Description 
1 online resource (xxiii, 739 pages) : illustrations 
Contents 
1. Biology and epidemiology of HIV/AIDS. 1.1. Introduction. 1.2. Emergence of a new disease. 1.3. A new virus as a causal agent. 1.4. On the evolutionary origins of HIV. 1.5. AIDS therapies and vaccines. 1.6. Clinical effects of HIV infection. 1.7. An international perspective of the AIDS epidemic. 1.8. Evolution of antibiotic resistance. 1.9. Mathematical models of the HIV/AIDS epidemic. 1.10. References  2. Models of incubation and infectious periods. 2.1. Introduction. 2.2. Distribution function of the incubation period. 2.3. The Weibull and gamma distributions. 2.4. The lognormal, loglogistic and logCauchy distributions. 2.5. Quantiles of a distribution. 2.6. Some principles and results of Monte Carlo simulation. 2.7. Compound distributions. 2.8. Models based on symptomatic stages of HIV disease. 2.9. CD4[symbol] T lymphocyte decline. 2.10. Concluding remarks. 2.11. References  3. Continuous time Markov and semiMarkov jump processes. 3.1. Introduction 3.2. Stationary Markov jump processes. 3.3. The Kolmogorov differential equations. 3.4. The sample path perspective of Markov processes. 3.5. Nonstationary Markov processes. 3.6. Models for the evolution of HIV disease. 3.7. Time homogeneous semiMarkov processes. 3.8. Absorption and other transition probabilities. 3.9. References  4. SemiMarkov jump processes in discrete time. 4.1. Introduction. 4.2. Computational methods. 4.3. Age dependency with stationary laws of evolution. 4.4. Discrete time nonstationary jump processes. 4.5. Age dependency with time inhomogeneity. 4.6. On estimating parameters from data. 4.7. References  5. Models of HIV latency based on a logGaussian process. 5.1. Introduction. 5.2. Stationary Gaussian processes in continuous time. 5.3. Stationary Gaussian processes in discrete time. 5.4. Stationary logGaussian processes. 5.5. HIV latency based on a stationary logGaussian process. 5.6. HIV latency based on the exponential distribution. 5.7. Applying the model to data in a Monte Carlo experiment. 5.8. References  6. The threshold parameter of onetype branching processes. 6.1. Introduction. 6.2. Overview of a onetype CMJprocess. 6.3. Life cycle models and mean functions. 6.4. On modeling point processes. 6.5. Examples with a constant rate of infection. 6.6. On the distribution of the total size of an epidemic. 6.7. Estimating HIV infectivity in the primary stage of infection. 6.8. Threshold parameters for staged infectious diseases. 6.9. Branching processes approximations. 6.10. References  7. A structural approach to SIS and SIR models. 7.1. Introduction. 7.2. Structure of SIS stochastic models. 7.3. Waiting time distributions for the extinction of an epidemic. 7.4. Numerical study of extinction time of logistic SIS. 7.5. An overview of the structure of stochastic SIR models. 7.6. Algorithms for SIRprocesses with large state spaces. 7.7. A numerical study of SIRprocesses. 7.8. Embedding deterministic models in SISprocesses. 7.9. Embedding deterministic models in SIRprocesses. 7.10. Convergence of discrete time models. 7.11. References  8. Threshold parameters for multitype branching processes. 8.1. Introduction. 8.2. Overview of the structure of multitype CMJprocesses. 8.3. A class of multitype life cycle models. 8.4. Threshold parameters for twotype systems. 8.5. On the parameterization of contact probabilities. 8.6. Threshold parameters for malaria. 8.7. Epidemics in a community of households. 8.8. Highly infectious diseases in a community of households. 8.9. References  9. Computer intensive methods for the multitype case. 9.1. Introduction. 9.2. A simple semiMarkovian partnership model. 9.3. Linking the simple life cycle model to a branching process. 9.4. Extinction probabilities for the simple life cycle model. 9.5. Computation of threshold parameters for the simple model. 9.6. Extinction probabilities and intrinsic growth rates. 9.7. A partnership model for the sexual transmission of HIV. 9.8. Latent risks for the partnership model of HIV/AIDS. 9.9. Linking the partnership model to a branching process. 9.10. Some numerical experiments with the HIV model. 9.11. Stochasticity and the development of major epidemics. 9.12. On controlling an epidemic. 9.13. References 

