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The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are presented in the book would serve to reveal the consequences of the logical structure of the disease transmission, quantitatively as well as qualitatively. One of the chapters introduces the optimal control approach towards the mathematical models, describing the optimal drug dosage process that is discussed with the basic deterministic models dealing with stability analysis. Another one chapter deals with the mathematical analysis for the perfect drug adherence for different drug dynamics during the treatment management. The last chapter of the book consists the stochastic approach to the disease dynamics on HIV/AIDS. This method helps to move the disease HIV/AIDS to extinction as the time to increase. This book will appeal to undergraduate and postgraduate students, as well as researchers, who are studying and working in the field of bio-mathematical modelling on infectious diseases, applied mathematics, health informatics, applied statistics and qualitative public health, etc. Social workers, who are working in the field of HIV, will also find the book useful for complements.

Biology - General --- Biology --- Health & Biological Sciences --- HIV infections --- Prevention --- Mathematical models. --- HIV (Viruses) infections --- HTLV-III infections --- HTLV-III-LAV infections --- Human T-lymphotropic virus III infections --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Biomathematics. --- Mathematical and Computational Biology. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Lentivirus infections --- Sexually transmitted diseases --- Math --- Science --- Engineering --- Engineering analysis --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Mathematics

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This book discusses several mathematical models highlighting the disease dynamics of psoriasis and its control. It explains the control of keratinocyte concentration through a negative feedback mechanism and the effect of including a realistic time delay in that system. The effect of cytokine release is described in a mathematical model of psoriasis and further elucidated in two different mathematical pathways: the ordinary differential equation model system, and the fractional-order differential equation model system. The book also identifies the role of CD8+ T-cells in psoriasis by investigating the interaction between dendritic cells and CD8+ T-cells. Presenting an approach to control the fractional-order system to prevent excess production of keratinocyte cell population, the book is intended for researchers and scientists in the field of applied mathematics, health informatics, applied statistics and qualitative public health, as well as bio-mathematicians interested in the mathematical modeling of autoimmune diseases like psoriasis.

Mathematics. --- Medicine. --- Mathematical and Computational Biology. --- Mathematical Modeling and Industrial Mathematics. --- Applications of Mathematics. --- Health Promotion and Disease Prevention. --- Health Workforce --- Math --- Science --- Biomathematics. --- Mathematical models. --- Applied mathematics. --- Engineering mathematics. --- Health promotion. --- Health promotion programs --- Health promotion services --- Promotion of health --- Wellness programs --- Preventive health services --- Health education --- Engineering --- Engineering analysis --- Mathematical analysis --- Models, Mathematical --- Simulation methods --- Biology --- Mathematics

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Mathematical analysis --- Mathematics --- Biomathematics. Biometry. Biostatistics --- analyse (wiskunde) --- biomathematica --- mathematische modellen --- wiskunde