Skip to main content
Mathematical Epidemiology and More
A Course on Compartmental Models
Meredith L. Greer
Contents
Search Book
Search Results:
No results.
Read aloud
Continue
Read aloud settings
Voice
Reading speed
1Ă—
Collapsed content
Announce, do not read
Read automatically
Follow along (auto-scroll)
Continue to the next page automatically
Readability settings
Readability settings
Line height
1.35
Content font size
100%
Theme
System
Light
Dark
Assistive technologies
đź”—
Expose permalinks
Reset All
Prev
Up
Next
\(\newcommand{\R}{\mathbb R} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)
Front Matter
Colophon
Acknowledgements
Preface
To Students: How to Get the Most from This Text
I
Core Modeling Concepts
1
Prelude: Diseases in Popular News
1.1
Possible Discussion Themes
1.2
Follow Up By Seeking More Precise Data
1.3
For Further Thought
2
Zombies: Can Math Help?
2.1
We Now Have Data: Qualitative Musings
2.2
A First Model
2.3
For Further Thought
3
Visualization: Graphing Model Results and Data
3.1
“Solving” Differential Equations Using Graphs
3.2
Estimating
\(\beta\)
and Building Visualization Skills
3.3
For Further Thought
4
Compartmental Diagrams
4.1
Compartmental Diagrams: Vocabulary and Comments
4.2
From Zombie Game Variation to Compartmental Diagram
4.3
Estimating Gamma and Other Rates
4.4
For Further Thought
5
Model Analysis and the Basic Reproduction Number
\(\mathcal{R}_0\)
5.1
Using Calculus to Analyze Models
5.2
The Basic Reproduction Number
\(\mathcal{R}_0\)
5.3
For Further Thought
6
Vaccines
6.1
Determining a Threshold Vaccine Level
6.2
How Vaccination Level Affects Long Term Outcomes
6.3
Vaccine Efficacy and Effectiveness
6.4
For Further Thought
7
Incubation Periods
7.1
Including an Incubation Period: The SEIR Model
7.2
Practice with an Incubation Model
7.3
For Further Thought
8
Isolation
8.1
Complete Isolation: Models and Parameter Estimation
8.2
Incomplete Isolation, and Quarantine vs. Isolation
8.3
Practice with an Isolation Model
8.4
For Further Thought
9
Residual Sum of Squares: Improving a Model’s Fit to Data
9.1
Residual Sum of Squares: An Introductory Example
9.2
The Underlying Math of RSS
9.3
Residual Sum of Squares: Quickly Comparing Multiple Parameter Values
9.4
RSS With the SIR Model
9.5
For Further Thought
10
Comparing New Cases Data With a Model
10.1
Incidence and Prevalence
10.2
Translating a Typical Data Set Into Numbers We Can Compare With a Model
10.3
For Further Thought
11
Epidemic vs. Endemic Illness
11.1
Comparing Endemic Illnesses with Epidemics
11.2
Equilibrium Values in Endemic Illness Models
11.3
For Further Thought
12
* Modeling the Spread of an Idea
12.1
II
Providing Greater Depth
13
The Next Generation Method
13.1
Mathematical Background for the Next Generation Method
13.2
The Next Generation Method: Steps to Follow
13.3
Python Code for the Next Generation Method
13.4
For Further Thought
14
* Aligning Simulations with Data
14.1
15
* Case Studies: Vaccination and Isolation
15.1
A Varicella Example with Vaccination
15.2
H1N1 with Testing and Strict Isolation
15.3
A Measles Example with a Vaccine Campaign
16
Articles Showing Further Examples
16.1
Compartmental Models for Diseases
16.1.1
Legionnaires’ Disease
16.2
Compartmental Models for Applications Other Than Diseases
16.2.1
Elections
16.2.2
Bumblebees and Pollination
17
* Tips on Reading a Scientific Paper
17.1
Finding and Selecting Articles
17.1.1
Searching for Articles
17.1.2
Choosing an Article
17.2
Layout of Scientific Articles
Back Matter
A.
Greek Letters
Glossary of Mathematical Epidemiology Terms
Colophon
Colophon
©2020–present Meredith L. Greer
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, CC BY-NC-SA. To view a copy of this license, visit
CreativeCommons.org.
đź”—
