The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of disease transmission models. It includes (i) an introduction to the main concepts of compartmental models including models with heterogeneous mixing of individuals and models for vector-transmitted diseases, (ii) a detailed analysis of models for important specific diseases, including tuberculosis, HIV/AIDS, influenza, Ebola virus disease, malaria, dengue fever and the Zika virus, (iii) an introduction to more advanced mathematical topics, including age structure, spatial structure, and mobility, and (iv) some challenges and opportunities for the future.
There are exercises of varying degrees of difficulty, and projects leading to new research directions. For the benefit of public health professionals whose contact with mathematics may not be recent, there is an appendix covering the necessary mathematical background. There are indications which sections require a strong mathematical background so that the book can be useful for both mathematical modelers and public health professionals.
Author(s): Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng
Series: Texts in Applied Mathematics 69
Edition: 1
Publisher: Springer
Year: 2019
Language: English
Pages: 625
Front Matter ....Pages i-xviii
Front Matter ....Pages 1-1
Introduction: A Prelude to Mathematical Epidemiology (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 3-19
Simple Compartmental Models for Disease Transmission (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 21-61
Endemic Disease Models (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 63-116
Epidemic Models (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 117-178
Models with Heterogeneous Mixing (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 179-227
Models for Diseases Transmitted by Vectors (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 229-245
Front Matter ....Pages 247-247
Models for Tuberculosis (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 249-272
Models for HIV/AIDS (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 273-310
Models for Influenza (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 311-350
Models for Ebola (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 351-390
Models for Malaria (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 391-408
Dengue Fever and the Zika Virus (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 409-425
Front Matter ....Pages 427-427
Disease Transmission Models with Age Structure (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 429-455
Spatial Structure in Disease Transmission Models (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 457-476
Epidemiological Models Incorporating Mobility, Behavior, and Time Scales (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 477-504
Front Matter ....Pages 505-505
Challenges, Opportunities and Theoretical Epidemiology (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages 507-531
Correction to: Mathematical Models in Epidemiology (Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng)....Pages C1-C2
Back Matter ....Pages 533-619
