Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention

Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention
Author: W. Y. Tan
Publisher: World Scientific
Total Pages: 610
Release: 2005
Genre: Mathematics
ISBN: 9812561390
GET BOOK

Download Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention Book in PDF, Epub and Kindle

- Only book on extensive, deterministic models, statistic models, stochastic models and state space models and statistical methods for HIV epidemic involving IV drug usage and HIV epidemic in homosexual populations. - Provides most recent biological insights into HIV pathogenesis and HIV kinetics at the cellular level, and illustrates how to build up mathematical models based on these biological insights. - Only publication that provides in-depth analysis of HAART treatment protocols and discusses possible improvements to the HAART protocol. The book also provides connection between pharmacokinetics with treatment in HIV-infected individuals.

Stochastic Modeling of AIDS Epidemiology and HIV Pathogenesis

Stochastic Modeling of AIDS Epidemiology and HIV Pathogenesis
Author: W. Y. Tan
Publisher: World Scientific
Total Pages: 458
Release: 2000
Genre: Mathematics
ISBN: 9789810241223
GET BOOK

Download Stochastic Modeling of AIDS Epidemiology and HIV Pathogenesis Book in PDF, Epub and Kindle

This book discusses systematically treatment on the development of stochastic, statistical and state space models of the HIV epidemic and of HIV pathogenesis in HIV-infected individuals, and presents the applications of these models. The book is unique in several ways: (1) it uses stochastic difference and differential equations to present the stochastic models of the HIV epidemic and HIV pathogenesis; in this sense, the deterministic models are considered as special cases when the numbers of different type of people or cells are very large (2) it provides, a critical analysis of deterministic and statistical models in the literature; (3) it develops state space models by combining stochastic models and statistical models; and (4) it provides a detailed discussion on the pros and cons of the different modeling approaches. This book is the first to introduce state space models for the HIV epidemic. It is also the first to develop stochastic models and state space models for the HIV pathogenesis in HIV-infected individuals.

Deterministic and Stochastic Models for HIV

Deterministic and Stochastic Models for HIV
Author: sarkhosh seddighi chaharborj
Publisher: LAP Lambert Academic Publishing
Total Pages: 116
Release: 2014-01
Genre:
ISBN: 9783659513848
GET BOOK

Download Deterministic and Stochastic Models for HIV Book in PDF, Epub and Kindle

Mathematical modeling is an important tools to analyze and control the spread of infection disease in a society. One of the fundamental questions of mathematical epidemiology is to find threshold conditions that determine whether an infectious disease will spread in a susceptible population when the disease is introduced into the population. The threshold conditions are characterized by the so-called reproductive number, the reproduction number, the reproductive ratio, basic reproductive value, basic reproductive rate, or contact number. This book present the deterministic and stochastic epidemic models for HIV and study of reproductive numbers. The homotopy perturbation method and homotopy analysis method which was used to solve the linear and nonlinear differential equations. Also, the generation of stochastic models in the epidemic disease has been studied.

Stochastic Processes in Epidemiology

Stochastic Processes in Epidemiology
Author: Charles J. Mode
Publisher: World Scientific
Total Pages: 765
Release: 2000
Genre: Mathematics
ISBN: 9812779256
GET BOOK

Download Stochastic Processes in Epidemiology Book in PDF, Epub and Kindle

This text deals with the mathematical and statistical techniques underlying the models used to understand the population dynamics of not only HIV/AIDS, but also of other infectious diseases. Attention is given to the development of strategies for the prevention and control of the international epidemic within the frameworks of the models. The text incorporates stochastic and deterministic formulations within a unifying conceptual framework.

Stochastic Modeling of the Persistence of HIV

Stochastic Modeling of the Persistence of HIV
Author: Peter Albert Roemer
Publisher:
Total Pages: 124
Release: 2013
Genre: Biology
ISBN:
GET BOOK

Download Stochastic Modeling of the Persistence of HIV Book in PDF, Epub and Kindle

Mathematical modeling of biological systems is crucial to effectively and efficiently developing treatments for medical conditions that plague humanity. Systems of differential equations are the traditional tools used to theoretically describe the spread of disease within the body. In this project we consider the dynamics of the Human Immunodeficiency Virus (HIV) in vivo during the initial stages of infection. Both mathematical and biological results support the idea that contact with the HIV retrovirus does not automatically imply permanent infection. Given factors such as the CD4+ T-cell growth rate, infection rate, and viral clearance rate, it is possible to correctly predict the end viral state in a deterministic model. While this is useful, such a model lacks the randomness inherent in physical processes and parameter estimation. To account for this, our project examines both discrete and continuous stochastic models for the early stages of HIV infection. These models use the knowledge of biological interactions and fundamental mathematical principles. We also examine the well-known three-component deterministic model in greater detail, proving existence and uniqueness of the solutions. Furthermore, we prove that the solutions remain biologically meaningful, and perform a thorough stability analysis for the equilibrium states of the system. Finally, we develop two new stochastic models and obtain extensive numerical results to measure the probability of infection given the transmission of the virus to a new individual. To simulate the dynamics of the virus, we employ Runge-Kutta methods and the Euler-Maruyama scheme.

Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission

Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission
Author: Priti Kumar Roy
Publisher: Springer
Total Pages: 228
Release: 2015-12-08
Genre: Mathematics
ISBN: 9812878521
GET BOOK

Download Mathematical Models for Therapeutic Approaches to Control HIV Disease Transmission Book in PDF, Epub and Kindle

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.