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Product Code:  SURV/102 
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Hardcover ISBN:  9780821804995 
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Hardcover ISBN:  9780821804995 
Product Code:  SURV/102 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413293 
Product Code:  SURV/102.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821804995 
eBook ISBN:  9781470413293 
Product Code:  SURV/102.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 102; 2003; 261 ppMSC: Primary 92
The study of epidemic models is one of the central topics of mathematical biology. This volume is the first to present in monograph form the rigorous mathematical theory developed to analyze the asymptotic behavior of certain types of epidemic models.
The main model discussed is the socalled spatial deterministic epidemic in which infected individuals are not allowed to again become susceptible, and infection is spread by means of contact distributions. Results concern the existence of traveling wave solutions, the asymptotic speed of propagation, and the spatial final size. A central result for radially symmetric contact distributions is that the speed of propagation is the minimum wave speed. Further results are obtained using a saddle point method, suggesting that this result also holds for more general situations.
Methodology, used to extend the analysis from onetype to multitype models, is likely to prove useful when analyzing other multitype systems in mathematical biology. This methodology is applied to two other areas in the monograph, namely epidemics with return to the susceptible state and contact branching processes.
This book presents an elegant theory that has been developed over the past quarter century. It will be useful to researchers and graduate students working in mathematical biology.
ReadershipGraduate students and research mathematicians interested in mathematical biology.

Table of Contents

Chapters

1. Introduction

2. The nonspatial epidemic

3. Bounds on the spatial final size

4. Wave solutions

5. The asymptotic speed of propagation

6. An epidemic on sites

7. The saddle point method

8. Epidemics with return to the susceptible state

9. Contact branching processes

Appendices


Reviews

The material of the book is presented in full detail ... a thorough account ... with a nice and rather complete bibliography ... a useful reference source for forthcoming research in the field.
Mathematical Reviews


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The study of epidemic models is one of the central topics of mathematical biology. This volume is the first to present in monograph form the rigorous mathematical theory developed to analyze the asymptotic behavior of certain types of epidemic models.
The main model discussed is the socalled spatial deterministic epidemic in which infected individuals are not allowed to again become susceptible, and infection is spread by means of contact distributions. Results concern the existence of traveling wave solutions, the asymptotic speed of propagation, and the spatial final size. A central result for radially symmetric contact distributions is that the speed of propagation is the minimum wave speed. Further results are obtained using a saddle point method, suggesting that this result also holds for more general situations.
Methodology, used to extend the analysis from onetype to multitype models, is likely to prove useful when analyzing other multitype systems in mathematical biology. This methodology is applied to two other areas in the monograph, namely epidemics with return to the susceptible state and contact branching processes.
This book presents an elegant theory that has been developed over the past quarter century. It will be useful to researchers and graduate students working in mathematical biology.
Graduate students and research mathematicians interested in mathematical biology.

Chapters

1. Introduction

2. The nonspatial epidemic

3. Bounds on the spatial final size

4. Wave solutions

5. The asymptotic speed of propagation

6. An epidemic on sites

7. The saddle point method

8. Epidemics with return to the susceptible state

9. Contact branching processes

Appendices

The material of the book is presented in full detail ... a thorough account ... with a nice and rather complete bibliography ... a useful reference source for forthcoming research in the field.
Mathematical Reviews