A control‐based mathematical study on psoriasis dynamics with special emphasis on IL−21 and IFN−γ interaction network

Roy, Arunabha; Nelson, Mark; Roy, Priti Kumar

doi:10.1002/mma.7635

Cited by 8 publications

(10 citation statements)

References 36 publications

(92 reference statements)

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“…It is easy to see that system (2.6) is a further development of the ideas previously presented in papers [19,17,18].…”

Section: Model Of Psoriasis Dynamics and Its Modificationsmentioning

confidence: 64%

“…Much attention is paid to detailed analysis of such singular regimens in the paper. By the possible occurrence of singular regimens, our study differs from the studies for a similar model presented in [19], although is their continuation. The objective function that we use in this article is also different from the objective function used in [19].…”

Section: Introductionmentioning

confidence: 72%

“…In more detail, such terms in the objective functions are discussed in [3,13]. Note also that in the papers [18,19] the general cost of such biological treatment is determined in a different way, namely the integral part of the type:…”

Section: Optimal Control Problemmentioning

confidence: 99%

“…(6.7) Note that due to the formulas (2.5), the first inequality in (6.7) is equivalent to the inequality β 2 > β 1 , which, as follows from [19], is satisfied.…”

Section: Useful Transformations and Important Assumptionmentioning

confidence: 99%

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Investigation of singular regimens in a controlled model of psoriasis treatment

2022

Commu. Optim. Theory

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Psoriasis is characterized by an overgrowth of keratinocytes (skin cells) resulted from chaotic signaling in the immune system and irregular release of cytokines. Anti-inflammatory cytokines, such as IL−21 and IFN −γ released by the T h 1 -cells and activated killer cells (NK-cells) play a central role in pathogenesis of this disease. So, in this paper, we propose two systems of nonlinear differential equations: one system describes the growth of immune cells (T -helper cells of type I and II, as well as activated NK-cells) along with keratinocytes; another system sets the dynamics of cytokines (IL − 21 and IFN − γ). Since these systems use different time scales, we transform them into one system of differential equations, including the immune T h 1 -and T h 2 -cells, activated NKcells, and epidermal keratinocytes. Within this description of the dynamics of psoriasis, we study the effect of combined bio-therapy, including the action of the IL − 21 inhibitor together with anti-IFN − γ therapy. To do this, we introduce two bounded control functions into the system and formulate on a given time interval, the problem of minimizing the total cost of the applied immune therapy and its impact on the proliferation of activated NK-cells and keratinocytes at the end of the treatment time. Analysis of such a problem is carried out using the Pontryagin maximum principle. As a result of this analysis, the properties of optimal controls and their possible types are established. It is shown that each such control is either a bang-bang function over the entire time interval, or in addition to non-singular bang-bang sections, it can have a singular regimen. Possible types of singular regimens are studied; for them, the necessary optimality conditions are checked, the singular regimens's formulas are found, so as the ways the singular regimens concatenate with non-singular (bang-bang) sections. Some numerically computed optimal controls are given alone with a discussion of the numerical difficulties in detection of singular regimens.

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“…It is easy to see that system (2.6) is a further development of the ideas previously presented in papers [19,17,18].…”

Section: Model Of Psoriasis Dynamics and Its Modificationsmentioning

confidence: 64%

Section: Introductionmentioning

confidence: 72%

Section: Optimal Control Problemmentioning

confidence: 99%

“…(6.7) Note that due to the formulas (2.5), the first inequality in (6.7) is equivalent to the inequality β 2 > β 1 , which, as follows from [19], is satisfied.…”

Section: Useful Transformations and Important Assumptionmentioning

confidence: 99%

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Investigation of singular regimens in a controlled model of psoriasis treatment

2022

Commu. Optim. Theory

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“…Here, we present the existence of the optimal control functions which minimizes the cost function in the period of the control measures. There are similar and detailed analysis on existence of optimal control in References 35,37‐40…”

Section: Cassava Disease Dynamics Model With Controlmentioning

confidence: 99%

Analysis and optimal control measures of diseases in cassava population

Onah

2022

Optim Control Appl Methods

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Cassava amongst other crops is ranked currently as the third most essential source of carbohydrate in the tropics and a major food source in Africa. In spite of these gains, cassava production is highly threatened by pathogen-causing diseases. In this study, a deterministic compartmental model is developed to investigate the effect of these diseases on cassava production. The local and global stabilities of the disease free and endemic equilibrium states of the model without control are analyzed. The model is extended to incorporate control techniques necessary in eradicating cassava diseases. Optimal control theory is applied on the control model to explore the impact of the introduction of resistant cassava plant, the use of all other traditional practices and the application of pesticides in the prevention and eradication of diseases in cassava production.Numerical simulation of the models are carried out and results obtained indicates that introduction of control measures should be done largely at the onset of cassava planting by introducing resistant cassava stems to reduce the spread of the disease and also maintain minimum cost for production and thereby maximize profit from its yield. The cost effectiveness analysis agreed with our earlier analysis and shows that the best and effective control is the use of resistant cassava stem together with the IPM approach.

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Bifurcation, sensitivity, and optimal control analysis of onchocerciasis disease transmission model with two groups of infectives and saturated treatment function

Ogunmiloro

Idowu

2022

Math Methods in App Sciences

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A model depicting the transmission of onchocerciasis disease in human host community with two distinct groups of infected humans exhibiting low and high microfilariae (mf) output with saturated treatment function is developed and analyzed. The model equilibrium solutions are obtained, and it is found that the model exhibits forward bifurcation and the effective basic reproduction number governing the spread of the disease is computed by the use of the next generation matrix method. The sensitivity results of model parameters reveal that the rates describing the recruitment of humans, blackflies, onchocerciasis disease transmission, and the biting rate of blackflies are positively sensitive to , which necessitate the need for controls to be implemented in order to curtail the infectious contact between humans and blackflies in the host environment. To this effect, the model is further transformed into an optimal control problem by applying control strategies of personal protection of using treated bednets and wearing of permethrin‐treated cloths , surgical care for humans with body deformation and impaired vision , education campaign , and the use of insecticide , respectively. The existence and uniqueness of the optimal control model are established, and the Pontryagin maximum principle (PMP) is employed to characterize the controls. The optimal control model is solved using the Runge–Kutta numerical scheme via MATLAB, and the simulations under different control combinations show that each of the controls have its own effect in minimizing onchocerciasis transmission, but the combined effects of the four control strategies proved to be more beneficial towards the elimination of the disease in human and blackfly host community. Also, the simulations of the control profiles reveal that each of these controls are sustained at maximum until 3 months before gradually declining to zero in terminal time of 12 months.

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A control‐based mathematical study on psoriasis dynamics with special emphasis on IL−21 and IFN−γ interaction network

Cited by 8 publications

References 36 publications

Investigation of singular regimens in a controlled model of psoriasis treatment

Investigation of singular regimens in a controlled model of psoriasis treatment

Analysis and optimal control measures of diseases in cassava population

Bifurcation, sensitivity, and optimal control analysis of onchocerciasis disease transmission model with two groups of infectives and saturated treatment function

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