Stochastic processes in epidemiology: HIV/AIDS, other infectious diseases, and computers
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2000
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| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references and indexes 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 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 |
| Beschreibung: | 1 Online-Ressource (xxiii, 739 p.) |
| ISBN: | 1281938009 9781281938008 9789810240974 9789812779250 981024097X 9812779256 |
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| 245 | 1 | 0 | |a Stochastic processes in epidemiology |b HIV/AIDS, other infectious diseases, and computers |c Charles J. Mode, Candace K. Sleeman |
| 264 | 1 | |a Singapore |b World Scientific |c 2000 | |
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| 500 | |a Includes bibliographical references and indexes | ||
| 500 | |a 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 | ||
| 500 | |a 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 | ||
| 500 | |a 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 -- | ||
| 500 | |a - 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. | ||
| 500 | |a - Mutations and the evolution of epidemics. 11.19. References -- | ||
| 500 | |a - 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. | ||
| 500 | |a - 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 | ||
| 650 | 4 | |a Épidémiologie / Modèles mathématiques | |
| 650 | 4 | |a Épidémiologie / Modèles statistiques | |
| 650 | 4 | |a Analyse stochastique | |
| 650 | 7 | |a Épidémiologie / Modèles mathématiques |2 ram | |
| 650 | 7 | |a Analyse stochastique |2 ram | |
| 650 | 7 | |a MEDICAL / Forensic Medicine |2 bisacsh | |
| 650 | 7 | |a MEDICAL / Preventive Medicine |2 bisacsh | |
| 650 | 7 | |a MEDICAL / Public Health |2 bisacsh | |
| 650 | 7 | |a Epidemiology / Mathematical models |2 fast | |
| 650 | 7 | |a Epidemiology / Statistical methods |2 fast | |
| 650 | 7 | |a Stochastic analysis |2 fast | |
| 650 | 4 | |a Epidemiologic Methods | |
| 650 | 4 | |a Acquired Immunodeficiency Syndrome / epidemiology | |
| 650 | 4 | |a HIV Infections / epidemiology | |
| 650 | 4 | |a Models, Theoretical | |
| 650 | 4 | |a Stochastic Processes | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Medizin | |
| 650 | 4 | |a Epidemiology |x Mathematical models | |
| 650 | 4 | |a Epidemiology |x Statistical methods | |
| 650 | 4 | |a Stochastic analysis | |
| 700 | 1 | |a Sleeman, Candace K. |e Sonstige |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804175547099512832 |
|---|---|
| any_adam_object | |
| author | Mode, Charles J. |
| author_facet | Mode, Charles J. |
| author_role | aut |
| author_sort | Mode, Charles J. |
| author_variant | c j m cj cjm |
| building | Verbundindex |
| bvnumber | BV043119310 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)824698665 (DE-599)BVBBV043119310 |
| dewey-full | 614.50151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 614 - Forensic medicine; incidence of disease |
| dewey-raw | 614.50151 |
| dewey-search | 614.50151 |
| dewey-sort | 3614.50151 |
| dewey-tens | 610 - Medicine and health |
| discipline | Medizin |
| format | Electronic eBook |
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Age dependency with time inhomogeneity. 4.6. On estimating parameters from data. 4.7. References -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 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 -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 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 -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 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 -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 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</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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 -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 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. </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - Mutations and the evolution of epidemics. 11.19. References -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 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. </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Épidémiologie / Modèles mathématiques</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Épidémiologie / Modèles statistiques</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse stochastique</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Épidémiologie / Modèles mathématiques</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse stochastique</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MEDICAL / Forensic Medicine</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MEDICAL / Preventive Medicine</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MEDICAL / Public Health</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Epidemiology / Mathematical models</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Epidemiology / Statistical methods</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastic analysis</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Epidemiologic Methods</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Acquired Immunodeficiency Syndrome / epidemiology</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">HIV Infections / epidemiology</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Models, Theoretical</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic Processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematisches Modell</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Medizin</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Epidemiology</subfield><subfield code="x">Mathematical models</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Epidemiology</subfield><subfield code="x">Statistical methods</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic analysis</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sleeman, Candace K.