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The effect of vaccination to dendritic cell and immune cell interaction in HIV disease progression

International Journal of Biomathematics 2016年第1期9卷 91-110页

作者： Priti Kumar Roy amar nath chatterjee Xue-Zhi Li Center for Mathematical Biology and EcologyDepartment of Mathematics Jadavpur UniversiSy Kolkata 700032 India College of Mathematics and Information Science Xinyang Normal University Xinyang 464000 P. R. China

In this research paper, our main objective is to find out the meticulous role of activated dendritic cells （DCs） during the human immunodeficiency virus （HIV） infection process. DCs play a dual role by enhancing both HIV infection progression, as well as antiviral immune response. To explore the implications of these dual roles, we have formulated our mathematical model and analyzed the model by both analytical and numerical approaches. By using an impulsive differential equation, we have studied the effect of DC-based vaccination. Analytically we have determined the threshold value of drug dosage and dosing interval for optimum levels of injection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that, systematic drug dose of the immune cells leads to its maximum level.

关键词： HIV dendritic cell DC-based immune therapy first-order elimination Michaelis-Menten elimination.

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Saturation Effects on Immunopathogenic Mechanism of Psoriasis:A theoretical approach

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应用泛函分析学报 2011年第3期13卷 310-318页

作者： Priti Kumar Roy Abhirup Datta amar nath chatterjee Center for Mathematical Biology and Ecology Department of MathematicsJadavpur University

Psoriasis vulgaris is a common chronic autoimmune inflammatory skin disease characterized by T-cell mediated hyper proliferation of *** type of skin disorder is characterized by macroscopic and also microscopic skin *** was observed that,psoriatic lesions are sharply demarcated,red and slightly raised lesions along with silver whitish *** striking feature of T-cell mediated chronic psoriatic lesions are the epidermal infiltration of predominantly oligoclonal CD8^+T-cells and probably also of CD4^+T-cells in the *** this research article we proposed a mathematical model for the chronic disease,psoriasis,consisting a set of differential equations, involving T-Lymphocytes cells,Dendritic cells and the epidermal Keratinocytes,incorporating half saturation constant through the T lymphocyte cells and also in that sense,it has been infiltrated in the activation process of keratinocytes in the course of the plaque of *** biological research on psoriasis has been established the suppression of epidermal T-cell *** we are interested to know how the cell biological system changes for introducing the half saturation constant in presence of suppression taking place DCs on the model *** analytical and numerical result reveal that due to control effect,the macrophages population density does not impede for the interaction between T-cell and keratinocytes.T-cell and keratinocyte population ultimately become stable after a certain period of time span.

关键词： dendritic cells helper T-cells Keratinocytes DCs dermis epidermis drug efficacy

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Insight of Viral Infection of Jatropha Curcas Plant(Future Fuel):A control based mathematical study

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应用泛函分析学报 2011年第4期13卷 366-374,412页

作者： Sumit Nandi Subhas Khajanchi amar nath chatterjee Priti Kumar Roy Department of Chemistry Narula Institute of TechnologyKolkata-700109 Center for Mathematical Biology and Ecology Department of MathematicsJadavpur UniversityKolkata-700032 India

Jatropha Curcas Linnaeous(Jatropha Curcas L)is a wonder plant with a variety of applications and enormous economic ***,an alternative fuel from non edible vegetable oil of Jatropha Curcas plant,has the requisite potential of providing a promising and commercially viable alternative to diesel oil since it has the desirable physicochemical and performance characteristics comparable to *** alternative fuel is eco-friendly,cost effective and has the huge potentiality for the future generations throughout the *** effective cultivation of this plant, protection from different viral diseases is *** this paper,we describe the eco-epidemiological model of the plant Jatropha Curcas L for understanding the disease dynamics which helps to control the viral infection of the Jatropha Curcas plant *** this approach,this plant can grow ideally for the renewable green fuel of the future world.

关键词： Jatropha Curcas cell biodiesel asymptotic stability optimal control remedial application

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Human immunodeficiency virus/acquired immune deficiency syndrome: Using drug from mathematical perceptive

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World Journal of Virology 2015年第4期4卷 356-364页

作者： amar nath chatterjee Shubhankar Saha Priti Kumar Roy Centre for Mathematical Biology and Ecology Department of Mathematics Jadavpur University

Entry of acquired immune deficiency syndrome virus into the host immune cell involves the participation of various components of host and viral cell unit. These components may be categorized as attachment of the viral surface envelope protein subunit, gp120, to the CD4+ receptor and chemokine coreceptors, CCR5 and CXCR4, present on T cell surface. The viral fusion protein, gp41, the second cleaved subunit of Env undergoes reconfiguration and the membrane fusion reaction itself. Since the CD4+ T cell population is actively involved; the ultimate outcome of human immunodeficiency virus infection is total collapse of the host immune system. Mathematical modeling of the stages in viral membrane protein-host cell receptor-coreceptor interaction and the effect of antibody vaccine on the viral entry into the susceptible host cell has been carried out using as impulsive differential equations. We have studied the effect of antibody vaccination and determined analytically the threshold value of drug dosage and dosing interval for optimum levels of infection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that systematic drug dosage of the immune cells leads to longer and improved lives.

关键词： Human immunodeficiency virus Acquired immune deficiency syndrome Antibody vaccine Perfect drug adherence Impulsive differential equation

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A Partially Heat Integrated Ternary Distillation Column

A Partially Heat Integrated Ternary Distillation Column

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International Conference on Environmental Engineering and Applications（ICEEA 2011）

作者： Bandaru Kiran Amiya K. Jana amar nath Samanta Department of Chemical Engineering Indian Institute of Technology-Kharagpur

In this work,a ternary distillation column is used for internal thermal *** influence of the partially heat integrated ternary distillation column（HITDC） on the energetic aspects is evaluated through intensive comparison against the conventional standalone *** simulated column has been used for finding the quasi-optimal values of the design and operating *** is observed that the HITDC system appears superior to its conventional counterpart providing about energy savings of 59.9%.

关键词： Partial HITDC simulation parametric sensitivity energy savings

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