Consider someone who the index case in their household; they would be expected to infect R G = 1.21 people out of their household and m 2 = 0.64 within their household. This validates assumed proportions of transmission within and between households from earlier simulation studies [17, 20] . The sum of these is greater than R since the reproduction number R is an average over different generations of infection within the household. For this value, the estimate of R which takes into account local saturation effects was determined numerically to be R = 1.79. Fig 3 shows that for all values of r, numerically estimated values for R (r ) are close to the curve estimated from application of equation (12) which ignores local saturation effects.