Mathematical Modeling in Epidemiology

1. Front Matter

   Pages I-IX

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2. Deterministic Epidemic Models

   • James C. Frauenthal

   Pages 1-11

3. Rumors and Mousetraps

   • James C. Frauenthal

   Pages 12-24

4. Stochastic Epidemic Models

   • James C. Frauenthal

   Pages 25-40

5. Chain Binomial Models

   • James C. Frauenthal

   Pages 41-53

6. Branching Process Model

   • James C. Frauenthal

   Pages 54-65

7. Smallpox Vaccination Discontinuation

   • James C. Frauenthal

   Pages 66-78

8. Schistosomiasis Eradication

   • James C. Frauenthal

   Pages 79-88

9. Gonorrhea

   • James C. Frauenthal

   Pages 89-98

10. Sickle Cell Anemia

    • James C. Frauenthal

    Pages 99-109

11. Back Matter

    Pages 117-120

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The text of this book is derived from courses taught by the author in the Department of Applied Mathematics and Statistics at the State University of New York at Stony Brook. The audience for these courses was composed almost entirely of fourth year undergraduate students majoring in the mathematical sciences. The students had ordinarily completed four semesters of calculus and one of probability. Few had any prior experience with differential equations, stochastic processes, or epidemiology. It also seems prudent to mention that the author's background is in engineering and applied mathematics and not in epidemiology; it is hoped that this is not painfully obvious. The topics covered in this book have in some cases been modified from the way they were originally presented. However, care has been taken to include a suitable amount of material for a one semester course; the temptation to add gratuitous subject matter has been resisted. Similarly, when a choice between clarity and rigor was available, the more easily understood exposition was selected. By looking only at the table of contents, the casual reader could be easily misled into thinking that the main concern of this book is with epidemiology. This is not the case. The purpose of this book is to illustrate the process of formulating and solving mathematical models.

• Epidemiologie
• Modeling
• biologisch-mathematisches Modell
• epidemiology
• linear optimization
• mathematical modeling
• mathematics

• Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, USA

  James C. Frauenthal

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