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SATURATION EFFECTS FOR CTL MEDIATED CONTROL OF HIV-1 INFECTION： A MATHEMATICAL STUDY

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International Journal of Biomathematics 2013年第3期6卷 33-51页

作者： priti kumar roy SONIA CHOWDHURY XUE-ZHI LI Centre for Mathematical Biology and EcologyDepartment of Mathematics Jadavpur University Kolkata 700032 India Department of Mathematics Xinyang Normal UniversityXinyang 464000 P. R. China

The relations between the Human Immunodeficiency Virus-1 （HIV-1） and the human immune system are astonishingly multifaceted, where the critical role for cytotoxic T lymphocytes （CTLs） in the suppression of viral replication in HIV-1 infected individuals cannot be ignored. In this research paper, we have proposed a mathematical model incorporating half saturation constant through the CTL mediated killing process and also in that sense, it has been infiltrated in the generation process of CTL through infected cells. To make the model more realistic, a time lag is introduced in the generation term of CTL population. Also an optimal control theory paradigm is used in our mathematical model to suppress the viral production. From our entire analysis, we have found threshold condition of half saturation constant and treatment schedule so that we can handle the situation of Acquired Immunodeficiency Syndrome （AIDS） patients in a better way. Our analysis reveals that, if the half saturation constant is around 47 mm^-3 in the saturation process and the drug therapy is to be used around 76 days, then we can get adequate results for better treatment of a HIV-1 patient. Based on numerical results, we observed that in a highly unstable situation, administration of chemotherapy at a high dose can stabilize the system.

关键词： CD4^+T cells HIV-1 Cytotoxic T-Lymphocyte (CTL) highly active antiretroviral therapy optimal control.

How can HPV-induced cervical cancer be controlled by a combination of drug therapy?A mathematical study

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International Journal of Biomathematics 2019年第6期12卷 181-197页

作者： Sudip Chakraborty Xue-Zhi Li priti kumar roy Centre for Mathematical Biology and Ecology Department of Mathematics Jadavpur University Kolkata 700032.India College of Mathematics and Information Science Henan Normal Untverstly Xmu-tang 45300P.R.China Centre for Mathematical Biology and Ecology Department of Mathematics Jadavpur University Kolkata 700032India

This paper deals with a control strategy through impulsive drug treatment to study the effect of Chemotherapy and CTL activator drug to eradicate the cervical *** kills the HPV infected cells and helps to prevent cervical *** cell(DC)plays a crucial role in this disease dynamics in enhancing the act ivity of *** explore these effects,we have formulated a mathematical model consisting of six compartments to describe the interactions between HPV and three classes of cervical cells(susceptible,infected,cancerous),with DC and *** the basic reproduction ratio,we find that there exists a disease-free equilibrium point and an endemic equilibrium *** our study,we have sltown that though DC enhances the activity of *** te not sufficient to eradicate the disease *** we could restrict the cancer development by using double drug in an impulsive way with particular drug doses is being reflected in the *** illustrate our results,numerical simulations are also presented.

关键词： Human Papilloma Virus(HPV) cervical cancer dendritic cell cytotoxic T-Lymphocytes chemotherapy

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

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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.

Role of antibiotic therapy in bacterial disease：A mathematical study

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International Journal of Biomathematics 2018年第3期11卷 131-154页

作者： priti kumar roy Yanhui Zhang Priyanka Ghosh Joydeep Pals Fahad Al Basir Centre for Mathematical Biology and Ecology Department of Mathematics Jadavpur University Kolkata 700032 India Beijing Technology and Business University Beijing 100048 P. R. China Department of Zoology Visva-Bharati University Shantiniketan West Bengal 731235 India

Pathogenic bacteria in human system mature through the bin-synthesis of protective layer known as cell wall. This bacterial cell wall growth occurs in the presence of enzyme released by it. After maturation by the cell wall formation, pathogenic bacteria become harmful for human body as they are responsible for different diseases. Antibiotics or drugs are employed for curing bacterial diseases through the inhibition of this maturation process and it occurs by the binding progression of antibiotics with the released enzyme. But nowadays, drugs or antibiotics like β-lactum family （Amoxcillin） which are generally used for inhibition of bin-synthesis of cell wall become ineffective due to evolution of antibiotic resistance by the bacteria. Antibiotic resistance occurs when an antibiotic has lost its ability to effectively control or kill bacterial growth. As a result, the bacteria becomes ＂resistant＂ and continue to multiply for the generation of robust pathogenic bacteria in spite of drug administration. This is due to the release of another type of enzyme by the resistant bacteria which binds with the active antibiotic or drug making it ineffective. Hence, another type of drug （Clauvanic acid） is combined to resist the activity of drug hydrolyzing enzyme so that the initial drug can act effectively. Hence a combination of drug therapy is applied to cure the bacterial diseases successfully. We developed a mathematical model based on the bacterial enzyme and bacterial cell wall proliferation mechanism and showed how we can reduce the bacterial infection in the resistant cases with application of combination drugs （Amoxcillin and Clauvanic acid） to restore normal health. Based on the enzymatic activity and individual drug dynamics we studied the overall system under the single drug and combinational drug administra- tion through our formulated model analysis. We also demonstrated the different dosing time interval and dosing concentration to evaluate the optimized drug a

