Record:   Prev Next
Author Ma, Zhien
Title Dynamical Modeling And Analysis Of Epidemics
Imprint Singapore : World Scientific Publishing Company, 2009
©2009
book jacket
Descript 1 online resource (513 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Contents -- Preface -- List of Contributors -- 1. Basic Knowledge and Modeling on Epidemic Dynamics -- 1.1 Introduction -- 1.2 The Fundamental Forms of Epidemic Models -- 1.2.1 Two fundamental dynamic models of epidemics -- 1.2.1.1. Kermack-Mckendrick SIR compartment model -- 1.2.1.2. Kermack-Mckendrick SIS compartment model -- 1.2.2 Fundamental forms of compartment models -- 1.2.2.1. Models without vital dynamics -- 1.2.2.2. Models with vital dynamics -- 1.3 Basic Concepts of Epidemiologic Dynamics -- 1.3.1 Adequate contact rate and incidence -- 1.3.2 Basic reproductive number and modified reproductive number -- 1.3.2.1. Basic reproductive number -- 1.3.2.2. Modi.ed reproductive number -- 1.3.3 Average lifespan and average infection age -- 1.4 Epidemic Models with Various Factors -- 1.4.1 Epidemic models with latent period -- 1.4.2 Epidemic models with time delay -- 1.4.2.1. Ideas for the modeling -- 1.4.2.2. Examples of models with time delay -- 1.4.3 Epidemic models with prevention, control, or treatment -- 1.4.3.1. Models with quarantine -- 1.4.3.2. Models with vaccination -- 1.4.3.3. Models with treatment -- 1.4.4 Epidemic models with multiple groups -- 1.4.4.1. Models with di.erent subgroups -- 1.4.4.2. Models with multiple populations -- 1.4.4.3. Models with vector-host -- 1.4.5 Epidemic models with age structure -- 1.4.5.1. Population models with age structure -- 1.4.5.2. Epidemic models with age structure -- 1.4.6 Epidemic models with impulses -- 1.4.6.1. Concepts of impulsive differential equations -- 1.4.6.2. Epidemic models consist of impulsive differential equations -- 1.4.7 Epidemic models with migration -- 1.4.7.1. Epidemic models with migration among di.erent patches -- 1.4.7.2. Epidemic models with continuous di.usion in space -- 1.4.8 Epidemic models with time-dependent coe.cients
1.4.8.1. SIR model with time-dependent coefficients -- 2. Ordinary Differential Equations Epidemic Models -- 2.1 Simple SIRS Epidemic Models with Vital Dynamics -- 2.1.1 SIRS models with constant immigration and exponential death -- 2.1.1.1. SIRS models with bilinear incidence -- 2.1.1.2. SIRS models with standard incidence -- 2.1.2 SIRS models with logistic growth -- 2.1.2.1. Equilibrium and threshold -- 2.1.2.2. Stability analysis -- 2.1.2.3. Global stability of the equilibria for speci.c case: a = 0 or a = 0 -- 2.2 EpidemicModels with Latent Period -- 2.2.1 Preliminaries -- 2.2.1.1. Method I: Proving global stability using the Poincaŕe-Bendixson property. -- 2.2.1.2. Method II: Proving global stability using autonomous convergence theorems -- 2.2.2 Applications -- 2.2.2.1. Application of method I -- 2.2.2.2. Application of method II -- 2.3 Epidemic Models with Immigration or Dispersal -- 2.3.1 Epidemic models with immigration -- 2.3.1.1. SIR model with no immigration of infectives -- 2.3.1.2. SIR model with immigration of infectives -- 2.3.2 Epidemic models with dispersal -- 2.4 Epidemic Models with Multiple Groups -- 2.4.1 The global stability of epidemic model only with differential susceptibility -- 2.4.2 The global stability of epidemic model only with differential infectivity -- 2.5 Epidemic Models with Different Populations -- 2.5.1 Disease spread in prey-predator system -- 2.5.1.1. Disease spread only in the prey population -- 2.5.1.2. Disease spread in prey-predator populations -- 2.5.2 Disease spread in competitive population systems -- 2.6 Epidemic Models with Control and Prevention -- 2.6.1 Epidemic models with quarantine -- 2.6.1.1. SIQS model with bilinear incidence -- 2.6.1.2. SIQR model with quarantine-adjusted incidence -- 2.6.2 Epidemic models with vaccination -- 2.6.2.1. The existence and local stability of equilibria
2.6.2.2. Global analysis of (2.97) -- 2.6.3 Epidemic models with treatment -- 2.7 Bifurcation -- 2.7.1 Backward bifurcation -- 2.7.2 Hopf and Bogdanov-Takens bifurcations -- 2.7.2.1. Hopf bifurcation -- 2.7.2.2. Bogdanov-Takens bifurcations -- 2.8 Persistence of Epidemic Models -- 2.8.1 Persistence of epidemic models of autonomous ordinary differential equations -- 2.8.1.1. Preliminaries -- 2.8.1.2. Applications -- 2.8.2 Persistence of epidemic models of nonautonomous ordinary differential system -- 3. Modeling of Epidemics with Delays and Spatial Heterogeneity -- 3.1 Model Formulations -- 3.1.1 Models incorporating delays -- 3.1.2 Patchy models -- 3.2 Basic Techniques for Stability of Delayed Models -- 3.3 An SIS Epidemic Model with Vaccination -- 