Theoretical Assessment of the Transmission Dynamics of Leprosy

Abstract

<p align="justify"> <span style="font-family:;">Leprosy is a communicable disease which can cause hideous deformities to the afflicted and social stigmatization to them and their families. The continued high endemicity of leprosy in pockets of Sub-Saharan Africa is a source of bafflement to researchers. In this paper, we investigate non-compliant behavior by patients on treatment and possible inadequacy of the prescribed treatments as the reason for the persistence of the disease in the region. We construct theoretical, deterministic mathematical models of the transmission dynamics of leprosy. These models are modified to encapsulate non-compliance and inadequate treatment. The models are then analyzed to gain insight into the qualitative features of the equilibrium states, which enable us to determine the basic reproduction number. We also employ analytical and numerical techniques to investigate the impact of non-compliance and inadequate treatment on the transmission dynamics of the disease. Our results show that, as long as there is treatment, leprosy will eventually be eliminated from the region and that the disposition under investigation only serves to slow the rate at which the disease is eradicated.</span> </p

Use of Approximate Bayesian Computation to Assess and Fit Models of Mycobacterium leprae to Predict Outcomes of the Brazilian Control Program

“…Deterministic compartment models for M . leprae ( Fig 1 ) were previously developed and analyzed mathematically [ 8 , 10 – 12 ]. Regional model parameters are listed in Table 1 and model-specific parameters are listed in Table 2 ; all parameters are based on the parameters used by the developers of the models.…”

“…Model 2 assumes that recovered individuals (R) may relapse to either multibacillary or paucibacillary disease. Model 3 [ 12 ] is identical to Model 1 except for the assumption that multibacillary individuals (M) do not recover. Model 4 [ 12 ] is identical to Model 2 except for the assumption that latent cases (E) cannot be detected and cannot recover.…”

“…Model 3 [ 12 ] is identical to Model 1 except for the assumption that multibacillary individuals (M) do not recover. Model 4 [ 12 ] is identical to Model 2 except for the assumption that latent cases (E) cannot be detected and cannot recover. The transmission rate, λ, is calculated in Models 1, 2, 3, and 4 as , where β P is the transmission coefficient for paucibacillary individuals and β M is the transmission coefficient for multibacillary individuals.…”

“…The transmission rate, λ, is calculated in Models 1, 2, 3, and 4 as , where β P is the transmission coefficient for paucibacillary individuals and β M is the transmission coefficient for multibacillary individuals. Model 5 [ 12 ] divides the multibacillary and paucibacillary compartments into untreated (M N , P N ) and treated (M T , P T ) states, with the assumption that treated multibacillary cases do not suffer from extra mortality. Model 5 [ 12 ] assumes that treated individuals may recover (R) or relapse to the untreated state.…”

“…In these countries, models may assist in identifying the most effective control points. Generalized mathematical modeling of HD has been limited to a series of discrete-time Reed-Frost models [ 8 , 9 ] and deterministic compartmental models that have not been fitted to data [ 10 – 12 ]. An individual-based model has been produced [ 9 ], but is specific to the demographic situation in Bangladesh.…”