The 8th International Conference on Fuzzy Systems and Data Mining (FSDM 2022)

Abstract: Chronic lymphocytic leukemia (CLL) is a type of slowgrowing cancer that affects developing B-lymphocytes (also known as B-cells) in the bone marrow. B-lymphocytes are specialised white blood cells in which the bone marrow makes too many lymphocytes and in case of CLL, lymphocytes undergo a malignant (cancerous) change and become leukemic cells. Among the non-communicable diseases, cancer is the most killer diseases and hence is a worldwide public health problem. It is the result of unconstrained growth of immature white blood cells in the blood. In this talk, we discuss a compartmental model of leukemia cancer in terms of a system of coupled nonlinear ordinary differential equations to describe the cell-cell interactions inside the body. We then introduce two control variables; namely, u_1 (representing immune boosting drugs) as well as u_2 (representing engineered T-cell therapy) as immunotherapeutic treatment strategies to apply optimal control technique in obtaining optimal strategies to minimize the number of infected cells in the blood. Initially, a mathematical model of leukemia is formulated and verified for the well posedness of the solution. We also verify the stability of the equilibria (disease-free and endemic equilibrium point) of the model based on the basic reproduction number. After words, in order to minimize the number of infected cells as well as the costs of the controls, we develop an appropriate optimal control model by applying Pontryagin’s minimum principle. Finally, numerical simulation of the proposed model and optimal control model are performed to show that the effectiveness of immune boosting drugs as well as immunotherapy to defend leukemia in the blood.

Keywords: Compartmental model, CLL, Immunotherapeutic treatment, Optimal control, Pontryagin’s minimun principle, Computational analysis

Biography: Dr. Md. Haider Ali Biswas is currently affiliated with Khulna University, Bangladesh as a Professor of Mathematics under Science Engineering and Technology School and he served as the Head of Mathematics Discipline from 2015 to 2018. Prof. Biswas obtained his B Sc (Honors) in Mathematics and M Sc in Applied Mathematics in the year 1993 and 1994 respectively from the University of Chittagong, Bangladesh, M Phil in Mathematics in the year 2008 from the University of Rajshahi, Bangladesh and PhD in Electrical and Computer Engineering from the University of Porto, Portugal in 2013. He has more than 22 years teaching and research experience in the graduate and post-graduate levels at different public universities in Bangladesh. He published Three Books, Seven Book Chapters and more than 200 research papers in the peer reviewed journals and international conferences. Prof. Biswas supervised (is supervising) more than 80 undergraduate students (Undergraduate Project Thesis), 30 MSc Students (MSc Thesis and Project Thesis), 3 MPhil Students and 5 PhD Students at Different Public Universities including Khulna University in Bangladesh. Prof. Biswas has worked at several R & D projects in home and abroad as PI and/or Researcher, particularly he conducted several research projects funded by Khulna University Research Cell, the Ministry of Science and Technology, Bangladesh, University Grants Commission of Bangladesh and The World Academy of Science (TWAS), Trieste, Italy.
His present research interests include Optimal Control with Constraints, Nonsmooth Analysis, ODEs and Dynamical Systems, Mathematical Modeling, Mathematical Ecology, Environmental modeling and Climate change, Mathematical Biology and Biomedicine, Epidemiology of Infectious Diseases. Since the last ten years, Prof. Biswas has been working on the applications of mathematical models for designing and implementing those to real life problems, specially for the sustainable/optimal management under the changing environment due to global warming.
He is the life/general members of several professional societies and/or research organizations like Bangladesh Mathematical Society (BMS), Asiatic Society of Bangladesh (ASB), Institute of Mathematics and its Applications (IMA), UK, European Mathematical Society (EMS) and Society for Mathematical Biology (SMB). Dr. Biswas is the founder member of Mathematical Forum Khulna and served as the General Secretary of the Forum in 2013-2015. Dr. Biswas organized several national and international seminars/workshops/conferences in home and abroad and he has been working as Editor/Member of editorial boards of several international peer-reviewed journals. Professor Biswas delivered more than 50 Talks as Keynote/Invited/Plenary/Panel Speaker at several international conferences/seminars/workshops in home and abroad. Professor Biswas was nominated as the Member of the Council of Asian Science Editors (CASE) for 2017-2020 and the Associate Member of the Organization for Women in Science for the Developing World (OWSD) since 2017. Recently, Professor Biswas has been elected as a Vice-President of Bangladesh Mathematical Society (BMS) for the year 2022-2023, and also appointed as the Associate Editor of the international journal GANIT- Journal of Bangladesh Mathematical Society (BMS) for the year 2022-2023. Dr. Biswas has been nominated as a Member of Executive Committee of the IEOM Society, Bangladesh Chapter and also serving as the Treasurer of the IEOM Society, Bangladesh Chapter. He is also serving as the Faculty Advisor of the IEOM Society Khulna University Chapter. Professor Biswas is presently serving as the Founding President of Bangladesh Society for Mathematical Biology (BSMB) for the year 2022-2023.