Inferring transmission trees to guide targeting of interventions against visceral leishmaniasis and post-kala-azar dermal leishmaniasis

Lloyd A. C. Chapman; Simon E. F. Spencer; Timothy M. Pollington; Chris P. Jewell; Dinesh Mondal; Jorge Alvar; T. Deirdre Hollingsworth; Mary M. Cameron; Caryn Bern; Graham F. Medley

Given these pieces of information, the simulation algorithm proceeds as follows: negative binomially distributed (48). The PMF of a size-biased negative binomial random variable X ú corresponding to 542 X ≥ NB is: and assign a PKDL infectious by drawing from Cat({h1, h2, h3, hu}, p) . 562 ii. Else the individual recovers without developing PKDL, so draw a recovery time: Figure 575 S5 and Table S4 respectively. Based on the deviance distributions and DIC values, the best-fitting model is the model with 576 additional within-household transmission and the highest level of relative pre-symptomatic and asymptomatic infectiousness 577 (both 2% as infectious as VL). Hence, we focus on the output of this model in the main text and below. and ") and incubation period distribution parameter p for the di erent models are shown in Table S4 . The parameter estimates 580 are very similar across the di erent models and vary in the way expected -the spatial transmission rate constantand 581 background transmission rate ' are lower for models with additional within-household transmission (" > 0) and decrease with 582 increasing relative asymptomatic infectiousness h4, and the mode foris slightly larger for models with " > 0 (since a flatter 583 kernel shape compensates for the extra within-household transmission). The posterior distributions for the incubation period 584 distribution parameter p correspond to a mean incubation period of 5.7-6.9 months (95% HPDIs (4.8,6.6)-(6.0,7.8) months). The log-likelihood trace and posterior distributions for the parameters for the best-fitting model are shown in Figure S6 .