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Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains [Kõva köide]

(Point Pleasant, New Jersey, USA), (Point Pleasant, New Jersey, USA)
  • Formaat: Hardback, 274 pages, kõrgus x laius: 229x152 mm, kaal: 471 g, 44 Illustrations, color; 5 Illustrations, black and white
  • Ilmumisaeg: 07-Dec-2018
  • Kirjastus: Apple Academic Press Inc.
  • ISBN-10: 1771886714
  • ISBN-13: 9781771886710
Teised raamatud teemal:
Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal DomainsSuurem pilt
  • Formaat: Hardback, 274 pages, kõrgus x laius: 229x152 mm, kaal: 471 g, 44 Illustrations, color; 5 Illustrations, black and white
  • Ilmumisaeg: 07-Dec-2018
  • Kirjastus: Apple Academic Press Inc.
  • ISBN-10: 1771886714
  • ISBN-13: 9781771886710
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781771886710.html
Märksõnad:

In today’s era, the spread of diseases happens very quickly as a large population migrates from one part to another of the world with the readily available transportation facilities. In this century, mankind faces even more challenging environment- and health-related problems than ever before. Therefore, the studies on the spread of the communicable diseases are very important. This book, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, provides a useful experimental tool in making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, devising control strategies, and much more.

This new volume, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, focuses on the study of population dynamics with special emphasis on the migration of populations in a heterogeneous patchy habitat, the human and animal population, and the spreading of epidemics, an important area of research in mathematical biology dealing with the survival of different species. The volume also provides the background needed to interpret, construct, and analyze a wide variety of mathematical models. Most of the techniques presented in the book can be readily applied to model other phenomena, in biology as well as in other disciplines.

The studies presented here on the prey-predator models can be helpful for conservation strategies in forestry habitats, and the epidemic model studies can helpful to the public health policymakers in determining how to control the rapid outbreak of infectious diseases. In this book, the authors have proposed eleven different models in order to facilitate understanding:

  • Two models with different prey-predator interactions
  • Four population models with diffusion in two-patch environment
  • One prey-predator model with disease in the prey
  • Four epidemic models with different control strategies.

This book will be of interest to interdisciplinary researchers and policymakers, especially mathematical biologists, biologists, physicists, and epidemiologists. The book can be useful as textbook or reference book for graduate and postgraduate advanced level mathematical biology courses.

