A mathematical model for the dynamics of HIV-1 during the typical course of infection

Gumel, Abba B.; Shivakumar, P. N.; Sahai, Beni M.

doi:10.1016/s0362-546x(01)00309-1

Cited by 63 publications

(40 citation statements)

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“…This schema was originally presented in the case of ODE system in [36], used similarly by [37] and enhanced for delay differential equation system [38][39][40].…”

Section: Numerical Simulationsmentioning

confidence: 99%

Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection

Allali

Meskaf

Tridane

2018

International Journal of Differential Equations

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The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies. In this stage, the growth of the healthy hepatocyte cells is logistic while the growth of the infected ones is linear. To investigate the role of the treatment at this stage, we also consider two types of treatment: interferon-(IFN) and nucleoside analogues (NAs). To find the best strategy to use this treatment, an optimal control approach is developed to find the possibility of having a functional cure to HBV.

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“…This schema was originally presented in the case of ODE system in [36], used similarly by [37] and enhanced for delay differential equation system [38][39][40].…”

Section: Numerical Simulationsmentioning

confidence: 99%

Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection

Allali

Meskaf

Tridane

2018

International Journal of Differential Equations

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“…The resolution of the optimality system (19) is created improving the Gauss Seidel -like implicit finite-difference method developed in ( [10]) and denoted GSSI1 method. It consist on descretizing the interval [0, 1] by the point t k = kl (k = 0, 1. .…”

Section: The Improved Gssi1 Methodementioning

confidence: 99%

“…Most of them are interested in the epidemic disease studied when spreading into a population with immigrants see [2], [7]- [9], [16], [17], [20] and [21]. Optimal control theory provides a valuable tool to begin to assess the trade-offs between vaccination and treatment strategies [7], [10], [12] and [13]. Optimal control is a mathematical technique derived from the calculus of variations.…”

Section: Introductionmentioning

confidence: 99%

Free Optimal Time Control Problem for a SEIR-Epidemic Model with Immigration of Infective

Lhous¹,

Rachik²,

Larrache³

2017

IJCA

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In the present paper, we consider a mathematical model of a SEIR with immigration of infectives. The optimal control theory is applied to reduce the latent and infectious groups, increase the number of recovered individuals and this with an optimal cost. We use two controls representing the effort that reduces the contact between the infectious and susceptible individuals and a therapeutic treatment. We presents an approach that investigates a free terminal optimal time control witch give a minimum duration of a vaccination campaign. The Pontryagin's maximum principle is used to characterize the optimal controls and the optimal final time. We obtained an optimality system that we sought to solve numerically by an iterative discrete scheme that converges following an appropriate test similar the one related to the forward-backward sweep method.

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“…The resolution of the optimality system is created improving the Gauss-Seidel-like implicit finite-difference method developed by Gumel et al [12], presented in [13] and denoted GSS1 method. It consists on discretizing the interval [t 0 ; t end ] the points t k = kh + t 0 k = 0, 1, ..., n, where h is the time step.…”

Section: The Improved Gss1 Methodsmentioning

confidence: 99%

Optimal control strategies in square root dynamics of smoking model

Zeb¹,

Bibi²,

Zaman³

2015

IJSW

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License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. AbstractIn a recent paper [Anwar Zeb, Gul Zaman, Shaher Momani, Square-root Dynamics of a Giving Up Smoking Model, Appl. Math. Model., 37 (2013) 5326-5334], the authors presented a new model of giving up smoking model. In this paper, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medecine for the eradication of smoking in a community. Using the optimal control theory, the optimal levels of the three controls are characterized, and then the existence and uniqueness for the optimal control pair are established. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of quit smokers. We use Pontryagin's maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by Matlab.

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A mathematical model for the dynamics of HIV-1 during the typical course of infection

Cited by 63 publications

References 0 publications

Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection

Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection

Free Optimal Time Control Problem for a SEIR-Epidemic Model with Immigration of Infective

Optimal control strategies in square root dynamics of smoking model

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