Fig. 2
Hypothesis of contact parameter and relapsed reporting rate. The grey area shows the period TB data were collected. In panel (a), the blue line and red line represent two different scenarios on transmission rate function ß(t). While the blue line stands for the case in which transmission function is constant over time, the red line shows the case where this function is assumed to be piece-wise and linearly decreasing (or increasing) from 1996 to 2015. In total, two parameters at most (ß1 and ß2) are employed to parameterize for the transmission function. In panel (b), the blue and the red line represent two different hypotheses of relapsed reporting rate rrelapsed-tb(t). The blue line corresponds to the case in which reporting rate of relapsed cases is constant over time. The red line corresponds to the case that the relapsed reporting rate changed over time. Note that the incidence reporting rate rnew-tb(t) is always assumed to be constant over time, and equal r1. Therefore, in total, three unknowns at most (r1, r2, and breaking-year) are used to describe both rnew-tb(t) and rrelapsed-tb(t). The breaking-year just takes discrete value from 1996 to 2015