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.

This volume stems from two DIMACS activities, the U.S.-Africa Advanced Study Institute and the DIMACS Workshop, both on Mathematical Modeling of Infectious Diseases in Africa, held in South Africa in the summer of 2007. It contains both tutorial papers and research papers. Students and researchers should find the papers on modeling and analyzing certain diseases currently affecting Africa very informative. In particular, they can learn basic principles of disease modeling and stability from the tutorial papers where continuous and discrete time models, optimal control, and stochastic features are introduced.

This book discusses significant research and study topics related to mathematical modelling and analysis of infectious diseases. It includes several models and modelling approaches with different aims, such as identifying and analysing causes of occurrence and re-occurrence, causes of spreading, treatments and control strategies. A valuable resource for researchers, students, educators, scientists, professionals and practitioners interested in gaining insights into various aspects of infectious diseases using mathematical modelling and mathematical analysis, the book will also appeal to general readers wanting to understand the dynamics of various diseases and related issues. Key Features Mathematical models that describe population prevalence or incidence of infectious diseases Mathematical tools and techniques to analyse data on the incidence of infectious diseases Early detection and risk estimate models of infectious diseases Mathematical models that describe the transmission of infectious diseases and analyse data Dynamical analysis and control strategies for infectious diseases Studies comparing the utility of particular models in describing infected diseases-related issues such as social, health and economic

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of disease transmission models. It includes (i) an introduction to the main concepts of compartmental models including models with heterogeneous mixing of individuals and models for vector-transmitted diseases, (ii) a detailed analysis of models for important specific diseases, including tuberculosis, HIV/AIDS, influenza, Ebola virus disease, malaria, dengue fever and the Zika virus, (iii) an introduction to more advanced mathematical topics, including age structure, spatial structure, and mobility, and (iv) some challenges and opportunities for the future. There are exercises of varying degrees of difficulty, and projects leading to new research directions. For the benefit of public health professionals whose contact with mathematics may not be recent, there is an appendix covering the necessary mathematical background. There are indications which sections require a strong mathematical background so that the book can be useful for both mathematical modelers and public health professionals.

ABSTRACT: My study develops mathematical models to investigate prevention strategies aimed at a reduction of HIV prevalence in a population. It focuses primarily on the impact of coupling prevention effort with treatment delivery. It gives an overview of possible prevention strategies for the entire population as well as for the subgroup of individuals who are undergoing treatment and/or receiving HIV-related medical attention. My study focuses on exploring the effects of the most recent trend having a major impact in the HIV/AIDS epidemic: HAART treatment. Specifically, through simulation, it demonstrates the impact of integrating prevention efforts with the distribution of treatment and HIV-related medical support. It shows that educating HIV patients about risks of HIV transmission, reliability of condoms, and safer sexual behavior may effectively decrease the prevalence of HIV in the population as effectively as aiming these prevention programmes at the entire population, provided that availability of testing and HIV-related medical attention is adequate.

This book presents models describing HIV transmission rates at population level, discussing the main statistical methods and analytical interventions. It also assesses the practical applicability of the various modelling techniques, offering readers insights into what methods are available and, more importantly, when they should be used to address HIV transmission at global level. The book includes realistic simulation models fitted to clarify the rate of HIV mother-to-child transmission (HIV MTCT), and substantiates the conclusions that can be drawn as well as the appropriate time for making global-level clinical decisions concerning people living with HIV/AIDS (PLHIVs). Intended for students, academics and researchers, the book offers more than just an introduction to the topic – it also features in-depth, yet easy-to-understand, descriptions of a new mathematical/statistical HIV mother-to-child transmission model, making it a useful resource for clinicians, public health workers and policymakers involved in implementing HIV-prevention programmes at national /global level.

A self-contained and comprehensive guide to the mathematical modeling of disease transmission, appropriate for graduate students.