We consider n = 100 individuals and set the constants as δ = 0.2, c0 = 1 and c1 = 0.24. We let for top, middle, and bottom figures, respectively. The dotted dashed lines are the R0 upper bound value (2) with respect to the c2 value on x-axis. For c2 = 0, we have the red circled points corresponding to the R0 upper bound when there is no behavior response by the initial sick individual. Note that all the red circled points indicate R0 > 1. From (3), the critical values of c2 that make R0 < 1 equal to 0.02, 0.16, and 0.36 for , respectively. These points are marked in blue. R0 upper bound increases linear in β according to (2). We simulate R0 values as follows. We generate a scale-free network with γ = 2 according to the preferential attachment algorithm38. For each β and c2 value pair, we consider 100 realizations with randomly selecting patient zero and counting the number of individuals infected by patient zero until patient zero heals. Each point in the solid lines corresponds to the average of the total count values in 100 initializations. We observe that the simulated average R0 is less than one above the critical c2 value in (3).