Critical observation of WHO recommended multidrug therapy on the disease leprosy through mathematical study

Ghosh, Salil; Saha, Shubhankar; Roy, Priti Kumar

doi:10.1016/j.jtbi.2023.111496

Cited by 5 publications

(14 citation statements)

References 34 publications

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“…It is easy to prove that a unique solution (S H (t), S I (t), B(t)) of system (21) with initial data given as…”

Section: Parametermentioning

confidence: 99%

“…] dt (23) subject to the optimal control induced delayed system (21). Here, in the first two terms in the objective functional that is, P i u 2 i , i = 1, 2, P i is the positive weight parameters associated with the control u i (t) and the square of the control variables indicate the severity of the side effects of the Ofloxacin and Dapsone drug therapies.…”

Section: Objective Functional and Its Descriptionmentioning

confidence: 99%

“…27,33 For the bounded Lebesgue measurable controls and the non-negative initial conditions, there exist non-negative bounded solutions 34 to the optimal control induced delayed system (21), (22). Now, first, we investigate the existence of an optimal control for system (21) in the next subsection.…”

Section: Objective Functional and Its Descriptionmentioning

confidence: 99%

“…To prove the existence of an optimal control pair for system (21), we use the results described in References 35 and 36.…”

Section: Existence Of An Optimal Controlmentioning

confidence: 99%

“…18,19 Besides, a few cell dynamical mathematical studies were accomplished for exploring the infection and dissemination process of leprosy from the perspective of an ODE-based system and also the density dependence property of M. leprae bacteria. 4,20,21 In this context, it is to be mentioned that analysis of mathematical models based on delayed differential equations instead of simple ODE-based systems has gained major importance in current times and several mathematical studies on various infectious and noninfectious diseases like HIV-1, dengue, malaria, tumor, and cutaneous leishmaniasis have been performed recently that primarily focuses on the delayed dynamics of the systems. 22,23 Nevertheless, the investigation of cell dynamical mathematical model considering the aspects of intracellular delays in leprosy are still unexplored by the researchers and most importantly, the implementation of a suitable optimal control therapeutic approach on delayed systems are not investigated at all previously from a mathematical point of view for constructing a more accurate drug dose regimen for leprosy.…”

Section: Introductionmentioning

confidence: 99%

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Implementation of suitable optimal control strategy through introspection of different delay induced mathematical models for leprosy: A comparative study

Ghosh,

Roy,

Roy

2023

Optim Control Appl Methods

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Involving intracellular delay into a mathematical model and investigating the delayed systems by incorporating optimal control is of great importance to study the cell‐to‐cell interactions of the disease leprosy. Keeping this in mind, we have proposed two different variants of delay‐induced mathematical models with time delay in the process of proliferation of Mycobacterium leprae bacteria from the infected cells and a similar delay to indicate the time‐lag both in the proliferation of M. leprae bacteria and the infection of healthy cells after getting attached with the bacterium. In this research article, we have performed a comparative study between these two delayed systems equipped with optimal control therapeutic approach to determine which one acts better to unravel the complexities of the transmission and dissemination of leprosy into a human body as far as scheduling a perfect drug dose regime depending on this analysis remains our main priority. Our investigations suggest that adopting optimal control strategy consisting of combined drug therapy eliminates the oscillatory behavior of the delayed systems completely. Existence of optimal control solutions are demonstrated in detail. To achieve the optimal control profiles of the drug therapies and to obtain the optimality systems, Pontryagin's Minimum principle with delay in state are employed for our controlled systems. Furthermore, the analytical as well as the numerical outcomes obtained in this research article indicate that the delayed bacterial proliferation and M. leprae‐induced infection model equipped with optimal control policy performs more realistically and accurately in the form of a safe and cost‐effective double‐drug therapeutic regimen. All the mathematical results are verified numerically and the numerical results are compared with some recent clinical data in our article as well.

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“…It is easy to prove that a unique solution (S H (t), S I (t), B(t)) of system (21) with initial data given as…”

Section: Parametermentioning

confidence: 99%

Section: Objective Functional and Its Descriptionmentioning

confidence: 99%

Section: Objective Functional and Its Descriptionmentioning

confidence: 99%

“…To prove the existence of an optimal control pair for system (21), we use the results described in References 35 and 36.…”

Section: Existence Of An Optimal Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Implementation of suitable optimal control strategy through introspection of different delay induced mathematical models for leprosy: A comparative study

Ghosh,

Roy,

Roy

2023

Optim Control Appl Methods

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Insights of infected Schwann cells extinction and inherited randomness in a stochastic model of leprosy

Ghosh,

Rana,

Mukherjee

et al. 2024

Mathematical Biosciences

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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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Critical observation of WHO recommended multidrug therapy on the disease leprosy through mathematical study

Cited by 5 publications

References 34 publications

Implementation of suitable optimal control strategy through introspection of different delay induced mathematical models for leprosy: A comparative study

Implementation of suitable optimal control strategy through introspection of different delay induced mathematical models for leprosy: A comparative study

Insights of infected Schwann cells extinction and inherited randomness in a stochastic model of leprosy

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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