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

where aj is the age of individual j in months at t = 0. Since we assume that non-symptomatic individuals who are born, or 183 who immigrate into the study area, after the start of the study (with Vj > 0) are susceptible, for notational convenience we 184 define the probabilities for these individuals as pS 0 (aj) = 1, pA 0 (aj) = pR 0 (aj) = 0. We estimate the historical asymptomatic infection rate, ⁄0, by fitting the model to age-prevalence data on leishmanin skin 186 test (LST) positivity amongst non-symptomatic individuals from a cross-sectional survey of three of the study paras conducted 187 in 2002 (28) (see Figure S4 ). We assume that entering state R corresponds to becoming LST-positive, as LST positivity is 188 a marker for durable, protective cell-mediated immunity against VL (28, 29), and estimate ⁄0 by maximising the binomial With these definitions, the complete data likelihood for the augmented data Z = (Y, X) given the model parameters ◊ = (-, -, ', ", p) is composed of the products of the probabilities of all the di erent individual-level events over all months: the joint posterior distribution of the model parameters ◊ = (-, -, ', ", p) and the missing data X given the observed data Y