Time trajectories and heterogeneity for emergent disease in the stochastic model.

<p>(A) Population numbers, <i>S</i>(<i>t</i>), <i>I</i>(<i>t</i>), and <i>N</i>(<i>t</i>). (B) Proportion of sub-populations containing infectives, , effective transmission rate <i>β</i>, and dispersal rate. (C) Distribution of <i>I</i> across sites. (D) Effective transmission rate <i>β</i> for disease transmission vs population reduction coverage <i>p</i>₁. Parameters are given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086563#pone-0086563-t002" target="_blank">Table 2</a>, and initial conditions are at the disease free equilibrium , while in 20% of sites randomly chosen, a single individual is infected, resulting in . Population reduction occurs annually from years 50–69, and in of sites (chosen randomly each year) the removal rate is set to , without regard to disease status (equivalent to an overall culling rate of ). An initial reduction in <i>I</i> is rapidly replaced by an increase, which is due to the increased chance of invasion of naïve groups by infectives due to the density dependent dispersal. The CI for the effective transmission rate increases for large due to the increasing number of simulations where the disease becomes extinct.