The following results are based on numerical simulations of the model equations in the Appendix
using the baseline parameter set. We assume that the new influenza virus would be already adapted for transmission in humans, so it is started in the human population with 1% of the humans initially infected, proportionally distributed among CAFO workers and the general population. Communities in which 0%, 15%, 30%, and 45% of the population are CAFO workers are considered. shows the simulated epidemic prevalence curves for humans (both CAFO workers and the general population). Note that the presence of CAFO workers increases dramatically the size of the epidemic and that these effects are greater as the percentage of CAFO workers increases. The peak of the epidemic is delayed and is approximately doubled when the percentage of CAFO workers is increased from 0% to 45%. This epidemic delay reflects the time that it takes for transmission of the infection into the swine followed by an outbreak in the swine and then transmission back to the local population.
Epidemic prevalence curves for humans corresponding to different percentages of CAFO workers in the community.
The bottom graphs in show how the increase in the epidemic curves for the local population coincides with the epidemic in swine. Notice also that the swine epidemic curve is independent of the percentage of CAFO workers in the community, since the majority of the new cases in hogs are due to contacts with other hogs. The peak in the CAFO workers epidemic coincides with the swine epidemic peak due to their close interaction with the confined species and is almost independent of the percentage of CAFO workers.
Epidemic curves showing the prevalences for the confined species, CAFO workers, and local population. Local communities consisting of 0%, 15%, 30%, and 45% CAFO workers are considered in each case.
Another way to evaluate the impact that the CAFO species, through the CAFO workers, might have on the influenza epidemic is by the percentage of seropositive individuals in the community at the end of the epidemic. shows the percentage increases in the total number of humans infected compared to the situation when no other species are present. For the baseline case (no vaccination) the total number of infected persons is increased by 42% and 86% when the CAFO workers represent 15% and 45% of the local population, respectively.
FIG. 4 Percentage increases in the final size of the human influenza epidemic as a function of the percentage of CAFO workers in the community. The curves correspond to pre-epidemic successful vaccination of 0% to 70% of the CAFO workers. Local communities with (more ...)
shows that when vaccination of CAFO workers is included in the simulations, the impact of the CAFO species is reduced. When 30% of the CAFO workers are successfully vaccinated prior to the epidemic, the percentage increase of human cases is reduced by more than half. Successful vaccination of 50% of the CAFO workers approximately cancels the amplification. The decrease in the number of human cases is even larger when 70% of the CAFO workers are successfully vaccinated.
shows the impact of
in humans on the percentage increase in human cases. The effect of the CAFO species is much larger when
decreases to 1.1 from its baseline value of 1.2. Even with 5% of CAFO workers in the community the percentage increase in cases is 38%. There would be a 154% increase, if 45% of the local population worked in a CAFO. The impact of CAFOs becomes more significant as
is decreased from its baseline value of 1.2. As the value of
decreases, the increase in amplification may be explained by the relative increase of
with respect to
, so that the role of the CAFO species becomes more important in the epidemic dynamics.
FIG. 5 Percentage increases in the final size of the epidemic as a function of the percentage of CAFO workers in the community with , 1.2, 1.3, 1.4, and 1.5. CAFO workers are 5%, 15%, 25%, 35%, and 45% of the local population.
To consider the sensitivity of the basic reproduction number
in swine, we varied the total fraction S∞
of infected swine at the end of a swine epidemic in our model from 50% to 95%. Our simulations showed no change in the percentage increase of human cases. This occurs because as the total percentage of infected swine is varied, the parameter βws
changes so that 50% of CAFO workers are infected.
shows the increase in the percentage of total human cases as a function of the percentage of CAFO workers, when the total fraction of CAFO workers infected (with a swine influenza virus) varied from 20% to 80%. The parameter c in βws = cβss increases as the total fraction of infected CAFO workers increases. Higher seropositivity percentages of CAFO workers to swine influenza strains lead to larger increases in human cases.
FIG. 6 Percentage increases in the final size of the human epidemic as a function of the percentage of CAFO workers in the community. The contact rate βws is based on data in which 20-80% of CAFO workers were seropositive to specific strains of swine (more ...)
Variation of the value of d in βsw = dβws does not change the amplification of the epidemic, but does change the epidemic duration. For the baseline value d = 0.01, the duration of the epidemic was 110 days and the maximum size of the epidemic was reached at 60 days (). When the value of d is increased to d = 0.2, the epidemic lasts around 90 days and the peak of the epidemic is at 40 days, but for d = 0.002 the epidemic lasts about 125 days with the peak at 75 days. Sensitivity analyses of the infectious periods were not done because consistent estimates for them exist in the literature.