关键词： Bacteria cell wall resistance enzyme inhibition modeling impulsive drug dosing.

CTL Response Suppression in Chronic Phase of Infection:A mathematical study

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应用泛函分析学报 2012年第1期14卷 46-54页

作者： Sonia Chowdhury priti kumar roy Center for Mathematical Biology and Ecology Department of Mathematics Jadavpur UniversityKolkata-700032India

Human immunodeficiency virus(HIV)has had an insightful impact about the state of healthiness of human immune *** to great improvement in drug therapy,HIV infections have been reduced by 17%over the past eight *** has been proved that most effective treatment HAART(Highly Active Anti Retroviral Therapy)mainly controls the diseases progression but it does not eradicate the diseases *** Transcriptase Inhibitor drugs specially associated with virus specific Cytotoxic T-Lymphocyte(CTL)that declines with disease progression. CTL responses against AIDS pathogenesis could be potential in the dynamics of virus replication, recognition and clearance of infected *** this research article a mathematical model has been proposed on the basis of CTL response suppression in the chronic phase of infection due to presence of *** also consider the growth of the virus population from the infected CD4^+T cells budding process and from the other infected cells like macrophages and *** analytical and numerical studies are consistent with existing observations from allied areas.

关键词： CD4^+T cells HIV T-cell proliferation cytotoxic T lymphocyte(CTL) time series solutions asymptotic stability

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

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

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

Practice patterns among ophthalmic surgeons in treating concomitant oculoplastic conditions in preoperative period:A questionnaire-based study

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World Journal of Clinical Cases 2025年第1期13卷 29-37页

作者： Bijnya Birajita Panda Chitaranjan Mishra Bhagabat Nayak Avik kumar roy Logesh Balakrishnan Priyadarshini Mishra Department of Ophthalmology All India Institute of Medical SciencesBhubaneswar 751019OdishaIndia Department of Vitreo-Retina Trilochan NetralayaSambalpur 768004India Department of Glaucoma Services LV Prasad Eye InstituteBhubaneswar 751013India Department of Statistics Apollo HospitalsChennai 823104India

BACKGROUND Addressing oculoplastic conditions in the preoperative period ensures both the safety and functional success of any ophthalmic *** oculoplastic conditions,like nasolacrimal duct obstruction,have been extensively studied,whereas others,like eyelid malposition and thyroid eye disease,have received minimal or no *** To investigate the current practice patterns among ophthalmologists while treating concomitant oculoplastic conditions before any subspecialty ophthalmic *** A cross-sectional survey was disseminated among ophthalmologists all over *** survey included questions related to pre-operative evaluation,anaesthetic and surgical techniques preferred,post-operative care,the use of adjunctive therapies,and patient follow-up *** A total of 180 ophthalmologists responded to the *** practitioners(89%)felt that the ROPLAS test was sufficient during pre-operative evaluation before any subspecialty surgery was *** most common surgical techniques employed were lacrimal drainage procedures(Dacryocystorhinostomy)(63.3%),eyelid malposition repair(36.9%),and ptosis repair(58.7%).Post-operatively,47.7%of respondents emphasized that at least a 4-week gap should be maintained after lacrimal drainage procedures and eyelid ***-seven percent of ophthalmologists felt that topical anaesthetic procedures should be preferred while performing ocular surgeries in thyroid eye disease *** Approximately 50%of ophthalmologists handle prevalent oculoplastic issues themselves,seeking the expertise of an oculoplastic surgeon under particular *** ophthalmologists still favor using ROPLAS as a preliminary screening method before proceeding with cataract *** conditions and thyroid eye disease are not as commonly addressed before subspecialty procedures compared to issues like nasolacrimal duct obstruction and periocular infections.

关键词： Oculoplasty Ophthalmic plastic surgery Nasolacrimal duct obstruction Practice patterns Survey