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The Dynamics of Infectious Diseases

Modelling Epidemiology with R

Jacob Koella

Understanding the dynamics of epidemiology is indispensable to control infectious diseases. The Dynamics of Infectious Diseases will help you to get a grasp of the fundamentals, and it will show you how to use and develop these aspects with the programming language R.

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About the Book

Epidemiology is complex. To understand its dynamics, and thus to be able control infectious disease, we must link what we know about the biology of the disease – its transmission and its effect on the host – into mathematical models describing how epidemiology works. This book is developed as a tutorial that will help you to understand and perform this process.

It will show you why you should understand dynamic processes by discussing simple epidemiological examples. You will learn how to model simple epidemiological dynamics and how to measure the parameters of these epidemiological systems. You will not only understand the theoretical basis of these aspects, but learn to program them with R, a software package that is becoming the standard in academic research.

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Author

About the Author

Jacob Koella

Jacob Koella writes about population biology for conservation, the evolutionary ecology of infectious diseases, and theoretical population genetics. His books combine biological insight with mathematical clarity, with a particular emphasis on parameter estimation—helping readers connect theory to real data and real inference.

He is a professor of evolutionary biology and parasitology at the University of Neuchâtel (Switzerland). With training equivalent to a Master’s degree in mechanical engineering (systems dynamics), a PhD in evolutionary ecology, and several years of experience working on the epidemiology of malaria in Tanzania, his research develops mathematical theory at the interface of epidemiology and evolutionary ecology.

He teaches courses in mathematical modelling, parasitology, and evolutionary ecology at the University of Neuchâtel and ETH Zurich.

Contents

Table of Contents

Introduction

  1. Why model epidemiology?
  2. Understanding the complexity with R
  3. Overview

How can we describe epidemics with R?

  1. Stochastic model
  2. Deterministic approximation
  3. Take-home

How can we model a flu epidemic?

  1. Density- or frequency-dependence
  2. Epidemiological model
  3. Take-home

How can we estimate the parameters of the flu epidemic?

  1. Linear regression
  2. Non-linear regression
  3. Parameters of a flu epidemic
  4. Assumptions of regression
  5. Likelihood
  6. Pitfalls
  7. Take-home

How do we know whether there will be an outbreak?

  1. Basic reproductive number
  2. Vaccines
  3. Estimating \(R_0\)
  4. Take-home

How can we deal with endemic infectious diseases?

  1. Epidemiological patterns
  2. Basic reproductive number
  3. Control with vaccine
  4. Estimating the basic reproductive number
  5. Take-home

Why does measles cycle?

  1. Intrinsic cycling
  2. What maintains cycles?
  3. Take-home

What if contact rates vary?

  1. Effect of heterogeneity on \(R_0\)
  2. Effect of heterogeneity on prevalence
  3. Take-home

Epilogue

About the author

Essentials of R

  1. Installing R and an R interface
  2. Getting started: R as a calculator
  3. What if we want to store the results of our calculations?
  4. Object types
  5. Vectors
  6. Matrices
  7. Data frames
  8. Control structures
  9. Functions
  10. Simple plots

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