Fig 1.
A compartment model of Hansen’s disease.
Table 1.
Starting parameter values and ranges for a compartmental model of Hansen’s Disease.
Regional values are set based on the demographics of the area providing observed data for fitting. Fitted values (unfitted assumption in parentheses) are estimated using Approximate Bayesian Computation.
Table 2.
Posterior distribution median and 95% prediction intervals determined by ABC fitting of Approximate Bayesian Computation models for Hansen’s Disease to data from the 5 regions of Brazil.
Version 4 consisted of fitting the regional best-fit model to each region’s observed data separately with both frequency and density-dependent transmission assumptions; all other versions used a hierarchical structure with density-dependent transmission in which at least some parameters were shared across regions, and fitting was done simultaneously across all 5 regions. Mean error refers to the average value of d per iteration of each version, based on a sample of 1,000 iterations, with confidence intervals based on 100 samples of 100 iterations each.
Fig 2.
Number of initial population in infected categories for a dynamic model of Mycobacterium leprae in Brazilian regions.
The colors represent different model fits (black H1: fitted transmission parameters shared across all regions, red H2: fitted transition parameters shared across all regions, green H3: all fitted parameters shared across all regions, dark blue RF: no fitted parameters shared across regions, and light blue RD: no fitted parameters shared across regions and density-dependent transmission). Each row is a different region. The infected categories are: EP, latent paucibacillary (PB); PN, undetected PB; PT, treated PB; PR, recovered PB; PA, recurrent PB; EM, latent multibacillary (MB); MN, undetected MB; MT, treated MB; MR, recovered MB; and MA, recurrent MB.
Fig 3.
Posterior predictions for incidence and multibacillary (MB) incidence of the compartmental model of Hansen’s disease for the regions of Brazil, compared to the observed values for 2000–2012.
Unknown parameters were fitted to each region individually. All models were fit using Approximate Bayesian Computation with the Sequential Monte Carlo algorithm.
Table 3.
Posterior predictions (mean and range) from the regional model for Hansen’s Disease fit to regional data from Brazil.
Incidence of Hansen’s Disease in the year 2050 is reported overall (i2050) and for multibacillary (iM2050) and paucibacillary (iP2050). The time to elimination (telim) was calculated as the year in which overall incidence was ≤1/10,000, starting from 2001.
Table 4.
Posterior distribution median and 95% prediction intervals determined by ABC fitting of Approximate Bayesian Computation models for Hansen’s Disease to data simulated by the best-fit model.
The values fit were βM = 1.9, βP = 1.2, φM = 0.2, and φP = 0.2 for all but the North, where φ2 = 0.46. Version 4 consisted of fitting the regional best-fit model to each region’s observed data separately with both frequency and density-dependent transmission assumptions; all other versions used a hierarchical structure with density-dependent transmission in which at least some parameters were shared across regions, and fitting was done simultaneously across all 5 regions. Values in bold italics contained the simulated value within their range. Mean error refers to the average value of d per iteration of each version, based on a sample of 1,000 iterations, with confidence intervals based on 100 samples of 100 iterations each.