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

Leprosy (Hansen’s disease) is an infectious, neglected tropical disease caused by the Mycobacterium Leprae (M. Leprae). About 2,02,189 new cases are diagnosed worldwide each year. Lepra reactions are an off shoot of leprosy infection causing major nerve damage leading to disability. Early detection of lepra reactions through the study of biomarkers can prevent subsequent disabilities. Motivated by these observations, in this study, we have proposed and analyzed a three-dimensional mathematical model to capture the dynamics of susceptible schwann cells, infected schwann cells, and the bacterial load based on the pathogenesis of leprosy. We did the stability analysis, numerical simulations, and also performed the sensitivity analysis using Spearman’s rank correlation coefficient, partial rank correlation coefficient, and Sobol’s index methods. We later performed the optimal control studies with both multi-drug therapy and steroid interventions as control variables. Finally, we did the comparative and effectiveness study of these different control interventions.

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A study of qualitative correlations between crucial bio-markers and the optimal drug regimen of Type I lepra reaction: A deterministic approach

Nayak,

Sangeetha,

Vamsi

2023

Computational and Mathematical Biophysics

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Mycobacterium leprae is a bacterium that causes the disease leprosy (Hansen’s disease), which is a neglected tropical disease. More than 2,00,000 cases are being reported per year worldwide. This disease leads to a chronic stage known as lepra reaction that majorly causes nerve damage of the peripheral nervous system leading to loss of organs. The early detection of this lepra reaction through the level of bio-markers can prevent this reaction occurring and the further disabilities. Motivated by this, we frame a mathematical model considering the pathogenesis of leprosy and the chemical pathways involved in lepra reactions. The model incorporates the dynamics of the susceptible Schwann cells, infected Schwann cells, and the bacterial load and the concentration levels of the bio-markers interferon- γ \hspace{0.1em}\text{interferon-}\hspace{0.1em}\gamma , tumor necrosis factor- α \hspace{0.1em}\text{tumor necrosis factor-}\hspace{0.1em}\alpha , IL (interleukin)- 10 \hspace{0.1em}\text{IL (interleukin)-}\hspace{0.1em}10 , IL- 12 \hspace{0.1em}\text{IL-}\hspace{0.1em}12 , IL- 15 \hspace{0.1em}\text{IL-}\hspace{0.1em}15 , and IL- 17 \hspace{0.1em}\text{IL-}\hspace{0.1em}17 . We consider a nine-compartment optimal control problem considering the drugs used in multi drug therapy (MDT) as controls. We validate the model using 2D heat plots. We study the correlation between the bio-markers levels and drugs in MDT and propose an optimal drug regimen through these optimal control studies. We use the Newton’s gradient method for the optimal control studies.

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

Cited by 4 publications

References 11 publications

Mathematical Modeling and Control of the Cell Dynamics in Leprosy

Mathematical Modeling and Control of the Cell Dynamics in Leprosy

A comprehensive and detailed within-host modeling study involving crucial biomarkers and optimal drug regimen for type I Lepra reaction: A deterministic approach

A study of qualitative correlations between crucial bio-markers and the optimal drug regimen of Type I lepra reaction: A deterministic approach

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