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Author Mode, Charles J., 1927-

Title Stochastic processes in epidemiology : HIV/AIDS, other infectious diseases, and computers / Charles J. Mode, Candace K. Sleeman
Published Singapore ; River Edge, NJ : World Scientific, 2000


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 log-normal, log-logistic and log-Cauchy 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 semi-Markov 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. Non-stationary Markov processes. 3.6. Models for the evolution of HIV disease. 3.7. Time homogeneous semi-Markov processes. 3.8. Absorption and other transition probabilities. 3.9. References -- 4. Semi-Markov 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 non-stationary 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 log-Gaussian process. 5.1. Introduction. 5.2. Stationary Gaussian processes in continuous time. 5.3. Stationary Gaussian processes in discrete time. 5.4. Stationary log-Gaussian processes. 5.5. HIV latency based on a stationary log-Gaussian 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 one-type branching processes. 6.1. Introduction. 6.2. Overview of a one-type CMJ-process. 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 SIR-processes with large state spaces. 7.7. A numerical study of SIR-processes. 7.8. Embedding deterministic models in SIS-processes. 7.9. Embedding deterministic models in SIR-processes. 7.10. Convergence of discrete time models. 7.11. References -- 8. Threshold parameters for multi-type branching processes. 8.1. Introduction. 8.2. Overview of the structure of multi-type CMJ-processes. 8.3. A class of multi-type life cycle models. 8.4. Threshold parameters for two-type 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 multi-type case. 9.1. Introduction. 9.2. A simple semi-Markovian 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. Non-linear 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. Semi-Markovian processes as models for life cycles. 10.5. Stochastic evolutionary equations for the population. 10.6. Embedded non-linear difference equations. 10.7. Embedded non-linear 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 : one-stage model, random assortment. 10.15. Invasion thresholds: one-stage 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 extra-marital contacts. 11.7. Stochastic evolutionary equations for the population. 11.8. Embedded non-linear difference equations. 11.9. Embedded non-linear 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 extra-marital contacts. 11.13. General form of the Jacobian for extra-marital 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 extra-marital contacts. 12.6. Stochastic evolutionary equations. 12.7. Embedded non-linear difference equations. 12.8. Embedded non-linear differential equations. 12.9. Coefficient matrices for the two-sex model. 12.10. The Jacobian matrix and stationary points. 12.11. Overview of the Jacobian for extra-marital contacts. 12.12. General form of the Jacobian for extra-marital 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. Four-stage model applied to epidemics of HIV/AIDS. 12.17. Highly active anti-retroviral 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. Age-dependent 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