# Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission

• Priti KumarÂ Roy
Book

Part of the Industrial and Applied Mathematics book series (INAMA)

1. Front Matter
Pages i-xix
2. Priti Kumar Roy
Pages 1-14
3. ### Dynamics of Immune System Against HIV

1. Front Matter
Pages 15-18
2. Priti Kumar Roy
Pages 19-42
3. Priti Kumar Roy
Pages 43-58
4. Priti Kumar Roy
Pages 59-69
4. ### Control-Based Therapeutic Approach

1. Front Matter
Pages 71-77
2. Priti Kumar Roy
Pages 79-117
3. Priti Kumar Roy
Pages 119-153
4. Priti Kumar Roy
Pages 155-182
5. Priti Kumar Roy
Pages 183-213

### Introduction

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.

### Keywords

Delay dynamics HIV control HIV disease transmission HIV inhibitor drug HIV treatment drug dynamics

#### Authors and affiliations

• Priti KumarÂ Roy
• 1

### Bibliographic information

• DOI https://doi.org/10.1007/978-981-287-852-6
• Publisher Name Springer, Singapore
• eBook Packages Mathematics and Statistics
• Print ISBN 978-981-287-851-9
• Online ISBN 978-981-287-852-6
• Series Print ISSN 2364-6837
• Series Online ISSN 2364-6845