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=514091</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028543501</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=514091</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=514091</subfield><subfield code="l">FAW02</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043119310 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:18:01Z |
| institution | BVB |
| isbn | 1281938009 9781281938008 9789810240974 9789812779250 981024097X 9812779256 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028543501 |
| oclc_num | 824698665 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xxiii, 739 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Mode, Charles J. Verfasser aut Stochastic processes in epidemiology HIV/AIDS, other infectious diseases, and computers Charles J. Mode, Candace K. Sleeman Singapore World Scientific 2000 1 Online-Ressource (xxiii, 739 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references and indexes 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 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 Épidémiologie / Modèles mathématiques Épidémiologie / Modèles statistiques Analyse stochastique Épidémiologie / Modèles mathématiques ram Analyse stochastique ram MEDICAL / Forensic Medicine bisacsh MEDICAL / Preventive Medicine bisacsh MEDICAL / Public Health bisacsh Epidemiology / Mathematical models fast Epidemiology / Statistical methods fast Stochastic analysis fast Epidemiologic Methods Acquired Immunodeficiency Syndrome / epidemiology HIV Infections / epidemiology Models, Theoretical Stochastic Processes Mathematisches Modell Medizin Epidemiology Mathematical models Epidemiology Statistical methods Stochastic analysis Sleeman, Candace K. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=514091 Aggregator Volltext |
| spellingShingle | Mode, Charles J. Stochastic processes in epidemiology HIV/AIDS, other infectious diseases, and computers Épidémiologie / Modèles mathématiques Épidémiologie / Modèles statistiques Analyse stochastique Épidémiologie / Modèles mathématiques ram Analyse stochastique ram MEDICAL / Forensic Medicine bisacsh MEDICAL / Preventive Medicine bisacsh MEDICAL / Public Health bisacsh Epidemiology / Mathematical models fast Epidemiology / Statistical methods fast Stochastic analysis fast Epidemiologic Methods Acquired Immunodeficiency Syndrome / epidemiology HIV Infections / epidemiology Models, Theoretical Stochastic Processes Mathematisches Modell Medizin Epidemiology Mathematical models Epidemiology Statistical methods Stochastic analysis |
| title | Stochastic processes in epidemiology HIV/AIDS, other infectious diseases, and computers |
| title_auth | Stochastic processes in epidemiology HIV/AIDS, other infectious diseases, and computers |
| title_exact_search | Stochastic processes in epidemiology HIV/AIDS, other infectious diseases, and computers |
| title_full | Stochastic processes in epidemiology HIV/AIDS, other infectious diseases, and computers Charles J. Mode, Candace K. Sleeman |
| title_fullStr | Stochastic processes in epidemiology HIV/AIDS, other infectious diseases, and computers Charles J. Mode, Candace K. Sleeman |
| title_full_unstemmed | Stochastic processes in epidemiology HIV/AIDS, other infectious diseases, and computers Charles J. Mode, Candace K. Sleeman |
| title_short | Stochastic processes in epidemiology |
| title_sort | stochastic processes in epidemiology hiv aids other infectious diseases and computers |
| title_sub | HIV/AIDS, other infectious diseases, and computers |
| topic | Épidémiologie / Modèles mathématiques Épidémiologie / Modèles statistiques Analyse stochastique Épidémiologie / Modèles mathématiques ram Analyse stochastique ram MEDICAL / Forensic Medicine bisacsh MEDICAL / Preventive Medicine bisacsh MEDICAL / Public Health bisacsh Epidemiology / Mathematical models fast Epidemiology / Statistical methods fast Stochastic analysis fast Epidemiologic Methods Acquired Immunodeficiency Syndrome / epidemiology HIV Infections / epidemiology Models, Theoretical Stochastic Processes Mathematisches Modell Medizin Epidemiology Mathematical models Epidemiology Statistical methods Stochastic analysis |
| topic_facet | Épidémiologie / Modèles mathématiques Épidémiologie / Modèles statistiques Analyse stochastique MEDICAL / Forensic Medicine MEDICAL / Preventive Medicine MEDICAL / Public Health Epidemiology / Mathematical models Epidemiology / Statistical methods Stochastic analysis Epidemiologic Methods Acquired Immunodeficiency Syndrome / epidemiology HIV Infections / epidemiology Models, Theoretical Stochastic Processes Mathematisches Modell Medizin Epidemiology Mathematical models Epidemiology Statistical methods |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=514091 |
| work_keys_str_mv | AT modecharlesj stochasticprocessesinepidemiologyhivaidsotherinfectiousdiseasesandcomputers AT sleemancandacek stochasticprocessesinepidemiologyhivaidsotherinfectiousdiseasesandcomputers |