Figure 1.
Schematic of a standard commercial swine breeding farm showing the demographic and spatial structure assumed in our mathematical model.
This farm houses gilts (female pigs that have not yet been mated), sows (female pigs) and piglets (young pigs). There are three separate buildings (indicated by the shaded boxes), and the farrowing building is subdivided into four rooms. Farrowing means the production of a litter of piglets, and weaning 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 Table 1) are indicated.
Table 1.
The class of pigs (type and farm location) corresponding to each index value for the breeding farm model.
Table 2.
Parameters involved in the swine breeding farm model, with definitions, values and the sources of the values.
Table 3.
Parameters involved in the wean-to-finish farm model, with definitions, values and the sources of the values.
Figure 2.
Influenza dynamics as predicted by the breeding farm model, for (a) sows and gilts and (b) piglets, in a naïve (non-vaccinated) population.
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 Methods). The equilibrium dynamics are those after the initial peak in the number of infectious animals; these continue beyond the 40 days shown here.
Figure 3.
Influenza infection dynamics as predicted by the breeding farm model with variability in transmission rates, for (a) sows and gilts and (b) piglets.
The population of swine is naïve (non-vaccinated). At time 0, one infectious gilt enters the farm. These panels show the results of 15,000 runs, where for each run, all transmission rates are taken from random sampling from a uniform distribution spanning their 95% confidence intervals (Table 2).
Figure 4.
Summary of the effects of vaccination strategies on the number of infectious animals in the breeding farm, for (a) sows and gilts and (b) piglets.
In (a), note that the ‘Mass vaccination – homologous’ curve lies along the x axis (as infection is eliminated). In (b), the ‘Mass vaccination – heterologous’ curve is mainly obscured by the ‘Pre-farrow vaccination – heterologous’ curve, which is very similar. For these results, vaccination occurs prior to the introduction of influenza.
Figure 5.
Results from the wean-to-finish farm model, when all pigs have maternal immunity (from immune mothers).
At time 0, the farm becomes fully populated and one infectious pig enters.
Figure 6.
Model results for the wean-to-finish farm under two different reinfection assumptions.
In (a), we show the number of infectious pigs in a population without vaccination and assume that pigs that are infected early can reenter the susceptible pool once recovered. In (b), we assume that recovered individuals can become susceptible again, due to either a change in the influenza virus, or through the loss of immunity. The average rate at which recovered animals move into the susceptible pool () is
in this example. Panel (b) also shows the number of infectious pigs when the population is vaccinated at t = 70 (after maternal immunity has been lost). The heterologous vaccination at 70 days produces little effect on the number of infectious pigs.
Figure 7.
Breeding farm size effects on the proportion of infectious piglets at the maximum of the cycles at equilibrium.
Farm size is defined as the number of sows and gilts on the farm.
Figure 8.
Wean-to-finish farm size effects on the proportion of infectious pigs at the infection peak.
This proportion is a saturating function of farm size, defined as the number of pigs on the farm.