Erscheinungsdatum: 03.06.2016, Medium: Taschenbuch, Einband: Kartoniert / Broschiert, Titel: A Study on Some Stochastic Models for HIV Infection and AIDS, Autor: R. M., Palanivel, Verlag: LAP Lambert Academic Publishing, Sprache: Englisch, Rubrik: Mathematik // Wahrscheinlichkeitstheorie, Seiten: 124, Informationen: Paperback, Gewicht: 201 gr, Verkäufer: averdo
Erscheinungsdatum: 28.10.2015, Medium: Buch, Einband: Gebunden, Titel: Stochastic Models with Applications to Genetics, Cancers, AIDS and Other Biomedical Systems, Titelzusatz: Second Edition, Autor: Tan, Wai-Yuan, Verlag: WSPC, Sprache: Englisch, Schlagworte: MATHEMATICS // Applied, Rubrik: Mathematik // Sonstiges, Seiten: 524, Informationen: HC gerader Rücken kaschiert, Gewicht: 903 gr, Verkäufer: averdo
Stochastic Models with Applications to Genetics Cancers AIDS and Other Biomedical Systems ab 175.49 EURO Second Edition
This book has been aimed to apply the cox proportional hazard model to assess the determinant factors of survival time and discrete time homogeneous semi markov model to predict the clinical progression of AIDS disease using secondary data obtained from the antiretroviral therapy unit of Jimma University Specialized Hospital. The data were extracted from standard patient medical registration. A retrospective study was undertaken on a sample of 456 HIV/AIDS patients. Patients were followed for a median of 34 months. Of total sample, 312 (68.4%) were female and 144 (31.6%) were male. In the followed up period, 66 (14.5%) patients died and 390 (85.5%) patients were censored. The cox regression result indicated that the survival time of the HIV patient was significantly related with adherence level, age, alcohol use, CD4, condom use, functional status, marital status and WHO stage. The results of homogenous semi-markov model showed that the survival probability of a patient increased when CD4 count increased.
Since the first cases of HIV/AIDS disease were recognised in the early 1980s, a large number of mathematical models have been proposed. However, the mobility of people, which has an obvious impact on the spread of the disease, has not been much considered in the modelling studies. This book provides various new results pertaining to the spread of the disease, including epidemic intervention, in mobile populations. The results can serve as a basic framework how to formulate and analyse a more realistic stochastic model for the spread of HIV in mobile heterogeneous populations classifying all individuals by age, risk, and at the same time considering different modes of the disease transmission. Some strategies such as how to allocate a limited budget to minimise the number of new HIV cases over a finite time horizon as people move among regions might provide some useful information in controlling the spread of the disease. A novel approach using the Cross-Entropy (CE) method is introduced to solve such highly non-linear and multidimensional problems. This book, therefore, should be especially useful to those interested in Epidemic Modelling, Analysis, and Simulation fields.
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.
As Eugene Wigner stressed, mathematics has proven unreasonably effective in the physical sciences and their technological applications. The role of mathematics in the biological, medical and social sciences has been much more modest but has recently grown thanks to the simulation capacity offered by modern computers.This book traces the history of population dynamics---a theoretical subject closely connected to genetics, ecology, epidemiology and demography---where mathematics has brought significant insights. It presents an overview of the genesis of several important themes: exponential growth, from Euler and Malthus to the Chinese one-child policy, the development of stochastic models, from Mendel's laws and the question of extinction of family names to percolation theory for the spread of epidemics, and chaotic populations, where determinism and randomness intertwine.The reader of this book will see, from a different perspective, the problems that scientists face when governments ask for reliable predictions to help control epidemics (AIDS, SARS, swine flu), manage renewable resources (fishing quotas, spread of genetically modified organisms) or anticipate demographic evolutions such as aging.
In the study of HIV infection and its progress to AIDS the antigenic diversity of the invading antigen plays a vital role. The human immune system fails after a certain stage. The invading antigens namely the HIV develop stronger measures to suppress the human immune system and the antigenic diversity is one of the strategies adopted by the invading antigen. As and when the antigenic diversity crosses the threshold level the human immune system fails completely and the seroconversion occurs. There are very many situations in which this phenomenon occurs. Suitable stochastic models are developed by different authors to meet properly the situation. Using such models an attempt is made to estimate the likely time at which the seroconversion occurs.
The Athens Conference on Applied Probability and Time Series in 1995 brought together researchers from across the world. The published papers appear in two volumes. Volume I includes papers on applied probability in Honor of J.M. Gani. The topics include probability and probabilistic methods in recursive algorithms and stochastic models, Markov and other stochastic models such as Markov chains, branching processes and semi-Markov systems, biomathematical and genetic models, epidemilogical models including S-I-R (Susceptible-Infective-Removal), household and AIDS epidemics, financial models for option pricing and optimization problems, random walks, queues and their waiting times, and spatial models for earthquakes and inference on spatial models.