About the Authors xiii
List of Figures
xv
List of Tables
xxi
List of Symbols
xxiii
Preface xxvii
1 Introduction and Mathematical Preliminaries
1(22)
1.1 Introduction
1(9)
1.1.1 Population Dynamics
1(1)
1.1.2 Prey-Predator Interactions
2(1)
1.1.3 Discrete Generations
2(1)
1.1.4 Diffusion of Population
3(2)
1.1.5 Patchy Environment
5(1)
1.1.6 Epidemiology
5(1)
1.1.7 Eco-Epidemiology
6(1)
1.1.8 Stage-Structure
6(1)
1.1.9 Time Delay
7(1)
1.1.10 Disease Acquired Immunity
7(1)
1.1.11 Vaccine Induced Immunity
8(1)
1.1.12 Non-Pharmaceutical Interventions (NPIs) Through Media Awareness
9(1)
1.2 Mathematical Preliminaries
10(11)
1.2.1 Equilibria of Temporal System
10(1)
1.2.2 Nature of Roots
10(2)
1.2.3 Stability of Equilibrium Points
12(1)
1.2.4 Lyapunov's Direct Method
12(1)
1.2.5 Bifurcation in Continuous System
13(2)
1.2.6 Euler's Scheme for Discretization
15(1)
1.2.7 Stability of Fixed Points in Discrete System
16(1)
1.2.8 Center Manifold in Discrete System
16(1)
1.2.9 Bifurcation in Discrete System
17(2)
1.2.10 Next Generation Operator Method
19(2)
1.2.11 Sensitivity Analysis
21(1)
1.3 Summary
21(2)
2 Discrete-Time Bifurcation Behavior of a Prey-Predator System with Generalized Predator
23(30)
2.1 Introduction
23(1)
2.2 Formulation of Mathematical Model-1
24(1)
2.3 Discrete Dynamical Behavior of Model-1
25(11)
2.3.1 Flip Bifurcation
29(4)
2.3.2 Hopf Bifurcation
33(3)
2.4 Formulation of Mathematical Model-2
36(1)
2.5 Discrete Dynamical Behavior of Model-2
37(5)
2.5.1 Flip Bifurcation
40(1)
2.5.2 Hopf Bifurcation
41(1)
2.6 Numerical Simulations
42(9)
2.7 Summary
51(2)
3 A Single Species Harvesting Model with Diffusion in a Two-Patch Habitat
53(16)
3.1 Introduction
53(2)
3.2 Formulation of Mathematical Model
55(1)
3.3 The Analysis of the Model
56(11)
3.3.1 Under Reservoir Boundary Conditions
56(6)
3.3.2 Under No-Flux Boundary Conditions
62(4)
3.3.3 The Case of Uniform Equilibrium State
66(1)
3.4 Summary
67(2)
4 A Single Species Model with Supplementary Forest Resource in a Two-Patch Habitat
69(24)
4.1 Introduction
69(1)
4.2 Formulation of Mathematical Model
70(3)
4.3 Analysis of the Model in a Homogeneous Habitat
73(2)
4.3.1 Model without Diffusion
73(1)
4.3.2 Model with Diffusion
74(1)
4.4 Analysis of the Model with Diffusion in a Two-Patch Habitat
75(6)
4.5 A Particular Case
81(10)
4.6 When the Species Population is Uniform Throughout the Habitat
91(1)
4.7 Summary
92(1)
5 A Two Competing Species Model with Diffusion in a Homo-geneous and Two-Patch Forest Habitats
93(28)
5.1 Introduction
93(1)
5.2 Formulation of Mathematical Model
94(3)
5.3 Analysis of the Model in a Homogeneous Habitat
97(5)
5.3.1 Model without Diffusion
97(4)
5.3.2 Model with Diffusion
101(1)
5.4 Analysis of the Model with Diffusion in a Two-Patch Habitat
102(18)
5.4.1 The Uniform Equilibrium State Under Both Sets of Boundary Conditions
103(2)
5.4.2 The Non-Uniform Equilibrium State
105(1)
5.4.3 The Model Under the Reservoir Boundary Conditions: When x*2 > x*1 and y*2 > y*1
106(9)
5.4.4 The Model Under No-Flux Boundary Conditions
115(4)
5.4.5 Both the Species have Uniform Steady State in the Second Patch
119(1)
5.5 Summary
120(1)
6 A Competing Species Model with Diffusion in Two-Patch Habitat with a Common Supplementary Resource
121(16)
6.1 Introduction
121(1)
6.2 Formulation of Mathematical Model
122(2)
6.3 Analysis of the Model in a Two Patch Habitat
124(12)
6.3.1 The Case of Nonuniform Steady State: Under Both Sets of Boundary Conditions
124(7)
6.3.2 The Case of Uniform Steady State: Under Both Sets of Boundary Conditions
131(5)
6.4 Summary
136(1)
7 Dynamics of a Prey and Generalized-Predator System with Disease in Prey and Gestation Delay for Predator in Single Patch Habitat
137(22)
7.1 Introduction
137(1)
7.2 Formulation of Mathematical Model
138(2)
7.3 Positivity and Boundedness of the System
140(3)
7.4 Dynamical Behavior of the System
143(11)
7.5 Sensitivity Analysis
154(4)
7.6 Numerical Simulations
158(1)
7.7 Summary
158(1)
8 An Epidemic Model of Childhood Disease Dynamics with Maturation Delay and Latent Period of Infection
159(16)
8.1 Introduction
159(1)
8.2 Formulation of Mathematical Model
160(1)
8.3 Positivity and Boundedness of the System
161(3)
8.4 Dynamical Behavior of the System
164(7)
8.5 Sensitivity Analysis
171(1)
8.6 Numerical Simulations
171(3)
8.7 Summary
174(1)
9 Bifurcation in Disease Dynamics with Latent Period of Infection and Media Awareness
175(20)
9.1 Introduction
175(1)
9.2 Formulation of Mathematical Model
176(3)
9.3 Positivity and Boundedness of the System
179(1)
9.4 Dynamical Behavior of the System
180(8)
9.5 Sensitivity Analysis
188(1)
9.6 Numerical Simulations
189(4)
9.7 Summary
193(2)
10 Continuous and Discrete Dynamics of SIRS Epidemic Model with Media Awareness
195(32)
10.1 Introduction
195(1)
10.2 Formulation of Mathematical Model
196(3)
10.3 Dynamical Behavior of the System
199(5)
10.4 Discrete-Time System
204(1)
10.5 Discrete Dynamical Behavior of the System
204(11)
10.5.1 Flip Bifurcation
208(4)
10.5.2 Hopf Bifurcation
212(3)
10.6 Sensitivity Analysis
215(2)
10.7 Numerical Simulations
217(7)
10.8 Summary
224(3)
11 Dynamics of SEIRVS Epidemic Model with Temporary Disease Induced Immunity and Media Awareness
227(18)
11.1 Introduction
227(1)
11.2 Formulation of Mathematical Model
228(4)
11.3 Dynamical Behavior of the System
232(7)
11.4 Sensitivity Analysis
239(1)
11.5 Numerical Simulations
240(3)
11.6 Summary
243(2)
Bibliography 245(20)
Index 265
Harkaran Singh, PhD, is an Associate Professor at Khalsa College of Engineering and Technology, Amritsar, India. He has many years of experience in teaching and research. He received an award for Young Investigator from India and Southeast Asia from the International Society of Infectious Diseases at the 17th International Congress on Infectious Diseases held at Hyderabad, India. He has published several research papers in peer-reviewed journals. He obtained his PhD degree in Mathematical Modeling in Population Biology from IKG-Punjab Technical University, Kapurthala, India.

Joydip Dhar, PhD, is an Associate Professor at the ABV-Indian Institute of Information Technology and Management, Gwalior, India. He has been involved with teaching and research for the past 21 years and has also published about 125 papers in international journals. He has guided PhD students as well as MTech and MBA theses. Dr. Dhar has delivered more than 50 invited lectures at different universities and institutions in India and abroad, including the UK and Sweden. He has co-authored a research book and has conducted several conferences and short-term courses. A life member of many professional societies (ISTE, IMS, ISMMACS) and an annual member of the American Mathematical Society (AMS), Dr. Dhar has participated in the prestigious ACM-ICPC world finals as a mentor at Stockholm, Sweden 2009. He was the recipient of a Dewang Mehta National Education Award, among other awards. Recently he attended a prestigious 8-day in-residence program for Inspired Teachers at Rashtrapati Bhavan, which is the highest recognition for any central government institution teacher.