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Mathematical models and theorems
01 Feb 2017 | | Contributor(s):: Winfried Just
In this module we introduce and compare various types of deterministic and stochastic mathematical models of disease transmission. We then illustrate how one can derive predictions of these models in the form of mathematical theorems.Level: Advanced undergraduate and graduate students of...
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Exploring generic scale-free networks
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...
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Clustering coefficients
02 Jun 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar
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,...
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Small-world models
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...
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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...
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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...
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The friendship paradox
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar
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...
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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...
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Exploring random regular graphs with IONTW
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar
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...
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Exploring Erdős-Rényi random graphs with IONTW
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar
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...
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Exploring contact patterns between two subpopulations
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar
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...
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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...
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Network-based models of transmission of infectious diseases: a brief overview
10 May 2015 | | Contributor(s):: Winfried Just, Hannah Lea Callender, Drew LaMar
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...
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Exploring Disease Transmission on Networks with NetLogo
10 May 2015 | | Contributor(s):: Winfried Just, Ying Xin
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Modeling Infectious Disease through Contact Networks
25 Mar 2015 | | Contributor(s):: Todd Graham, Claire Seibold, Rebecca Driessen, Hannah Lea Callender
This poster was presented at the University of Portland's Summer Research Symposium on November 9, 2014, in Portland, Oregon. The poster is aimed at readers with little or no background in modeling infectious diseases. The contents provide a brief overview of modeling infectious diseases on...
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A quick tour of IONTW
30 Jan 2015 | | Contributor(s):: Winfried Just, Ying Xin
In this module we guide you through some of the capabilities of IONTW. Highlights include the types of networks supported, setting up various types of models of disease transmission, observing the resulting dynamics, and collecting statistics on the outcomes. Along the way, the module also...