Study design for each model.

<p>For each <i>R</i>₀, two scenarios are tested which are described by the number of stages in the exposed period distribution (<i>m</i>) and the number of stages in the infectious period distribution (<i>n</i>). The abbreviated model notation is also included.</p

Influenza dynamics as predicted by the breeding farm model, for (a) sows and gilts and (b) piglets, in a naïve (non-vaccinated) population.

<p>At time 0, one infectious gilt enters the breeding farm. Note that in panel (b) the piglets include both those with no maternal immunity and those with a reduced susceptibility due to maternal immunity. The discontinuities in the curves in these figures (and in subsequent figures) are caused by the weekly movement of swine through the farm or the removal of weaned piglets from the farm (as described in the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0106177#s2" target="_blank">Methods</a>). The equilibrium dynamics are those after the initial peak in the number of infectious animals; these continue beyond the 40 days shown here.</p

Outbreak sizes.

<p>Frequency distribution of outbreak sizes based on 10,000 stochastic simulations of four SEIR models with <i>R</i>₀ of 1.2 or 1.8, and either exponentially distributed or gamma-distributed incubation and infectious periods (1∶1 and 3∶3, respectively). All outbreaks were retained for this figure regardless of the number of deaths.</p

Parameters involved in the wean-to-finish farm model, with definitions, values and the sources of the values.

<p>Parameters involved in the wean-to-finish farm model, with definitions, values and the sources of the values.</p

Wean-to-finish farm size effects on the proportion of infectious pigs at the infection peak.

<p>This proportion is a saturating function of farm size, defined as the number of pigs on the farm.</p

Outbreak schematic of our motivating assumption.

<p>Schematic of two infection histories of the first four infected individuals in an outbreak illustrating the times of infection (light gray squares), transitions from incubation to infectious period (gray triangles), and death of infectious individuals (black circles). We hypothesize that minor outbreaks are more likely when intervals between death times are wide and the number of concurrently infected individuals is low (A) and major outbreaks should occur with higher probability when death times are clustered and several individuals may be simultaneously infected (B). A more realistic pattern of deaths would include increased variability in incubating and infectious periods.</p

“Matched” versus “calculated” probabilities.

<p>The proportion of estimated <i>matched</i> outbreaks that are major (y axis) compared to calculated <i>p_m</i> values from the corresponding <i>observed_tm</i> outbreaks at the time of the 4^th death (x axis) for each of the four models. Each ‘predicted proportion of major outbreaks’ point on the figure represents the average of 200 to 4000 <i>matched</i> outbreaks. The lines represent fitted values from a linear regression model.</p

Schematic of a standard commercial swine breeding farm showing the demographic and spatial structure assumed in our mathematical model.

<p>This farm houses <i>gilts</i> (female pigs that have not yet been mated), <i>sows</i> (female pigs) and <i>piglets</i> (young pigs). There are three separate buildings (indicated by the shaded boxes), and the farrowing building is subdivided into four rooms. <i>Farrowing</i> means the production of a litter of piglets, and <i>weaning</i> is the separation of a sow and her piglets. New gilts enter the gilt development unit (building 1) at a replacement sow rate of 50% year⁻¹. From here, animals are moved to building 2 and inseminated. Typically, swine farmers rely primarily on artificial insemination for breeding and house only a small number of boars, thus we have excluded boars from the model. After 112 days, pregnant sows are moved to building 3, where 2–7 days later they give birth to an average of 12 piglets per sow. Sows remain in building 3 for 28 days, and then are moved back to building 2. After one week, insemination takes place again, and this cycle continues. Weaning occurs twice a week. After weaning, piglets are removed from the breeding farm. The overall death/removal rate for sows is 50% year⁻¹, with 80% of this occurring after weaning at the cull of unproductive sows. The natural death rate for piglets is 10% from birth to weaning. Class indices (gilts and sows) and (piglets) (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0106177#pone-0106177-t001" target="_blank">Table 1</a>) are indicated.</p

SEIR model with demographic stochasticity.

<p>SEIR model with demographic stochasticity.</p

Results from the wean-to-finish farm model, when all pigs have maternal immunity (from immune mothers).

<p>At time 0, the farm becomes fully populated and one infectious pig enters.</p