Proportions of the population infected at the end of an outbreak, conditional on the selection of vaccination strategy under different response times.

<p>Given population density, 60 simulation replicates were run for each vaccination diffusion rate <i>μ</i> under (A) a timely response, i.e. implemented at <i>t</i> = 0, and (B) a delayed response that lags behind the outbreak for 2 epidemic generations, i.e. implemented 10 time steps later. Time step <i>τ =</i> 0.1, transmission rate <i>δ =</i> 2, recovery rate <i>ρ</i> = 0.2, vaccine intensity <i>ε</i> = 20, and interaction scale <i>α =</i> 1. Large circles represent 1) the proportions of simulation replicates that result in a <i>major</i> outbreak event (red), defined by a threshold of ≥10% of total population infected, and 2) the expected proportional outbreak sizes of all simulation replicates under timely (green) and delayed (yellow) responses. Both (1) and (2) are fitted using 4^th order polynomial regression curves to smooth out simulation noise. Small circles of corresponding colors show the sizes of all major outbreaks in the events of occurrence.