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Mathematical Epidemiology and More:
A Course on Compartmental Models
Meredith L. Greer
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Front Matter
Colophon
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
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
Preparing Influenza Data to Compare With a Model
9.1
Incidence and Prevalence
9.2
Translating a Typical Data Set Into Numbers We Can Compare With a Model
9.3
For Further Thought
10
* Residual Sum of Squares: Improving a Model’s Fit to Data
10.1
Residual Sum of Squares: An Introduction
10.2
Residual Sum of Squares: Quickly Comparing Multiple Parameter Values
10.3
Influenza Data and RSS
10.4
For Further Thought
11
* Akaike Information Criterion: Comparing Different Models
11.1
12
* Epidemic vs. Endemic Models
12.1
13
* Modeling the Spread of a Rumor
13.1
II
Digging Deeper Mathematically
14
* The Next Generation Method
14.1
Mathematical Background for the Next Generation Method
14.2
The Next Generation Method: Steps to Follow
14.3
Python Code for the Next Generation Method
15
* Tips on Reading a Scientific Paper
15.1
III
Additional Modeling Examples
16
* Introducing an Incubation Period in the Zombie App
16.1
Activity: Introduce an Incubation Period
IV
Supplemental Materials
17
* Case Studies: Vaccination and Isolation
17.1
A Varicella Example with Vaccination
17.2
17.3
Backmatter
Glossary of Mathematical Epidemiology Terms
Chapter
13
* Modeling the Spread of a Rumor
***This chapter is under construction.***
Section
13.1
