Figure 5.

Cooperative contagion on mobile particles with velocity v for $d=30\gtrsim d_c$ and $q=1$. (a) The fraction ${\rho }_{ab}$ of doubly recovered particles in the final absorbing configuration has a first order phase transition for high velocities v. The dashed red line indicates the discontinuous transition point, while the square symbol represents $p\langle k\rangle =1$. The nature of the transition is confirmed by the time evolution of the number of infected particles, which is (b) continuous for $v=0.9d$ and (c) discontinuous for $v=5d$. The plotted curves correspond to $p\langle k\rangle =0.7$ (brown), 1.6 (dark violet), with $\mathrm{\Delta }(p\langle k\rangle )=0.1$.