Dynamics for varying disease invasion threshold.

<p>Plotting dynamics as a function of predator death rate <i>μ</i>_<i>P</i>, and disease invasion threshold <i>(μ</i>_<i>J</i>+<i>α)/β</i>. <i>(a)</i> Dynamics for the case of <i>δ</i> = 1. In the white area the disease cannot invade, and in the pink area there is a single endemic equilibrium. The blue area indicates bistability between a stunted endemic state and a non-stunted disease free state. The red line denotes predator extinction. The green and blue line are thresholds below which the disease can invade respectively, the stunted and non-stunted host population. The dashed black lines indicate the disease free region of bistability <i>(b)</i> Dynamics for the case of <i>δ</i> = 0. In the green area only the disease free non-stunted state is stable. The yellow area indicates stable recurrent epidemics, and in the purple area there is bistability of recurrent epidemics and an endemic state. The orange line is a Hopf bifurcation, either supercritical (solid line) or subcritical (dashed line). Other lines and areas are as described in Fig 4<i>a (c)</i> Bifurcation diagram for the subcritical Hopf bifurcation for <i>β</i> = 0.06. The bifurcation resembles that of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132251#pone.0132251.g003" target="_blank">Fig 3<i>c</i></a>, but now there is a region of bistability between an endemic state and a stable limit cycle for 0.588 < <i>μ</i>_<i>P</i> < 0.595. The red area denotes the amplitude of the stable limit cycle, and the dashed red line shows the minimum and maximum of the unstable limit cycle. For parameters see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132251#pone.0132251.g003" target="_blank">Fig 3</a>.