Figure 4

Hysteresis effect with varying collective cooperation threshold T. As T increases from 0 to 1 the proportion of infected I and cooperating C initially exhibit damped oscillations as in Fig. 3b, but instead of stabilizing at equilibrium 4, as it would for a fixed T, the increasing threshold eventually renders equilibrium 4 unstable and the system instead approaches and stabilizes at equilibrium 3 (\(C=0\) and \(I=1-r/g\)). From there, when T decreases from 1 back to 0, the proportion infected and cooperating does not follow the increasing T path in reverse. Instead, the system remains in equilibrium 3 until T has decreased beyond 0.25 at which point the system abruptly switches to approach equilibrium 4 and bypasses the oscillatory phase observed when T was increasing. Indicating that this system exhibits substantial hysteresis effects.