On Effectiveness of an Optimal Antiviral Bitherapy in HBV-HDV Coinfection Model

Zakary, Omar; Rachik, Mostafa; Elmouki, Ilias

doi:10.5120/ijca2015906554

Cited by 4 publications

(5 citation statements)

References 22 publications

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“…This smallness restriction on the length on the time interval is due to the opposite time orientations of (16)(17)(18) and (19)(20)(21), (22), the state problem has initial values and the adjoint problem has final values. This restriction is very common in control problems [18,19,20,21,22,23,24].…”

Section: Optimal Awareness Programmentioning

confidence: 99%

On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control

Zakary¹,

Rachik²,

Elmouki³

2016

IJCA

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In this work, a mathematical model for studying the impact of awareness programs on HIV/AIDS outbreak is proposed. The main idea is that people who are susceptible to infection can prevent it, if they are aware how the disease spreads and its consequences, and also the measures to control it. Various forms of communication media, educational, heath institutions and non-governmental organizations play a significant role to promote HIV/AIDS awareness amongst the most concerned people, namely couples and senior secondary school children. The developed HIV model is inspired from the classical SIR epidemic model where a control function is introduced to represent the effectiveness of an awareness program. The obtained optimal control, is characterized in terms of the optimality system, based on Pontryagin's maximum principle, and it is simulated using the Forward-Backward Sweep Method with a progressive-regressive Runge-Kutta fourth order scheme, which is adapted to solve a two-point boundary value problem.

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Section: Optimal Awareness Programmentioning

confidence: 99%

On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control

Zakary¹,

Rachik²,

Elmouki³

2016

IJCA

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“…Many optimal control strategies have been proposed for highlighting the advantage of optimization of some parameters in some biomathematical models . In this context, some applied mathematicians advise to rely dosage problems; also, on their optimal control approaches, they see beneficial for developing therapeutic strategies that aim to reduce tumor volume with lesser side‐effects, see, for instance, in the case of chemotherapy, the work in Yegorov and Todorov, and in the case of immunotherapy, papers in Hamdache et al…”

Section: Introductionmentioning

confidence: 99%

“…Many optimal control strategies have been proposed for highlighting the advantage of optimization of some parameters in some biomathematical models. [9][10][11] In this context, some applied mathematicians advise to rely dosage problems; also, on their optimal control approaches, they see beneficial for developing therapeutic strategies that aim to reduce tumor volume with lesser side-effects, see, for instance, in the case of chemotherapy, the work in Yegorov and Todorov, 12 and in the case of immunotherapy, papers in Hamdache et al 13,14 Some research papers on mathematical medicine have developed mathematical models which describe the evolution of tumors 15,16 and analyze the different interactions between the tumor, immune-system, and treatment. 17,18 In this paper, we formulate a minimization problem from which we aim to find the optimal dose and duration of the BCG immunotherapy procedure in the case of superficial bladder cancer, based on a prevalidated mathematical model 19 in the form of 4 ordinary differential equations which describe the superficial bladder tumor-immune interactions after the injection of BCG in the bladder of a hypothetical patient.…”

mentioning

confidence: 99%

Optimal duration and dosage of BCG intravesical immunotherapy: A free final time optimal control approach

Alkama

Larrache

Rachik

et al. 2018

Math Methods in App Sciences

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In this paper, we propose a free final time optimal control approach applied to 4 ordinary differential equations which describe the tumor‐immune interactions after the injection of the bacillus Calmette‐Guérin (BCG) in the bladder of a hypothetical patient. The main goal of this optimal control strategy is to find the optimal dosage amount needed in each instillation of BCG for stimulating the immune‐system and then killing superficial bladder tumors and to determine the optimal duration of treatment, adequate for stopping the intravesical therapy with lesser side‐effects. For this, we introduce into the model of interest, a control function which represents the dose of BCG immunotherapy procedure and we formulate a minimization problem where the final time is considered free (nonfixed). The characterization of the sought optimal control noted u∗ is derived based on Pontryagin's maximum principle, while the formulation of the sought optimal final time noted tfinal∗ is based on formulae of sensitivity which are obtained conditions from the derivative of the objective function with respect to tfinal∗. We investigate the resolution of the free final time optimal control problem in 3 possible cases: (a) when tfinal∗ is quadratic in the final gain function, (b) when the final gain function does not depend on tfinal∗, and (c) when tfinal∗ is linear in the final gain function. Finally, we obtain the sought optimal dose of BCG, and we conclude that in case (a), we obtain an optimal duration which is more beneficial regarding the activation of immune cells while cases (b) and (c) both provide an optimal duration which is more adequate for the minimization of the tumoral population.

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“…We will use this approach to formulate the model considered in this paper. Optimal control theory is well used as an available and effective option for diseases control, mainly Tuberculosis [16][17][18][19][20], Malaria [21,22], HIV [23][24][25][26][27][28][29][30][31], Hepatitis [32,33], Vector borne diseases [34], Cancer [35][36][37][38][39][40], and other diseases [41][42][43][44][45][46][47], but there are very few applications with both space and time as discrete variables.…”

Section: Introductionmentioning

confidence: 99%

On the analysis of a multi-regions discrete SIR epidemic model: an optimal control approach

Zakary

Rachik

Elmouki

2016

Int. J. Dynam. Control

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In this paper, we devise a discrete time SIR model depicting the spread of infectious diseases in various geographical regions that are connected by any kind of anthropological movement, which suggests disease-affected people can propagate the disease from one region to another via travel. In fact, health policy-makers could manage the problem of the regional spread of an epidemic, by organizing many vaccination campaigns, or by suggesting other defensive strategies such as blocking movement of people coming from borders of regions at high-risk of infection and entering very controlled regions or with insignificant infection rate. Further, we introduce in the discrete SIR systems, two control variables which represent the effectiveness rates of vaccination and travel-blocking operation. We focus in our study to control the outbreaks of an epidemic that affects a hypothetical population belonging to a specific region. Firstly, we analyze the epidemic model when the control strategy is based on the vaccination control only, and secondly, when the travel-blocking control is added. The multi-points boundary value problems, associated to the opti-This work is supported by the Systems Theory Network (Réseau Théorie des Systèmes), and Hassan II Academy of Sciences and Technologies-Morocco.

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On Effectiveness of an Optimal Antiviral Bitherapy in HBV-HDV Coinfection Model

Cited by 4 publications

References 22 publications

On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control

On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control

Optimal duration and dosage of BCG intravesical immunotherapy: A free final time optimal control approach

On the analysis of a multi-regions discrete SIR epidemic model: an optimal control approach

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