A Historical Introduction to Mathematical Modeling of Infectious Diseases

Seminal Papers in Epidemiology

Ivo M. Foppa

• Publisher: Academic Press
• Year: 2016
• Print ISBN:
  9780128022603
• eBook ISBN:
  9780128024997
• Topic: Medicine
• Subtopic: Applied Mathematics

A Historical Introduction to Mathematical Modeling of Infectious Diseases: Seminal Papers in Epidemiology offers step-by-step help on how to navigate the important historical papers on the subject, beginning in the 18th century. The book carefully, and critically, guides the reader through seminal writings that helped revolutionize the field. With pointed questions, prompts, and analysis, this book helps the non-mathematician develop their own perspective, relying purely on a basic knowledge of algebra, calculus, and statistics. By learning from the important moments in the field, from its conception to the 21st century, it enables readers to mature into competent practitioners of epidemiologic modeling. - Presents a refreshing and in-depth look at key historical works of mathematical epidemiology - Provides all the basic knowledge of mathematics readers need in order to understand the fundamentals of mathematical modeling of infectious diseases - Includes questions, prompts, and answers to help apply historical solutions to modern day problems

1

D. Bernoulli: A pioneer of epidemiologic modeling (1760)

Abstract

This chapter examines one of the earliest papers of mathematical epidemiology. Towards the end of the 18th century when Daniel Bernoulli published his famous paper, which is discussed in this chapter, smallpox was a very important public health problem, contributing significantly to childhood mortality. Bernoulli embarked on a mathematical attempt to evaluate the benefit of inoculation of people who had not yet suffered the disease with infectious material from smallpox patients. This immunization technique was a precursor to vaccination, namely inoculation with the cowpox virus which is antigenically similar, yet causes much less serious illness. Surprisingly, smallpox inoculation was highly effective and carried relatively few risks. Using calculations that were partly based on new techniques from the developing field of calculus, he showed that, under certain assumptions, the public health benefit of smallpox inoculation would be substantial, increasing life expectancy by several years. The reader is guided, step-by-step, through all relevant calculations.

Keywords

Smallpox; Inoculation; Mathematical model; Differential equation; Public health benefit

Chapter Outline

1.1 Bernoulli and the “speckled monster”

1.1.1 §1 through §4: Preamble

1.1.2 §5 through §6: Mathematical foundation

1.1.3 §7 through §9: T...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Dedication
• Introduction
• Acknowledgments
• 1: D. Bernoulli: A pioneer of epidemiologic modeling (1760)
• 2: P.D. En'ko: An early transmission model (1889)
• 3: W.H. Hamer (1906) and H. Soper (1929): Why diseases come and go
• 4: W.O. Kermack and A.G. McKendrick: A seminal contribution to the mathematical theory of epidemics (1927)
• 5: R. Ross (1910, 1911) and G. Macdonald (1952) on the persistence of malaria
• 6: M. Bartlett (1949), N.T. Bailey (1950, 1953) and P. Whittle (1955): Pioneers of stochastic transmission models
• 7: O. Diekmann, J. Heesterbeek, and J.A. Metz (1991) and P. Van den Driessche and J. Watmough (2002): The spread of infectious diseases in heterogeneous populations
• Index