We consider n = 100 individuals, and let δ = 0.2, and c0 = 1. The infection rate β values equal to 0.1, 0.2 and 0.3 for figures left, middle, and right, respectively. The runs start with a single infected individual and all individuals infected respectively for the top and bottom figures. In each plot, the axes correspond to the constant values of c1 and c2. For a given value of c1 and c2, we generate 50 scale-free networks using the preferential attachment algorithm and run the stochastic network disease game for 200 steps for each network. The grid color represents the ratio of runs in which disease is eradicated within 200 steps. For figures left, middle, and right the eradication of threshold is equal to 2.65, 5.3, and 8, respectively. That is, for all the figures. The critical values of the empathy constant, that make R0 < 1 for calculated using (6) are marked with white dotted dashed lines. The critical values of the empathy constant, , that make for calculated using (6) are accurate in determining fast eradication for any value of c1 (marked with red solid lines).