3.4 An SIS Epidemic Model for Vector-Borne Diseases -- 3.5 Stability Switches and Ultimate Stability -- 3.6 An SEIRS Epidemic Model with Two Delays -- 3.7 Quiescence of Epidemics in a Patch Model -- 3.8 Basic Reproductive Numbers in ODE Models -- 3.9 Basic Reproductive Numbers of Models with Delays -- 3.10 FisherWaves in an EpidemicModel -- 3.11 Propagation of HBV with Spatial Dependence -- 4. The Epidemic Models with Impulsive Effects -- 4.1 Basic Theory on Impulsive Differential Equations -- 4.1.1 Differential equations with impulses -- 4.1.2 Existence and uniqueness of solutions -- 4.1.3 Comparison principle -- 4.1.4 Linear homogeneous impulsive periodic systems and Floquet theory -- 4.2 SIR Epidemic Model with Pulse Vaccination -- 4.2.1 SIR epidemic models with pulse vaccination and disease-induced death -- 4.2.1.1. Existence and local stability of the disease-free periodic solution -- 4.2.1.2. Global stability of the disease-free periodic solution -- 4.2.1.3. Comparison between constant and pulse vaccinations -- 4.2.2 SIR epidemic model without disease-induced death
4.3 SIRS Epidemic Model with Pulse Vaccination -- 4.3.1 SIRS model with pulse vaccination and standard incidence rate -- 4.3.1.1. Existence and local stability of the disease-free periodic solution -- 4.3.1.2. Global stability of the disease-free periodic solution -- 4.3.2. SIRS model with pulse vaccination and nonmonotonic incidence rate -- 4.3.2.1. Existence and stability of the disease-free solution -- 4.3.2.2. Bifurcation and existence of epidemic periodic solutions -- 4.4 SIS Epidemic Model with Pulse Vaccination -- 4.5 SEIR Epidemic Model with Pulse Vaccination -- 4.6 SI Epidemic Model with Birth Pulse -- 4.6.1 The model with constant births -- 4.6.2 The model with birth pulse -- 4.7 SIR Epidemic Model with Constant Recruitment and Birth Pulse -- 4.7.1 The model with constant birth -- 4.7.2 The model with pulse birth -- 4.7.2.1. Existence and local stability of the disease-free periodic solution -- 4.7.2.2. Global asymptotic stability of the disease-free solution -- 4.7.3 The comparison between constant and pulse births -- 4.8 SIR Epidemic Models with Pulse Birth and Standard Incidence -- 4.8.1 The existence and local stability of disease-free periodic solution -- 4.8.2 The global stability of disease-free periodic solution -- 4.8.3 The uniform persistence of the infection -- 4.9 SIR Epidemic Model with Nonlinear Birth Pulses -- 4.9.1 Existence and stability of the disease-free periodic solution -- 4.9.2 Existence of positive T-periodic solutions and bifurcation -- 4.10 SI Epidemic Model with Birth Pulses and Seasonality -- 4.10.1 Existence and local stability of disease-free periodic solution -- 4.10.2 Bifurcation analysis -- 4.10.3 Global stability of disease-free periodic solution -- 5. Structured Epidemic Models -- 5.1 Stage-StructuredModels -- 5.1.1 A discrete epidemic model with stage structure
5.1.2 Epidemic models with di.erential infectivity structure -- 5.2 Age-StructuredModels -- 5.2.1 Model formulation -- 5.2.2 Existence of equilibrium -- 5.2.3 Stability of equilibria -- 5.3 Infection-Age-Structured Models -- 5.3.1 An infection-age-structured model with vaccination -- 5.3.2 An epidemic model with two age structures -- 5.4 Discrete Models -- 5.4.1 The model formulation -- 5.4.2 The existence of the endemic equilibrium -- 5.4.3 The stability of the disease-free equilibrium -- 5.4.4 The stability of the endemic equilibrium -- 5.4.5 Special cases -- 5.4.5.1. The case of m = 2 -- 5.4.5.2. The case of m = 3 -- 6. Applications of Epidemic Modeling -- 6.1 SARS Transmission Models -- 6.1.1 SARS epidemics and modeling -- 6.1.2 A simple model for SARS prediction -- 6.1.3 A discrete SARS transmission model -- 6.1.4 A continuous SARS model with more groups -- 6.2 HIV Transmission Models -- 6.2.1 The severity of HIV transmission -- 6.2.2 An age-structured model for the AIDS epidemic -- 6.2.3 Discrete model with infection age structure -- 6.3 TB Transmission Models -- 6.3.1 Global and regional TB transmission -- 6.3.2 A TB model with exogenous reinfection -- 6.3.3 TB models with fast and slow progression, case detection, and two treatment stages -- 6.3.4 TB model with immigration -- Bibliography -- Index
Key Features:Introduces both traditional and new models/methods for epidemiology through carefully selected examplesIncludes contributions from well-published authors in the field
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Ma, Zhien Dynamical Modeling And Analysis Of Epidemics Singapore : World Scientific Publishing Company,c2009 9789812797490
Subject Epidemiology -- Mathematical models.;Medical
Electronic books
Alt Author Li, Jia
Record:   Prev Next