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Exploring generic scale-free networks
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02 Jun 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar
This module is a companion module to Module [[Resource(384)]]. Here we study in more detail networks that are generic for a given network size and a given exponent of a power-law degree distribution. We explore predicted structural properties of such networks both mathematically and with...
In this module we introduce several definitions of so-called clustering coefficients. A motivating example shows how these characteristics of the contact network may influence the spread of an infectious disease. In later sections we explore, both with the help of IONTW and theoretically,...
02 Jun 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender
Small-world networks are classes of networks that have both the small-world property and exhibit strong clustering. Two constructions of such networks are implemented in IONTW. Here we study, both theoretically and with simulation experiments, the structure of these networks and how it influences...
ModelSim Population Biology Unit
18 May 2015 |
This resource has been updated - find the current version here: https://qubeshub.org/qubesresources/publications/902This resource provides rich student modeling activities and materials, teacher resources, and much more, in the realm of agent based models applied to population biology....
The preferential attachment model
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar, Ying Xin
Many empirically studied networks have approximately so-called power-law or scale-free degree distributions. In Section 1 we formally define such distributions and explore some of their properties. We also introduce and briefly compare two methods for constructing random...
Exploring distances with IONTW
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar
Section 1 is purely conceptual and invites readers to critically evaluate popular claims based on Stanley Milgram's famous experiment that gave birth to the phrases small-world property and six degrees of separation. In Section 2 we use IONTW to explore distances between nodes in several...
The friendship paradox
In this module we introduce the so-called friendship paradox and illustrate how it affects disease transmission on networks that exhibit this phenomenon.You also need to download the input file degreesFP.txt that will be used in this module.Level: Advanced undergraduate and graduate...
The replacement number
In this module we introduce the important notion of the replacement number, which generalizes the basic reproductive number R0. We investigate how this number behaves near the start of an outbreak in models based on the uniform mixing assumption and in models that assume a contact network that is...
Differential equation models of disease transmission
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender
In this module we explore ODE models of disease transmission and compare some of their predictions with those of agent-based models. Parts of this material will be referenced in later modules.Level: Advanced undergraduate and graduate students of mathematics or biology.DownloadStudent copy (no...
Exploring random regular graphs with IONTW
In this module we introduce and explore the structure of random regular graphs. Moreover, we compare the predictions of SIR-models on random regular contact networks with the predictions of corresponding models on Erdős-Rényi networks.Level: Undergraduate students of biology or...
Exploring Erdős-Rényi random graphs with IONTW
In this module we explore in detail the distribution of the sizes of connected components of Erdős-Rényi random graphs and discover the reasons for the similarities and differences between disease transmission on Erdős-Rényi networks and complete graphs that were observed in...
Exploring contact patterns between two subpopulations
In this module we introduce a construction of generic random graphs for a given degree sequence or degree distribution and explore whether mixing between hosts who belong to different subpopulations is assortative or disassortative.Level: Undergraduate students of biology or...
A brief review of basic probability theory
10 May 2015 | | Contributor(s):: Winfried Just
The spread of infectious diseases is inherently a stochastic process and the materials posted at this web site heavily rely on probability theory. Here we review some basic concepts of probability theory for easy reference. The material is restricted to notions that are used in teaching...
Network-based models of transmission of infectious diseases: a brief overview
The main purpose of this document is to give a brief but mathematically rigorous description of the network-based models of transmission of infectious diseases that are studied on this web site. Readers will be able to find a much more detailed development of this material in our book chapters...
Ecology and Epidemiology in R
09 May 2015 |
This resource has been updated - find the current version here: https://qubeshub.org/qubesresources/publications/837
AIM-UP! Reading scientific literature module
28 Mar 2015 | | Contributor(s):: Galen Rask
This resource has been updated - find the current version here: https://qubeshub.org/publications/336Designed to span 4 one-hour lectures, this module focuses upon developing the skill of thorough and critical reading of scientific literature.
AIM-UP! GIS and bats lesson
28 Mar 2015 |
This resource has been updated - find the current version here: https://qubeshub.org/publications/335This lesson introduces the use of GIS (geographic information systems) in the study of biological questions, using bats as the model organism. This activity requires access to GIS...
AIM-UP! Coal balls lesson
28 Mar 2015 | | Contributor(s):: Monte Garroutte, Jordan Metzgar, Hirotsugu Mori
This resource has been updated - find the current version here: https://qubeshub.org/publications/334In this activity, students learn about ancient plant life and climate change by examining coal balls. In addition to the lesson itself, information is provided on where to purchase coal ball...
Numbers Count!: Calculus 2 course
28 Mar 2015 | | Contributor(s):: Claudia Neuhauser
This resource has been updated - find the current version here: https://qubeshub.org/qubesresources/publications/751Based upon the University of Minnesota Bachelor's of Science in Health Science calculus curriculum (part 2), this course introduces linear transformations,...
Numbers Count!: Statistics course
This resource has been updated - find the current version here: https://qubeshub.org/qubesresources/publications/750This course in the Numbers Count! curriculum introduces the basics of statistical analysis, including basic definitions, data visualization, and application.