Mathematical Modelling of Leprosy and Its Control

Proposing a Compartmental Model for Leprosy and Parameterizing Using Regional Incidence in Brazil

“…The results of this study show that the density-dependent model was slightly preferred to the frequency-dependent model. This question would not arise with an individual-based model, such as SIMCOLEP [42], but those models are not as easy to adapt as they must rely on population-specific characteristics in their design, which may require parameters that are not locally available. The goal of this study was to provide an adaptable model that was still able to capture the regional dynamics of leprosy spread.…”

Mathematical and Computational and Modeling for Leprosy’s Dynamics

“…Taking as a starting point the conceptual schematic model proposed by MEIMA et al (1999), which considers the heterogeneity in susceptibility and the incubation period, constituting an advance at the time, this very complex model was presented only in schematic form as can be seen at Figure 1. BLOCK et al (2015) presented a survey on the models developed so far. One aspect that is evident is that the papers do not point out clearly the solution strategies.…”

“…This work analyzes a compartmental model in the investigation of leprosy dispersal in a population aiming to predict the transmission to new patients and to allow the analysis of different groups of individuals in the face of exposure to infection. For this, it uses a conceptual model (LECHAT et al,1985;MEIMA et al, 1999;BLOCK et al, 2015) to describe the dynamics of the disease. Thus, a mathematical model is constructed based on the conceptual model, and the resulting system of ordinary differential equations is solved numerically.…”

Multibacillary and paucibacillary leprosy dynamics: a simulation model including a delay

“…This disease is still a public health problem. According to global statistics reported by the WHO 96% of reported cases with leprosy disease they are located in 22 priority countries, of which five countries with the highest incidence are currently reported, India, Brazil, Indonesia, Bangladesh and Ethiopia [1,2,3,4]. This disease can be curable by means of a multidrug treatment (MDT) or polychemotherapy (PQT), which consists of a combination therapy of different antibiotics, rifampicin, clofazimine and dapsone, the combination between them is determined according to the leprosy classification.…”

“…Mathematical models throughout history aim to represent in a simplified way a situation or natural phenomenon. According to the literature, Lechat et al in 1970 and1980 were one of the first to implement a mathematical model that studies the dynamics of leprosy disease, which led to the research on the evolution of leprosy taking different assumptions and the effect of the control strategy [4,5,6,7,8]. Lietman et al in 1997 propose a model based on ordinary differential equations to interpret the dynamics of leprosy disease in the absence of tuberculosis disease and the tuberculosis in absence of leprosy, then combine them and investigate the importance of cross immunity [13].…”