10. Nonlinear stochastic models in homosexual populations. 10.1. Introduction. 10.2. Types of individuals and contact structures. 10.3. Probabilities of susceptibles being infected. 10.4. SemiMarkovian processes as models for life cycles. 10.5. Stochastic evolutionary equations for the population. 10.6. Embedded nonlinear difference equations. 10.7. Embedded nonlinear differential equations. 10.8. Examples of coefficient matrices. 10.9. On the stability of stationary points. 10.10. Jacobian matrices in a simple case. 10.11. Jacobian matrices in a more complex case. 10.12. On the probability an epidemic becomes extinct. 10.13. Software for testing stability of the Jacobian. 10.14. Invasion thresholds : onestage model, random assortment. 10.15. Invasion thresholds: onestage model, positive assortment. 10.16. Recurrent invasions by infectious recruits. 10.17. References  11. Stochastic partnership models in homosexual populations. 11.1. Introduction. 11.2. Types of individuals and partnerships. 11.3. Life cycle model for couples with one behavioral class. 11.4. Couple types for two or more behavioral classes. 11.5. Couple formation. 11.6. Probabilities of being infected by extramarital contacts. 11.7. Stochastic evolutionary equations for the population. 11.8. Embedded nonlinear difference equations. 11.9. Embedded nonlinear differential equations. 11.10. Examples of coefficient matrices for one behavioral class. 11.11. Stationary vectors and structure of the Jacobian matrix. 11.12. Overview of the Jacobian for extramarital contacts. 11.13. General form of the Jacobian for extramarital contacts. 11.14. Jacobian matrix for couple formation. 11.15. Couple formation for cases m ≥ 2 and n ≥ 2. 11.16. Invasion thresholds for m = 2 and n = 1. 11.17. Invasion thresholds of highly sexually active infectives. 11.18. Mutations and the evolution of epidemics. 11.19. References  12. Heterosexual populations with partnerships. 12.1. Introduction. 12.2. Types of individuals and partnerships. 12.3. Matrices of latent risks for life cycle models. 12.4. Marital couple formation. 12.5. Probabilities of being infected by extramarital contacts. 12.6. Stochastic evolutionary equations. 12.7. Embedded nonlinear difference equations. 12.8. Embedded nonlinear differential equations. 12.9. Coefficient matrices for the twosex model. 12.10. The Jacobian matrix and stationary points. 12.11. Overview of the Jacobian for extramarital contacts. 12.12. General form of the Jacobian for extramarital contacts. 12.13. Jacobian matrix for couple formation. 12.14. Couple formation for m ≥ 2 and n ≥ 2. 12.15. Invasion thresholds for m = n = 1. 12.16. Fourstage model applied to epidemics of HIV/AIDS. 12.17. Highly active antiretroviral therapy of HIV/AIDS. 12.18. Epidemics of HIV/AIDS among senior citizens. 12.19. Invasions of infectives for elderly heterosexuals. 12.20. Recurrent invasions of infectious recruits. 12.21. References  13. Agedependent stochastic models with partnerships. 13.1. Introduction. 13.2. Parametric models of human mortality. 13.3. Latent risks for susceptible infants and adolescents. 13.4. Couple formation in a population of susceptibles. 13.5. Births in a population of susceptibles. 13.6. Latent risks with infectives. 13.7. References  14. Epilogue  future research directions. 14.1. Modeling mutations in disease causing agents. 14.2. References 
Summary 
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 
Bibliography 
Includes bibliographical references and indexes 
Notes 
Print version record 
Subject 
Epidemiology  Mathematical models


Epidemiology  Statistical methods


Stochastic analysis.


Mathematical models.


Stochastic processes.


Epidemiologic Methods


Acquired Immunodeficiency Syndrome  epidemiology


HIV Infections  epidemiology


Models, Theoretical


Stochastic Processes


mathematical models.


MEDICAL  Forensic Medicine.


MEDICAL  Preventive Medicine.


MEDICAL  Public Health.


Stochastic processes


Mathematical models


Epidemiology  Mathematical models


Epidemiology  Statistical methods


Stochastic analysis


Épidémiologie  Modèles mathématiques.


Analyse stochastique.

Form 
Electronic book

Author 
Sleeman, Candace K

ISBN 
9789812779250 

9812779256 

1281938009 

9781281938008 
