>Flow diagram for a network with directed and nondirected edges. We consider the two edge types separately. The evolution of edges is similar to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0069162#pone-0069162-g002" target="_blank">figure 2</a>. We can assign different infection rates for each edge type.</p

Multiple infectious stages example.

<p>The spread of the disease described in 2.2.5 with three infectious stages. Simulations in a population of individuals (solid) and theory (dashed) are in good agreement. We choose to correspond to % cumulative incidence.</p

Variables and equations for the basic EBCM approach.

<p>Equations and variables assuming a negligibly small initial proportion infected. In each case is a randomly chosen test individual (prevented from transmitting to others) and is a random partner of .</p

Heterogeneous infectiousness/susceptibility model.

<p>We separate nodes by type , but assume that has no effect on connectivity. Both infectiousness and susceptibility may depend on . We must consider edges between each pair of types and separately. The evolution of edges is similar to before.</p

Assortative mixing by type model.

<p>We separate nodes by type. We assume that type may influence infectiousness and susceptibility as well as connections. For simplicity, we assume a finite number of groups. The resulting system is similar to our system for correlated infectiousness and susceptibility.</p

Models investigated in this article.

<p>The edge-based compartmental models considered here. All of these except serosorting are presented using the (static) Configuration Model network structure. Serosorting is presented in two different dynamic network contexts.</p

Multiple modes of transmission model.

<p>Flow diagram showing the flux of edges for the -th contact type for a disease which has multiple modes of transmission.</p

Multiple infectious stages model.

<p>Flow diagrams for a disease with several infected stages. When a disease progresses through several states (or has an infectious period that is not exponentially distributed) it is convenient to use a stage-progression model to represent the state of an edge.</p