Similarly R i can be modeled parametrically as a function of time. One example of a reasonable model for this is the four parameter logistic curve [22] [23] [24] given by The parameters of this curve describe the initial height of the curve (approximately a+b), the point of inflection (d), the curvature over the inflection (c) and the final height of the curve (a). These parameters have biological meaning in this setting where the initial height corresponds to the values of R i prior to intervention and significant depletion of the susceptible population. The inflection point and its steepness would describe the timing of intervention and the rapidity with which it impacts transmission. The final height would describe the ultimate value of R i, which typically is less than one, indicating that disease transmission is in a sub epidemic state.