Bifurcation diagram with , , and as given.

<p>The figure on right zooms in on the bifurcation point. Disease parameters are and . In each all members of the population have degree either or , with the proportions chosen so that takes the values on the horizontal axis. The dashed curves denote unstable equilibria and the solid curves stable equilibria. Approximate curves (dotted) come from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101421#pone.0101421.e390" target="_blank">equation (5)</a>. Only the equilibria with are biologically meaningful.</p

Epidemic final sizes in population of individuals with half having degree and half with degree .

<p>The disease parameters are , . Results of simulations having initial infections chosen with probability proportional to square of degree (left) or inverse square of degree (right). For each initial number of infections, simulations were performed, each with a different network. For the range , simulations were performed to give insight into how well resolved the distribution is. Note that for small numbers of initial infections, epidemics are less likely when the lower degree individuals are chosen.</p

Flow diagram showing the flux of individuals between the different compartments.

<p>Because we have an explicit expression for , if we know we do not need to explicitly determine the flux from to .</p

The variables we need to calculate the epidemic dynamics. In all of these is a test individual: randomly chosen from the population and modified so that it cannot infect others, although it can become infected.

<p>The variables we need to calculate the epidemic dynamics. In all of these is a test individual: randomly chosen from the population and modified so that it cannot infect others, although it can become infected.</p

A comparison of the observed and predicted number of infections from simulations.

<p>Left: 5% initially infected, chosen randomly from the population. Right: 5% initially infected, chosen with probability proportional to squared degree. Each simulation curve represents a single simulation of the given size. As population size increases, the results converge to the theoretical prediction.</p

The impact of interventions.

<p>Epidemics begin at with of the population infected. Left: epidemic curve without interventions, and with each intervention introduced at time . Right: horizontal axis is , showing final effectiveness if interventions introduced at different times</p

The degree distribution used in simulations in [14].

<p>The degree distribution used in simulations in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0101421#pone.0101421-Lindquist1" target="_blank">[14]</a>.</p

Sequence of events in each time step.

<p>We begin with a network with some infected individuals (red). Then infected individuals transmit to some partners (red edges). Then some individuals leave the population (white). Other individuals are born (blue). Then some partnerships break (dashed). Finally new partnerships are created so that the new individuals, the individuals whose partners left, and the individuals whose partnerships broke all return to their target number of partners. The sequence of events then repeats.</p

Sample scenarios comparing serially monogamous (top) and concurrent (bottom) relationships.

<p>Shaded regions denote the existence of a partnership between “Alex” and either “Bobbie” or “Charlie”, with darker shading representing a partnership having a higher transmission rate. Dashed lines denote transmission events within the relationship that would cause infection if one individual were infected and the other susceptible. Vertical red lines denote time at which an individual is infected, and horizontal red lines denote successful transmissions. In the concurrent case, the transmission events occur at exactly the same times, but the transmission could occur in either partnership. Thus the interaction rate within each partnership is half that of the serial case. Concurrency provides additional transmission routes and tends to speed up onwards transmission. In the left panels Bobbie begins infected, in the cenral panels Alex begins infected, and in the right panels Charlie begins infected.</p

The parameters for our simulations and equations.

<p>The last four are derived from the previous parameters.</p