Mathematical Modeling and Control of the Cell Dynamics in Leprosy

Ghosh, Salil; Chatterjee, Amar Nath; Roy, Priti Kumar; Grigorenko, N. L.; Хайлов, Е. Н.; Grigorieva, Ellina

doi:10.1007/s10598-021-09516-z

Cited by 16 publications

(20 citation statements)

References 26 publications

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“…We assume that the duration of the outbreak is short enough so that the total number of susceptible persons remains relatively unchanged, and natural deaths and births are ignored. 35 At the same time, because the sum of Equations ( 1 – 4 ) is zero, the system Equations ( 1 – 6 ) can be simplified to the following system:

The disease‐free equilibrium of system ( 7 ) is

For system ( 7 ), the next generation matrix method 36 , 37 , 38 , 39 is used to solve the basic regeneration number

. Note that

, so

, where

The Jacobin matrix of

and

can be written as

So, from Equation ( 12 ) we have

and

From Equation ( 14 ) the characteristic equation of

can be rewritten as

By solving the Equation ( 15 ), it can be obtained that

.…”

Section: Methods—sentiment‐enabled Seir Modelmentioning

confidence: 99%

Timely and effective media coverage's role in the spread of Corona Virus Disease 2019

Wang

Qing

et al. 2022

Math Methods in App Sciences

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For all humanity, the sudden outbreak of Corona Virus Disease 2019 has been an important problem. Timely and effective media coverage is considered to be one of the effective approaches to control the spread of epidemic in early stage. In this paper, a Sentiment‐enabled Susceptible‐Exposed‐Infected‐Recovered (SEIR) model is established to reveal the relationship between the propagation of the epidemic and media coverage. The authors take the positive and negative media coverage into consideration when implementing the Sentiment‐enabled SEIR model. This model is constructed by parameterizing the number of current confirmed cases, cumulative cured cases, cumulative deaths, and media coverage. The numerical simulation and sensitivity analysis are conducted based on the Sentiment‐enabled SEIR model. The numerical analysis confirms the rationality of the Sentiment‐enabled SEIR model. The sensitivity analysis shows that positive media coverage acts a pivotal part in reducing the figure for confirmed cases. Negative media coverage has an effect on the figure for confirmed cases is not as significant as that of positive media coverage, but it is not negligible.

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The disease‐free equilibrium of system ( 7 ) is

For system ( 7 ), the next generation matrix method 36 , 37 , 38 , 39 is used to solve the basic regeneration number

. Note that

, so

, where

The Jacobin matrix of

and

can be written as

So, from Equation ( 12 ) we have

and

From Equation ( 14 ) the characteristic equation of

can be rewritten as

By solving the Equation ( 15 ), it can be obtained that

.…”

Section: Methods—sentiment‐enabled Seir Modelmentioning

confidence: 99%

Timely and effective media coverage's role in the spread of Corona Virus Disease 2019

Wang

Qing

et al. 2022

Math Methods in App Sciences

View full text Add to dashboard Cite

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“…x, D) and dI17 dt = f 9 (t, x, D) of the control system (1) - (10). Here x ∈ X denotes the state variables and D ∈ U denotes the control variables.…”

Section: Existence Of An Optimal Solutionmentioning

confidence: 99%

“…Some studies dealing with the population level dynamics of the disease include [8,9]. The paper [10] explores the cellular dynamics within the host. To our knowledge there is no work done yet dealing with the dynamics of the bio-markers involved in Lepra reactions.…”

Section: Introductionmentioning

confidence: 99%

A Study of Qualitative Correlations Between CrucialBio-markers and the Optimal Drug Regimen of Type-I LepraReaction: A Deterministic Approach

Nayak

Vilvanathan

Dasu

2023

Preprint

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Mycobacterium leprae is a bacteria that causes the disease Leprosy (Hansen’s disease), whichis a neglected tropical disease. More than 200000 cases are being reported per year world wide.This disease leads to a chronic stage known as Lepra reaction that majorly causes nerve damageof peripheral nervous system leading to loss of organs. The early detection of this Lepra reactionthrough 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 andthe chemical pathways involved in Lepra reactions. The model incorporates the dynamics of thesusceptible schwann cells, infected schwann cells and the bacterial load and the concentrationlevels of the bio markers IF N − γ, T N F − α, IL − 10, IL − 12, IL − 15 and IL − 17. We considera 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 correlationbetween the bio-markers levels and drugs in MDT and propose a optimal drug regimen throughthese optimal control studies. We use the Newton’s Gradient Method for the optimal control studies.

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“…Due to sudden outbreak of cholera infection and its huge impact on economic resources, optimal control strategies toward infection is highly recommended [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. On the other hand, fractional derivative is one of the highly applicable di erential calculus to describe both biological and physical phenomena [1,[15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Fractional Derivative and Optimal Control Analysis of Cholera Epidemic Model

Cheneke

Koya

Edessa

2022

Journal of Mathematics

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In this study, a cholera model with fractional derivative and optimal control analysis is presented. Numerical simulation analysis shows that increasing the order of fractional derivatives contributes to updating the memory of the population to control the effects of cholera infection through available controlling techniques. On the other hand, the optimal analysis gives an indication of applying controlling infection with available treatment and prevention techniques. It provides a better mechanism to prevent the happening of cholera infection. Moreover, cost-effectiveness evaluation of cholera contamination intervention with feasible three or four combos of manipulate measures hygiene, vaccination, remedy of infectives, and chlorination indicates that hygiene, vaccination, and chlorination are the desired higher mixture to govern in addition propagation of cholera contamination. Numerical simulations are performed with the MATLAB platform and numerical solutions and results are discussed.

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Mathematical Modeling and Control of the Cell Dynamics in Leprosy

Cited by 16 publications

References 26 publications

Timely and effective media coverage's role in the spread of Corona Virus Disease 2019

Timely and effective media coverage's role in the spread of Corona Virus Disease 2019

A Study of Qualitative Correlations Between CrucialBio-markers and the Optimal Drug Regimen of Type-I LepraReaction: A Deterministic Approach

Fractional Derivative and Optimal Control Analysis of Cholera Epidemic Model

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