[PDF] Stochastic Modeling Of The Persistence Of Hiv eBook

Author : Peter Albert Roemer
Publisher :
Page : 124 pages
File Size : 36,75 MB
Release : 2013
Category : Biology
ISBN :

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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.

Author : Wai-yuan Tan
Publisher : World Scientific Publishing Company
Page : 449 pages
File Size : 29,46 MB
Release : 2000-09-29
Category : Mathematics
ISBN : 9813105623

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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.

Author : W. Y. Tan
Publisher : World Scientific
Page : 610 pages
File Size : 21,32 MB
Release : 2005
Category : Medical
ISBN : 981256926X

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With contributions from an international team of leading researchers, the book pulls together updated research results in the area of HIV/AIDS modeling to provide readers with the latest information in the field. Topics covered include: AIDS epidemic models; vaccine models; models for HIV/cell dynamics and interactions; cellular kinetics; viral dynamics with antiviral treatments; modeling of drug resistance and quasispecies.

Author : Charles J. Mode
Publisher : World Scientific
Page : 765 pages
File Size : 40,53 MB
Release : 2000
Category : Mathematics
ISBN : 9812779256

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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.

Author : Henry and Patrick Shipman Tuckwell
Publisher :
Page : pages
File Size : 17,94 MB
Release : 2011
Category :
ISBN :

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We consider the standard three-component differential equation model for the growth of an HIV virion population in an infected host in the absence of drug therapy. The dynamical properties of the model are determined by the set of values of six parameters which vary across host populations. There may be one or two critical points whose natures play a key role in determining the outcome of infection and in particular whether the HIV population will persist or become extinct. There are two cases which may arise. In the first case, there is only one critical point P1 at biological values and this is an asymptotically stable node. The system ends up with zero virions and so the host becomes HIV-free. In the second case, there are two critical points P1 and P2 at biological values. Here P1 is an unstable saddle point and P2 is an asymptotically stable spiral point with a non-zero virion level. In this case the HIV population persists unless parameters change. We let the parameter values take random values from distributions based on empirical data, but suitably truncated, and determine the probabilities of occurrence of the various combinations of critical points. From these simulations the probability that an HIV infection will persist, across a population, is estimated. It is found that with conservatively estimated distributions of parameters, within the framework of the standard 3-component model, the chances that a within host HIV population will become extinct is between 0.6% and 6.9%. With less conservative parameter estimates, the probability is estimated to be as high as 24%. The many factors related to the transmission and possible spontaneous elimination of the virus are discussed.

Author : Dinberu Seyoum
Publisher : LAP Lambert Academic Publishing
Page : 204 pages
File Size : 10,37 MB
Release : 2013
Category :
ISBN : 9783659126451

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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.

Author : sarkhosh seddighi chaharborj
Publisher : LAP Lambert Academic Publishing
Page : 116 pages
File Size : 43,94 MB
Release : 2014-01
Category :
ISBN : 9783659513848

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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.